Answers
The change in length of the purple spring be 6.77 cm.
What is spring constant?The spring stiffness is how we define the term "spring constant." In other words, we can define the spring constant as the force that was used to cause the spring's displacement to be one unit. It follows that a spring's spring constant would increase as it becomes more rigid.
Given parameters:
Spring constant: k = 45 N/m.
Mass of the load: m = 311 g = 0.311 kg.
So, weight of the load: w = mg = 0.311 × 9.8 N = 3.0478 N.
Hence, the purple spring's change in length be = w/k = 3.03478/45 m = 0.0677 m = 6.77 cm.
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Related Questions
8. Four vibrating objects X₁, X₂, X₃ and X₄ are producing sounds. The object that produces the loudest sound is
Answers
In this particular que, where four vibrating objects are available, the object that produces the loudest sound is X4.
What are examples of Sound Produced by Vibrations?
In order to understand how sound is produced by vibrations in physics, we must take an example. One of the best examples of sound produced by the vibration of objects is the guitar. In the guitar, we can observe some parallel strings. Here the air is the medium, which helps to produce sound when we create vibration among the strings.
The tuning fork is another widely used illustration that demonstrates how sound may be created by vibrating items. The handle of the tuning fork displays the two melodies. When the tuning fork is struck with the rubber hammer, the air molecules around it are disturbed, which causes vibrations between the two tines and compression or expansion of those molecules. If we repeatedly strike the rubber hammer, they continue to experience either compression or expansion, which causes the production of many waves. Sound travels over space as a result of these waves. This is how vibrating objects make sound whenever a force is applied to the medium or the object.
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If a bicycle and rider has a mass of 50kg if the bicycle has an acceleration of 8 m/s during a 100 m spirit , how much force is applied?
Answers
If a bicycle and rider has a mass of 50kg if the bicycle has an acceleration of 8 m/s during a 100 m spirit then the force applied is 400 N .
How is the applied force calculated ?Given is ,
mass (m) = 50 kg
acceleration (a) = 8 m/s²
We know,
force = mass × acceleration
∴ F = m × a
∴ F = 50 × 8
∴ F = 400 Newton
Hence, the force applied is 400 N .
What is applied force ?Applied force refers to the force applied to an object by another object/person.If an item is subjected to only one force, you can calculate its worth in relation to Newton's second law of motion.The formula is, Force = (mass of object) x (acceleration of object).If the item is subjected to two or more forces, the formula informs you what their total is when all of their magnitudes and orientations are added together are merged into a single force.Can learn more about applied force from https://brainly.com/question/248293
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(a) What is the minimum force of friction required to hold the system of Figure in equilibrium. Let W₁=100N and W₂=59N
(b) What coefficient of static friction between the 100N block and the table ensures equilibrium?
Answers
The minimum force of friction required to hold the system of Figure in equilibrium is 50 Newton.
What is frictional force?
Frictional force is the force produced when two surfaces slide against and touch each other. The surface texture and amount of force needing them together have the biggest an impact on these forces. The amount of frictional force is influenced by the object's position and angle.
The forces of adhesion between the sites of contact areas of the surfaces, which are always minutely uneven, are the primary cause of friction between objects. The action of the imperfections of the harder surface tilling across the softer surface shears these "fused" connections, causing friction.
If an object is placed against an object, then the frictional force will be the same as the weight of the object. If an object is pushed against the surface, then the frictional force will be increased and become extra than the weight of the object.
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A 75 g, 30-cm-long rod hangs vertically on a frictionless, horizontal axle passing through its center. A 10 g ball of clay traveling horizontally at 2.5 m/s hits and sticks to the very
bottom tip of the rod. To what maximum angle, measured from vertical, does the rod (with the attached ball of clay) rotate?
The maximum angle will be 67o
Answers
The maximum angle will be 67°.
Solution:
= 0.0088 = 0.0147(1 - cos∅)
= 0.59 = (1 - cos∅)
= cos∅ = 1 - 0.59
= ∅ = cos⁻¹(0.4) = 67°
When the angle of incidence on water reaches a certain critical value the refracted ray lies along the boundary and the refraction angle is 90 degrees. This angle of incidence is known as the critical angle. This is the maximum angle of incidence at which refraction can occur.
