Answer:
(a) θ = 45° = 0.78 rad
(b) θ = 32.27° = 0.56 rad
(c) θ = 57.27° = 1 rad
Explanation:
When a vector is resolved into its rectangular components, the formula for the direction angle of the vector with positive x-axis is given as:
tan θ = Ay/Ax
θ = tan⁻¹(Ay/Ax)
(a)
Ax = 12 m
Ay = 12 m
θ = tan⁻¹(12 m/ 12 m)
θ = tan⁻¹(1)
θ = 45° = 0.78 rad
(b)
Ax = 19 m
Ay = 12 m
θ = tan⁻¹(12 m/19 m)
θ = tan⁻¹(0.6315)
θ = 32.27° = 0.56 rad
(c)
Ax = 12 m
Ay = 19 m
θ = tan⁻¹(19 m/12 m)
θ = tan⁻¹(1.58333)
θ = 57.27° = 1 rad
Determine the force of gravitational attraction between a 92 kg student and a 550 g slice of pizza that are 25 cm apart
Answer:
F = 5.4 x 10⁻⁸ N
Explanation:
The gravitational force of attraction between two objects is given by Newton's Gravitational Law as follows:
F = Gm₁m₂/r²
where,
F = Gravitational Force = ?
G = Universal Gravitational Constant = 6.67 x 10⁻¹¹ N.m²/kg²
m₁ = mass of student = 92 kg
m₂ = mass of pizza slice = 550 g = 0.55 kg
r = distance between student and pizza slice = 25 cm = 0.25 m
Therefore,
F = (6.67 x 10⁻¹¹ N.m²/kg²)(92 kg)(0.55 kg)/(0.25 m)²
F = 5.4 x 10⁻⁸ N
A 0.12-m-radius grinding wheel takes 5.5 s to speed up from 2.0 rad/s to 11.0 rad/s. What is the wheel's average angular acceleration?
Answer:
0.56rad/s²
Explanation:
Using the equation of motion
wf = wi + αt
wf is the final angular velocity
wi is the initial angular velocity
α is the angular acceleration
t is the time
Given
wf = 11.0rad/s
wi =2.0rad/s
t = 5.5secs
Substitute into the formula and get α
11.0 = 2.0+5α
11.0-2.0 = 5α
9.0 = 5α
α = 5/9.0
α ≈ 0.56rad/s²
Hence the wheel's average angular acceleration is 0.56rad/s²
The wheel's average angular acceleration is equal to 1.64 [tex]rad/s^2[/tex].
Given the following data:
Radius = 0.12 meterTime = 5.5 secondsInitial angular velocity = 2.0 rad/sFinal angular velocity = 11.0 rad/sTo determine the wheel's average angular acceleration, we would apply the first equation of kinematics:
Mathematically, the angular acceleration of an object is given by the formula:
[tex]\alpha = \frac{\omega_f - \omega_i}{t}[/tex]
Where:
[tex]\omega_i[/tex] is the initial angular velocity.[tex]\omega_f[/tex] is the final angular velocity.t is the time.Substituting the given parameters into the formula, we have;
[tex]\alpha =\frac{11.0\;-\;2.0}{5.5} \\\\\alpha =\frac{9.0}{5.5}[/tex]
Angular acceleration = 1.64 [tex]rad/s^2[/tex]
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I NEED HELP PLZ I HAVE NO CLUE WHAT THE ANSWER IS AND I REALLY NEED TO GET AN A ON THIS TEST!
Answer:
I'm pretty sure its c
Hope you get a good grade-
g A ping pong ball (thin shell sphere) rolls down an incline at 30° from rest. What is its acceleration
Answer:
Explanation:
According to newtons second law of motion;
F = ma .... 1
Also the force acting aong the inclines is expressed as;
F = mgsintheta
m is the mass of the object
a is the acceleration
theta is angle of inclination
Equate 1 and 2
ma = mg sin theta
a = gsin(theta)
a = 9.8sin30
a = 9.8(0.5)
a = 4.9m/s²
Hence the acceleration of the ping pong is 4.9m/s²
A wire of radius 0.8 cm carries a current of 106 A that is uniformly distributed over its cross-sectional area. Find the magnetic field B at a distance of 0.07 cm from the center of the wire.