The velocity of the incident particle before impact is parallel to the velocity of the center of gravity. Therefore, the maximum deflection angle is equal to the maximum angle between the velocity of the center of mass and the velocity of the incident particle after the collision as shown below.
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place the bar magnet inside the long coil.try to find a location where the stationary magnet induces a current in the coil and causes the light bulb to shine and the voltmeter's needle to move from vertical (vertical
Answers
The magnetic field associated with the coil will change as it is moved near a stationary magnet, which will generate current in the coil. Galvanometer in Region C exhibits deflection in one direction as a result of this.
What do you mean of current?Electrical charge carriers, often electrons or atoms deficient in electrons, travel as current. The capital letter I is a typical way to represent current. The ampere, denoted by the letter A, is the common unit. A stream of charged particles, such as electrons or ions, travelling through an electrical conductor or a vacuum is known as an electric current. The net rate of electric charge flowing through a surface or into a control volume is how it is calculated.
What is current example and its uses?Charge is movable and can freely flow in certain substances, known as conductors. Conductors include metals and a select few additional elements and compounds. Copper, aluminium, and most other metals are examples.
The majority of its uses are low voltage ones, such aeroplane applications and battery charging. Appliances for both domestic and industrial and commercial use run on alternating current. Amperes are used to measure electric current
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A 2,500-kilogram roller coaster car is just reaching the bottom of a 30.00-meter hill. Assuming friction is 0, what are the potential energy (PE) and kinetic energy (KE) of the car at a height of 0 meters?
PE = 367,500 J; KE = 367,500 J.
PE = 0 J; KE = 735,000 J.
PE = 735,000 J; KE = 0 J.
PE = 735,000 J; KE = 735,000 J.
Answers
All of the potential energy has been converted to kinetic energy at the base of hills, resulting in greater speed. Potential energy = 735000 J ; kinetic energy = 0 J (option -C) is correct answer.
How does the energy change when a roller coaster is at the base of a hill?At the bottom of hills, roller coaster cars always move the fastest. This is connected to the first idea in that at the base of hills, all potential energy has been transformed into kinetic energy, leading to increased speed.
At a height of 0 meters,
Potential energy = mgh
Potential energy = 2,500×9.8×30
Potential energy = 735,000 J
Kinetic energy = 1/2mv²
Kinetic energy = 1/2×2,500×0
Kinetic energy = 0.
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Consider the following two-car accident: Two cars of equal mass m collide at an intersection. Driver E was traveling eastward, and driver N, northward. After the collision, the two cars remain joined together and slide, with locked wheels, before coming to rest. Police on the scene measure the length d of the skid marks to be 9 meters. The coefficient of friction μ between the locked wheels and the road is equal to 0.9. (Figure 1) Each driver claims that his speed was less than 14 meters per second (about 31 mph). A third driver, who was traveling closely behind driver E prior to the collision, supports driver E's claim by asserting that driver E's speed could not have been greater than 12 meters per second. Take the following steps to decide whether driver N's statement is consistent with the third driver's contention. Part A
Let the speeds of drivers E and N prior to the collision be denoted by ve and vn, respectively. Find v2, the square of the speed of the two-car system the instant after the collision.
Express your answer terms of ve and vn.
Answers
The square of speed of two car system is 11m/s.
Measurements of motion characteristics, such as velocity, can be made using the conservation of momentum principle. Imagine that while on a physics expedition you happen to pass by a frozen lake where a hockey game is being played. Just as he collides, rather brutally for a pick-up game, with another player who is initially at rest, you measure one player's speed as 11.0 m/s. Think about a scenario where car A hits an immovable, static wall. Car A starts off moving at a certain speed (v), and after hitting the wall, it slows to a stop at a speed of zero. Newton's second law of motion, which applies the formula force equals mass times acceleration, uses this equation to describe the force in this circumstance. The acceleration in this scenario is (v - 0)/t, where t is the amount of time required for car A to stop.According to Newton's third law of motion, the wall, which is static and unbreakable, applies an equal force back to the car in response to the force the car is applying in its direction.To study about Newton's third law of motion-
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A rocket engine consumes 118kg of fuel per second
If the exhaust speed is 5000m/s , calculate the thrust in the rocket.please give your answers in kN
Answers
The thrust force that is acting on the rocket engine is obtained as 5782 kN.
What is the thrust?We know that the thrust is the force that is acting on an object that enables the object to be able to move higher. The thrust force can be applied to a rocket such that the rocket can be able to move higher and then pass through the air.
This implies that the thrust force is about the most important force when we want to be able to launch a rocket or when we are trying to move an aeronautical engine. In this case, we are asked to be able to obtain the thrust force as we can see from the parameters that have been given.
We now know that the thrust force can be obtained as; 118kg * 9.8 m/s^2 * 5000m/s = 5782 kN
There would be a thrust of 5782 kN working on the engine.
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Can every finite group be written via generators and relations using a finite number of generators and a finite number of relations?
Answers
Since S can be assumed to represent G itself, every finite group is finitely produced. Countable groups need not be finitely generated, but every infinite finitely generated group must be countable.
What is generator explain?Any machine that transforms mechanical energy into electricity for transmission and distribution via power lines to residential, commercial, and industrial consumers is known as an electric generator, sometimes known as a dynamo. In addition, generators provide the additional electrical power needed for boats, trains, cars, and other types of transportation. A hydroelectric facility is one where turbine generators are propelled by falling water. Hydraulic motors that produce electricity power electrical generators.
What is a generator used for and its principal?In the event of a power outage, generators are practical equipment that supply electricity, keeping daily tasks or company operations operating smoothly. For usage in a number of applications, generators are available in a variety of electrical and physical designs.
It operates under the principles of Faraday's electromagnetic induction law. According to the faradays law, an electromagnetic field (EMF) is created anytime a conductor is subjected to a changing magnetic field.
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Manganese is a silver colored metal . It reacts with oxygen to form manGanesh oxide which has two oxygen atoms for every manganese atom white h statement descrubes the properties of manganese oxide
Answers
The properties of manganese oxide, which has two oxygen atoms for every manganese atom, are discussed in this answer.
What are the properties of manganese dioxide?Magnesium dioxide is widely utilized in the ceramics sector. Each and every one of the raw ingredients used to make glass contains some iron. Ferric oxides are the most common form of this iron. Manganese dioxide is a very useful and practical substance to employ in these sectors of the economy.Again, dry cell batteries frequently use manganese ores. Many of these cells need to be physically or chemically activated. These methods are manufacturing processes that only function at specific temperatures and call for specialized equipment.Because of the presence of impurities, glass frequently develops a tint. The various iron impurities cause a green color that manganese dioxide removes.In batteries, a coating of magnesium dioxide really protects the carbon positive electrode. Around It, carbon is also found.The steel sector uses manganese dioxide the most. Essentially, manganese is employed in the deoxidation of steel.The primary component of the black-brown pigments found in paint is manganese dioxide.Cans for soft drinks also include a particular alloy. Manganese dioxide is used to create this alloy.Learn more about manganese dioxide here:
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An object with a mass of 1.75kg is sitting on the floor and being pulled upwards at a 30° angle to the positive horizontal by a force of 5.5N. What is the force of the floor (in N) on the object?
Answers
The force exerted by gravity on a mass of 6.5 kg will be equal to 64 N. Hence, option A is correct.
What is Force?Any operation that has the ability to alter, maintain, or modify a body's motion is considered a force in mechanics. Isaac Newton's Principia Mathematica has three laws of motion that are usually used to demonstrate the idea of force (1687). A body at rest or consistently moving in a straight path is said to remain in that state before a power is applied to it, according to Newton's first law.