Answer:
The magnetic field is [tex]B = 2.319 *10^{-3} \ T[/tex]
Explanation:
From the question we are told that
The radius of the wire is [tex]r = 0.8 \ cm = 0.008 \ m[/tex]
The current is [tex]I = 106 \ A[/tex]
The position considered is d = 0.07 cm = 0.0007 m
Generally the magnetic field is mathematically represented as
[tex]B = \frac{\mu_o * I}{2\pi * \frac{r^2}{d} }[/tex]
Here [tex]\mu_o[/tex] is the permeability of free space with value [tex] 4\pi * 10^{-7} N/A^2[/tex]
So
[tex]B = \frac{ 4\pi * 10^{-7} * 106 }{2 * 3.142 * \frac{0.008^2}{0.0007} }[/tex]
=> [tex]B = 2.319 *10^{-3} \ T[/tex]
If a bicyclist has a mass of 70 kg and a velocity of 25 m/s, what is the momentum of the bicyclist? p=mv *
Answer:
1750Nm/s
Explanation:
70*25=1750Nm/s
Answer:
1750 kgm/s
Explanation:
The equation for momentum is p = mv = 70 * 25 = 1750
A stereo speaker is placed between two observers who are 35 m apart, along the line connecting them. If one observer records an intensity level of 64 dB, and the other records an intensity level of 85 dB, how far is the speaker from each observer
Answer:
x = 2,864 m , Ra = 32.1 m
Explanation:
Let's solve this problem in parts, let's start by finding the intensity of the sound in each observer
observer A β = 64 db
β = 10 log Iₐ / I₀
where I₀ = 1 10⁻¹² W / m²
Iₐ = I₀ 10 (β/ 10)
let's calculate
Iₐ = 1 10⁻¹² (64/10)
Iₐ = 2.51 10⁻⁶ W / m²
Observer B β = 85 db
I_b = 1 10-12 10 (85/10)
I_b = 3.16 10⁻⁴ W / m²
now we use that the emitted power that is constant is the intensity over the area of the sphere where the sound is distributed
P = I A
therefore for the two observers
P = Ia Aa = Ib Ab
the area of a sphere is
A = 4π R²
we substitute
Ia 4pi Ra2 = Ib 4pi Rb2
Ia Ra2 = Ib Rb2
Let us call the distance from the observer be to the haughty R = ax, so the distance from the observer A to the haughty is R = 35 ax; we substitute
Ia (35 -x) 2 = Ib x2
we develop and solve
35-x = Ra (Ib / Ia) x
35 = [Ra (Ib / Ia) +1] x
x (11.22 +1) = 35
x = 35 / 12.22
x = 2,864 m
This is the distance of observer B
The distance from observer A
Ra = 35 - x
Ra = 35 - 2,864
Ra = 32.1 m
Which theory explains why gravity between two objects changes when the distance between them changes?
Einstein's theory because he suggested that the more distance there is between objects, the more space-time
curves and the greater the strength of gravity is.
Einstein's theory because he suggested that the more distance there is between objects, the more space-time
curves and the weaker the strength of gravity is.
Newton's theory because he suggested that the greater the distance between objects, the greater the pull of gravity.
Newton's theory because he suggested that the greater the distance between objects, the weaker the pull of gravity.
Answer:
Newton's theory because he suggested that the greater the distance between objects, the weaker the pull of gravity.
Answer: The answer is Newton’s theory because he suggested that the greater the distance between objects, the weaker the pull of gravity
Explanation: Just took the test i hope this help you enjoy :D
An experiment consists of throwing balls straight up with varying initial velocities. Which quantity will have the same value in all trials?a) initial momentum.
b) maximum height.
c) time of travel.
d) acceleration.
Answer:
the correct answer is D, acceleration of gravity
Explanation:
In a projectile launch problem it is described by the expressions
v = v₀ - g t
v² = v₀² - 2 g y
y = v₀ t - ½ g t²
By examining these equations we can see that acceleration is the magnitude that appears constant in all expressions.