Now, let's find out the force exerted by gravity,
Given,
Mass, m = 6.5 kg
Use the value of acceleration due to gravity (g) as 9.8 m/s².
f = 6.5 × 9.8
f = 63.7 or,
f = 64 N.
Therefore, the force exerted by the gravity will be equal to 64 N.
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3. If the static friction between wood and concrete is 0.62,
determine the force required to make a wooden block of mass
2 kg start to slide
Answers
Refer to the photo taken
A 2 m tall barrel is closed on top except for a thin pipe extending 8 m up from the top. When the barrel is filled with water up to the base of the pipe (2 m deep), the water pressure on the bottom of the barrel is 20 KPa. What is the pressure on the bottom when water is added to fill the pipe to its top?
Answers
Pressure on the bottom when water is added to fill the pipe to its top is 180kPA.
In the first scenario, the atmospheric pressure is:
In the second scenario, h = 8m + 1 m. Therefore, the pressure at the bottom of the barrel is:
What is hydrostatic pressure meaning?
Hydrostatic pressure refers to the pressure that any fluid in a confined space exerts. If the fluid is in a container, there will be some pressure on the wall of that container.
What is hydrostatic pressure used for?
Hydrostatic pressure is one reason (along with the lack of oxygen) why it's not safe for humans to travel unprotected in space. You rely on hydrostatic pressure to keep your lungs at the right inflation and to keep the water in your body from vaporizing.
How is hydrostatic pressure calculated?
The pressure in a liquid at a given depth is called hydrostatic pressure. This can be calculated using the hydrostatic equation:
P = rho * g * d, where P is the pressure, rho is the density of the liquid, g is gravity (9.8 m/s^2) and d is the depth (or height) of the liquid.
Thus, the pressure on the bottom when water is added to fill the pipe to its top is 180kPa.
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If two objects collide and stick together, what must increase?
A.
the acceleration due to gravity
B.
the friction between the two objects
C.
the force of gravity between the objects
D.
the two objects' momentum
Answers
Calculate Q for each of the three processes. Express your answers in joules to three significant figures, separated by commas. A heat engine takes 0.350 mol of an ideal diatomic gas around the cycle shown in the pV diagram of (Figure 1). Process 1 + 2 is at constant volume, process 2 + 3 is adiabatic, and process 3 + 1 is at a constant pressure of 1.00 atm. The value of y for this gas is 1.40. The magnitude of the change in internal energy for each process is AU1–2= 2180 J, AU2-31 = 785 J, and |AU3_1] = 1396 J. Express your answers in joules to three significant figures, separated by commas. Q1+2, Q2+3, Q3+1 = ___ J, J, J Express your answers in joules to three significant figures, separated by commas.
W1+2, W2+3, W3+1 = ___ J, J, J
Answers
The three significant figures are ΔV2-3 = -785 J, W2-3 = 785.7 J and W3-1 = -558.72 J
Number of moles n=0.350
r = 1.40
| ΔV1-2 | = 2180 J | ΔV2-3| = 785 J
| Δ V3-1 | = 1396 J
From first law of thermodynamic
Q = ΔV + W
Internal Energy increases in this case as the temperature is increasing ΔV is positive and work done in a constant volume process is 0 as
W1-2 = P ΔV = P (O) = O
Q1-2 = Δ V1-2 + W1-2 = ΔV1-2 + O
Q1-2 = 2180 J
Change in internal energy is negative since temperature is decreasing as
R = 8.314 J
Δv2-3 = -785 J
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Problem 15:
Lava has an area of 0.80 m², and emissivity of 1.0, and a temperature of 1450 K. The
temperature of the surroundings is 300 K. What is the rate of heat transfer, from the lava to the
surroundings, due to radiation?
a. 1.0 x 105 W
c. 3.0 x 105 W
d. 4.0 x 105 W
b. 2.0 x 105 W
Answers
The heat transfer by an emitted radiation is calculated using Stefan-Boltzmann law of radiation. The rate of heat transfer is 2.0 × 10⁵ W.
What is Stefan-Boltzmann law of radiation?According to Stefan-Boltzmann law of radiation, the heat transfer by an emitted radiation Q/t is related to the absolute temperature T and the area A as:
Q/t = σe AT⁴
Where σ is the Stefan-Boltzmann constant e be the emissivity. σ has a value of 5.67 × 10⁻⁸ J/s m² K⁴.
Given that, T = 1450 K
e = 1.0, A = 0.80 m².
Now, heat transfer Q/t = 5.67 × 10⁻⁸ J/s m² K⁴ × 0.80 m² × (1450 K)⁴
= 2.0 × 10⁵ W.
Therefore, the heat transfer to the surrounding to the radiation is 2.0 × 10⁵ W.
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can anyone please explain this question?
Answers
Step 1: ( 116+124 )/ 2 = 120mm
Remember, the question asks for the extension of the spring and not the total length. In the data given, at 0 Newton, the spring has a length of 108mm. To find the extension, subtract the new length with the original spring’s length to find out how much the string stretched.
Step 2: 120-108 = 12mm
Therefore, the answer is B. I hope this clarified for you.
ANSWER: B
A constant force of 10 N acts on a 2.5 kg object for 9 seconds. What is the velocity of the object?
Answers
Answer:
[tex]\huge\boxed{\sf v = 36 \ m/s}[/tex]
Explanation:
Given data:Force = F = 10 N
Mass = m = 2.5 kg
Time = t = ?
Required:Velocity = v = ?
Formula:[tex]\displaystyle F=\frac{mv}{t}[/tex]
Solution:Put the given data in the above formula.
[tex]\displaystyle 10=\frac{(2.5)v}{9} \\\\10 \times 9 = 2.5v\\\\90=2.5 v\\\\Divide \ 2.5 \ to \ both \ sides\\\\90/2.5=v\\\\36 \ m/s=v\\\\v = 36 \ m/s\\\\\rule[225]{225}{2}[/tex]
A bat flies toward a wall, emitting a steady sound of frequency 1.70 kHz. This bat hears its own sound plus the sound reflected by the wall. How fast should the bat fly in order to hear a beat frequency of 8.00 Hz?
Answers
A bat is flying at a wall and making a constant 1,70 kHz sound. The bat must fly at a speed of 0.8 m/s in order to detect an 8.00 Hz beat frequency.
Who defines frequency?The frequency of a repeated event is its number of instances per unit time. It differs from angular frequency and is sometimes referred to as sampling rate for clarification. The unit of frequency is hertz (Hz), or one occurrence per second.
Do people own a frequency?The spring constant of a standing human body is approximately 7.5 Hz, and the rate of a sitting position in a cab is typically 4-6 Hz, according to the research that has already been done. Table 1 displays the natural frequencies of the major body parts.
Briefing:Frequency = 1.70 kHz
New frequency = 8.00 Hz
V = ?
8.00 / 1700 = 2 * v / 340m/s
v = 0.8 m/s
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A ship A streaming in a direction 30 degrees with a steady speed 12km/h sites a ship B The velocity of B relative to A is 10km/h in a direction 270 degrees. Find the magnitude and direction of the velocity of ship B
Answers
The magnitude of the shop B is 15.62 m and the direction will de same as given.
What is magnitude?Magnitude is defined as the direction and size of an item at its largest. It reveals the absolute or relative size or direction that an object moves when in motion.
The product of vw - vs determines the relative velocity of a ship to water.
To calculate the magnitude we use formula
Magnitude = √vw² + vs²
Magnitude = √ 12² + 10²
Magnitude = √ 144 + 100
Magnitude = √ 244
Magnitude = 15.62 m
Thus, the magnitude of the shop B is 15.62 m and the direction will de same as given.
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A 54 kg pole vaulter falls from rest from a
height of 4.7 m onto a foam rubber pad. The
pole vaulter comes to rest 0.40 s after landing
on the pad.
a) Calculate the athlete’s velocity just before reaching the pad.