This acceleration is the acceleration of gravity with a value of g = 9.8 m/s² and directed towards the center of the Earth
therefore the correct answer is D
22. What happens to the volume of a 1 kg of water when it is heated from 4oC to 6oC? A. Increases B. Decreases C. Stays the same
Answer:
a
Explanation:
..................
car driving on a circular test track shows a constant speedometer reading of 100 kph for one lap. a. Describe the car's speed during this time. b.
Answer:
Speed = 100 km/h
Explanation:
Given:
Speedometer reading = 100 kph for one lap
Assume;
Time taken to complete one lap = 1 hour
Computation:
Speed = Distance / Time
Speed = 100 / 1
Speed = 100 km/h
An electric motor spins at a constant 2695.0 rpm. If the rotor radius is 7.165 cm, what is the linear acceleration of the edge of the rotor?A) 5707 m/s^2 B) 281.6 m/s^2 C) 28.20 m/s^2 D) 572,400 m/s^2
Answer:
5707 m/s^2
Explanation:
The spring constant, k, for a 22cm spring is 50N/m. A force is used to stretch the spring and when it is measured again it is 32cm long. Work out the size of this force
Answer:
5N
Explanation:
Given parameters:
Original length = 22cm
Spring constant, K = 50N/m
New length = 32cm
Unknown
Force applied = ?
Solution:
The force applied on a spring can be derived using the expression below;
Force = KE
k is the spring constant
E is the extension
extension = new length - original length
extension = 32cm - 22cm = 10cm
convert the extension from cm to m;
100cm = 1m;
10cm will give 0.1m
So;
Force = 50N/m x 0.1m = 5N
How do bones develop and grow?
Answer:
Explanation:
Bones grow in length at the epiphyseal plate by a process that is similar to endochondral ossification. The cartilage in the region of the epiphyseal plate next to the epiphysis continues to grow by mitosis. The chondrocytes, in the region next to the diaphysis, age and degenerate.
How long does it take a vehicle to reach a velocity of 32 m/s if it accelerates from rest at a rate of 4.2 m/s^2? ANSWER ALL PLEASE!! Im dumb:(
What is the initial velocity of the vehicle?
What is the final velocity of the vehicle?
What is the acceleration of the vehicle?
Write the equation you will use to solve the problem.
How long does it take the vehicle to reach its final velocity?
0.13 seconds
18.1 seconds
7.62 seconds
134.4 seconds
Answer: Givens
a = 4.4 m/s^2 This is an acceleration and is positive.
vi = 10.2 m/s
t = 4.2 seconds
vf = ????? The cruising speed in this case is vf.
Formula
a = (vf - vi)/t Notice the 3 givens and what you seek determine the formula
Solve
4.4 m/s^2 = (vf - 10.2)/4.2 Multiply both sides by 4.2
4.4 * 4.2 = vf - 10.2
18.48 = vf - 10.2 Add 10.2 to both sides
18.48 + 10.2 = vf 8.28 is the second best answer.
28.68 = vf This is your cruising speed.
C <<<< Answer
7.62 (2dp)
Explanation:
U = 0m/s
V = 32m/s
A = 4.2m/s^2
T = ?
[tex]a = \frac{v - u}{t}[/tex]
[tex]t = \frac{v - u}{a} [/tex]
[tex]t = \frac{32 - 0}{4.2} [/tex]
[tex]t = \frac{32}{4.2} [/tex]
[tex]t = 7.62 \: (2dp)[/tex]
If you liked this answer, brainliest?
Help!!! Need answer ASAP.
Answer:
a = 0.5 [m/s²]
Explanation:
To solve this problem we must use Newton's second law which tells us that the sum of forces is equal to the product of mass by acceleration.
ΣF = m*a
F = force = 200 [N]
m = mass = 400 [kg]
a = acceleration [m/s²]
Now replacing:
200 = 400*a
a = 0.5 [m/s²]
You can chew through very tough objects with your incisors because they exert a large force on the small area of a pointed tooth. What pressure in pascals can you create by exerting a force of 500 N with your tooth on an area of 1.00 mm?