Answer in units of m/s
Answers
Answer:
9.6
Explanation:
v² = u² + 2as
v² = 0 + 2(9.81)(4.7)
v² = 92.214
v = 9.6 m/s
a 8.0 cm -tall cylinder floats in pure water (density 1000 kg/m3) with its axis perpendicular to the surface. the length of the cylinder above water is 1.3 cm .
Answers
A cylinder 8.0 cm tall and 1000 kg/m3 in mass floats in clear water with its axis perpendicular to the surface. Its mass density is 0.8375. The cylinder is 1.3 cm long when it is above water.
The substance's mass per unit of volume is its density (also known as specific mass or volumetric mass density). The Latin letter D can also be used to represent density, however the most common symbol is (the lower case Greek letter rho). According to mathematics, density is determined by dividing mass by volume, where denotes the density, m denotes the mass, and V denotes the volume. An assertion of the perpendicular axis theorem The moment of inertia, for any axis that is perpendicular to the plane, is stated by the perpendicular axis theorem.
(8.0 - 1.3)/8.0 = 0.8375
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The complete question is -
a 8.0 cm -tall cylinder floats in pure water (density 1000 kg/m3) with its axis perpendicular to the surface. the length of the cylinder above water is 1.3 cm. What is the cylinder's mass density?
the braided metal shield is very good at blocking electromagnetic signals from entering the cable and producing noise.
a. true
b. false
Answers
This assertion is accurate; electromagnetic signals are effectively blocked from entering the cable and causing noise by the braided metal shield.
What is electromagnetic ?The study of charge, its forces, and the fields that surround it is known as electromagnetic. Two components of the electromagnetic electric field are electricity and magnetism. In science, electromagnetism is just an interaction that takes place between charged particles. It is also the dominant force in interactions between atoms and molecules and is also the second-strongest of a four basic interaction, after the strong force.
How does electromagnetic work and what was its purpose?Electromagnets are wire coils with electricity flowing through them. An electromagnet's wire coils act like magnets when an electric current flows through them because moving charges produce magnetic fields.
Consequently, electromagnetic governs much more than only electricity and magnetism. It is the force that holds oppositely charged electrons to oppositely charged atomic nuclei, allowing for the formation of stable atoms and the occurrence of chemistry, including the chemistry that gives rise to life.
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A droplet of water sits on a leaf. The contact angle of the water with the leaf is 135∘
and the circumference of the circular contact line is 11 mm. What is the magnitude of the net upward force exerted on the leaf by the droplet's surface tension? Use γ water = 73 mN/m
Answers
The magnitude of the net upward force exerted on the leaf by the droplet's surface tension is 1.136 x 10⁻³ N.
What is the net upward force exerted on the leaf ?The net upward force exerted on the leaf by the droplet's surface tension is calculated by applying the following formula as show below.
Mathematically, the formula for surface tension is given as;
γ = F/L
where;
F is the force applied by the water dropletL is the length of the leaf surfaceThe vertical component of the force is given as;
Fy = F sinθ
γ = F/L
γ = Fsinθ/L
Fsinθ = γL
F = γL / sinθ
The given parameters;
The surface tension of the water droplet = 73 mN/m = 0.073 N/mThe length of the leaf = 11 mm = 0.011 mThe angle of inclination of the leaf = 135∘F = (0.073 x 0.011) / sin135
F = 1.136 x 10⁻³ N
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K=1/2mv^2 the question is a dog mass is 16 kg and is running at 20 m/s . What is the kinetic energy
Answers
3200kg-m²s⁻² the kinetic energy of the dog which is 16Kg mass and moving with 20m/s velocity.
Kinetic Energy the energy possessed by the body due to the motion of the object. Si unit of kinetic energy is Joule or kg-m²s⁻². And it is denoted by K.E
Formula of Kinetic Energy is (KE) = 1/2mv²where as m= Mass and v= Velocity
m= 16kg mass of the dog
v =20m/s velocity of the dog, substitute these values in formula
K.E =1/2(16)(20)² = 3200 Kg-m²/s².
Hence the kinetic energy of the dog which is having mass of 16kg and running at a velocity of 20m/s is 3200J.
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16kg dog is moving with a velocity of 20m/s.
We know that the kinetic energy of a body is the energy possess by it due to its motion
So,
K=1/2mv^2
where,
K is kinetic energy
M is mass
V is velocity.
By substituting the values,
K= 1/2 * 16 * 20 *20
K = 6400/2
K = 3200J
So the kinetic energy of dog is 3200J.
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You move a 4n object 10m what if it’s done it 5 seconds
Answers
Answer:
W= 40 J
P=8 W
Explanation:
solution for work:
w=f d
= 4n (10 m)
= 40 J
Solution for Power
p= w/t
= 40 J/5 s
= 8 W
Three-point charges are arranged at the corner of a square of side l as shown in Fig. 17-39. what is the potential at the fourth corner (point A)?
Answers
The electric potential at the fourth corner (point A) is E4 = kQ.[ 2/a2 + 1/a√2 ]
What is electric potential?The electric potential is defined as the amount of work energy needed to move a unit of electric charge from a reference point to the specific point in an electric field.
Number of point charges = 3
Using the superposition principle to calculate the net electric field at the fourth point, so
E4 = E1 + E2 + E3
E4 = kQ/a2 + kQ/√(2a2) + kQ/a2
E4 = kQ.[ 1/a2 + 1/√(2a2) + 1/a2 ]
E4 = kQ.[ 2/a2 + 1/a√2 ]
Therefore the electric field at the fourth corner is E4 = kQ.[ 2/a2 + 1/a√2 ].
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Complete question:
Three-point charges are arranged at the corner of a square of side l as shown in Fig. 17-39. what is the potential at the fourth corner (point A)?
10. IB challenge question: Two masses hang from a pulley as shown. Calculate the acceleration of the smaller mass. Use 10 for acceleration due to gravity instead of 9.81. (Hint: look at each mass separately, and create a system of equations) I 1kg 3kg
Answers
The acceleration on the block of mass 1 kg will be equal to the acceleration due to gravity that is 9.81 m/s².
What is Acceleration?
Acceleration of an object is the rate of change of the velocity of the object with respect to time.
As the string and pulley system is ideal so the tension will be constant throughout the string and thus both of the blocks will move with the same acceleration, suppose the tension is T and the common acceleration is a
Then, 3kg being heavier weight will move downward.
The tension always act towards a direction away from the block.
The net downward force on 3kg block will be (3g − T)
So, the equation of Force will be F = ma or (3g − T)= 3a ...(1)
Similarly, the net upward force on 1kg block will be (T − 1g)
So, the equation of Force will be F = ma or (T − 1g) = 1a ...(2)
By adding both these equations 1 and 2.
We get,
2g = 2a
a = g
Therefore, acceleration on the block of 1 kg will be equal to the acceleration due to gravity that is 9.81m/s².
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2. A student, Jay, makes himself as cylindrical as possible while sitting on a spinning chair.
Imagine the cylinder with its flat end in the chair and directly above the chair. His center of
mass is 0.10 m from the axis of rotation of the chair. His mass is 65 kg and the cylindrical shape
he is making has a circumference of 1.2 m. The chair's mass is 30 kg. Assume the friction is
directly proportional to the weight of the chair and whatever is on the chair, and the distance
from the axis of rotation to where the friction is applied is constant.
(a) What is the student's moment of inertia about his center of mass?
(b) What is his moment of inertia about the axis of rotation of the chair?
To determine the angular acceleration due to torque from friction, Andrea spins the chair while
the Jay is in his first position (the cylindrical position described above), while John times
certain rotations after releasing the chair. The first complete revolution while spinning takes 1.8
seconds, and the first three complete revolutions take a total of 5.9 seconds. Then Jay gets into
a second position, and this test happens again. John times that it takes 2.3 seconds for the first
revolution and 7.2 seconds for the first three revolutions. Next, Jay gets out of the chair, and
they spin the chair and calculate that the angular acceleration of the chair is -0.0700 rad/s2
.
[Assume that the angular acceleration for a specific situation is constant.]
(c) What is the angular acceleration of the chair while Jay is in cylindrical position?
(d) What is the angular acceleration of the chair while Jay is in second position?
(e) What is the moment of inertia of the chair?
(f) What is the torque due to friction when Jay is in the chair?
(g) What is Jay's moment of inertia in his second position?
Jay then gets into his cylindrical position again and sits as described earlier. Andrea spins him
very fast. After Jay goes around a few times, John says, “Start” and begins timing. After two
revolutions (3.2 seconds), John says, “Change”, Jay switches instantly into final position, and
John times Jay until the chair stops.
Disk 1 Disk 2 Disk 3
F⃗ F⃗ F⃗
(h) What was Jay's angular speed when the timing started (before the position change)?
(i) What was Jay's angular speed just before changing positions?
(j) What was Jay+Chair's angular momentum just before changing position?
(k) What was Jay+Chair's angular momentum just after changing position?
(l) What was Jay's angular speed just after changing position?
Answers
Answer: (a) To find the moment of inertia of Jay about his center of mass, we can use the formula I = mr^2, where m is the mass of the object and r is the distance from the center of mass to the point of rotation. Plugging in the values, we get I = 65 kg * (0.10 m)^2 = 0.65 kg*m^2.
(b) To find the moment of inertia of Jay about the axis of rotation of the chair, we need to use the formula I = Icm + md^2, where Icm is the moment of inertia about the center of mass and d is the distance from the center of mass to the axis of rotation. Plugging in the values, we get I = 0.65 kgm^2 + 65 kg * (0.10 m)^2 = 0.65 kgm^2 + 0.65 kgm^2 = 1.30 kgm^2.
(c) To find the angular acceleration of the chair while Jay is in his cylindrical position, we can use the formula alpha = T/I, where T is the torque and I is the moment of inertia. The angular acceleration is given as -0.0700 rad/s^2, so we can rearrange the formula to solve for T: T = I * alpha = 1.30 kg*m^2 * (-0.0700 rad/s^2).
(d) To find the angular acceleration of the chair while Jay is in his second position, we can use the same formula as before: alpha = T/I. The angular acceleration is not given, so we cannot solve for T directly.
(e) To find the moment of inertia of the chair, we can use the formula I = mr^2, where m is the mass of the object and r is the distance from the center of mass to the point of rotation. The mass of the chair is given as 30 kg and the distance from the center of mass to the axis of rotation is not given, so we cannot solve for I directly.
(f) To find the torque due to friction when Jay is in the chair, we can use the formula T = Fd, where F is the force of friction and d is the distance from the axis of rotation to the point of application of the force. The force of friction is not given, so we cannot solve for T directly.
(g) To find the moment of inertia of Jay in his second position, we need to use the formula I = Icm + md^2, where Icm is the moment of inertia about the center of mass and d is the distance from the center of mass to the axis of rotation. The moment of inertia about the center of mass and the distance from the center of mass to the axis of rotation are not given, so we cannot solve for I directly.
(h) To find Jay's angular speed when the timing started, we need to know the time it took for Jay to complete one revolution and the radius of the circle he was rotating around. Both of these values are not given, so we cannot solve for the angular speed directly.
(i) To find Jay's angular speed just before changing positions, we need to know the time it took for Jay to complete one revolution and the radius of the circle he was rotating around. Both of these values are not given, so we cannot solve for the angular speed directly.
(j) To find Jay+Chair's angular momentum just before changing position, we need to know Jay's angular speed and the moment of inertia of Jay+Chair
A 60.0kg ice skater throws a large box with a mass of 15.0kg away from her (with an initial acceleration of 4.0 m/s2). What is the acceleration of the skater (in m/s2)?
Answers
Answer: 1.0 m/s2
Explanation:
This is a Newton's 3rd Law of Motion problem. The force applied on the box by the skater must equal the force applied on the skater by the box (and in the opposite direction). F = ma
Let x = acceleration of the skater
(15.0 kg)(4.0 m/s2) = (60.0 kg) (x)
x = 60 N / 60 kg = 1.0 m/s2