Answer:
sry i need points
Explanation:
1) When making a digital animation of a person running on a sidewalk in a scene, which parameter would be an initial condition?
-the maximum range of motion in the person's ankle
-the coefficient of friction between the person's foot and the sidewalk
-the position of the person's feet the mass of the person
2)Different models need to include different levels of detail. When a person runs, tiny pieces are lost from the bottom of the shoe. In which situation would it be most important to model the mass of the shoe over time, rather than making it a boundary condition?
-a kinesthesiologist studying the effects of foot position on running speed
-a running shoe company studying how different surfaces affect the life of a shoe tread
-a video game animator producing a scene where a running character slides to a stop
-a video game designer trying to determine how much damage is done to armor over time
Answer:
The position of the person's feet. a running shoe company studying how different surfaces affect the life of a shoe tread
Explanation:
100%
Answer:
1. The position of the person's feet.
2. A running shoe company studying how different surfaces affect the life of a shoe tread
Explanation:
100% correct
Calculate the distance covered by a bus moving at a rate of 11.5km/h with a time of 2060seconds
Answer:
6.56km
Explanation:
Given parameters:
Speed = 11.5km/hr
Time = 2060s
Unknown:
Distance covered = ?
Solution:
Speed is distance divided by the time taken.
Speed = [tex]\frac{distance}{time}[/tex]
Distance = Speed x time
Let us convert the seconds to hours;
3600s = 1hr
2060s = [tex]\frac{2060}{3600}[/tex] = 0.57hr
Now
Distance = 11.5km/hr x 0.57hr = 6.56km
An unbalanced 16.0N force is applied to a2.0kg mass. What is the acceleration of the mass?
Answer:
Yuh
Explanation:
Which of these should you always do at the end of a calculation
Answer:
Reverse check the answer
Explanation:
I believe it is very important that once someone is done with any calculation, the person ought to go over the calculations again. And even, recheck the answer in inverted form.
This is so because while doing the calculations, we can possibly make errors that we won't notice until after submission. Knowing 2 * 3 = 6, but writing 2 * 3 = 5 in the course of calculations can happen to anybody. So therefore, cross checking and reverse checking is needed
A 67.6-kg boy is surfing and catches a wave which gives him an initial speed of 1.56 m/s. He then drops through a height of 1.65 m, and ends with a speed of 8.30 m/s. How much nonconservative work was done on the boy?
Answer:
The nonconservative work was done on the boy is 1154.87 J.
Explanation:
Given;
mass of the boy, m = 67.6 kg
initial speed of the boy, u = 1.56 m/s
height of fall, h = 1.65 m
final speed of the boy, v = 8.30 m/s
The initial energy of the boy is given by;
E₁ = K.E₁ + P.E₁
E₁ = ¹/₂mu² + mgh
E₁ = ¹/₂(67.6)(1.56)² + (67.6 x 9.8 x 1.65)
E₁ = 82.134 + 1091.475
E₁ = 1,173.61 J
The final energy of the boy is given by;
E₂ = K.E₂
E₂ = ¹/₂mv²
E₂ = ¹/₂(67.6)(8.3)²
E₂ = 2,328.482 J
The nonconservative work was done on the boy is given by;
W = E₂- E₁
W = 2,328.482 J - 1,173.61 J
W = 1154.87 J
Therefore, the nonconservative work was done on the boy is 1154.87 J.
I need help pleaseee
Answer:
8) 709.8875 J
9) The object is at 7.24375 m from the ground
10) Kinetic energy increases as the object falls.
Explanation:
We use the expression for the displacement h(t) as a function of time of an object experiencing free fall:
h(t) = hi - (g/2) t^2
hi being the initial position of the object (10m) above ground, g the acceleration of gravity (9.8 m/s^2), and t the time (in our case 0.75 seconds):
h(0.75) = 10 - 4/9 (0.75)^2 = 7.24375 m
This is the position of the 10 kg object after 0.75 seconds (answer for part 9)
Knowing this position we can calculate the potential energy of the object when it is at this height, using the formula:
U = m g h = 10kg * 9.8 (m/s^2) * 7.24375 m = 709.8875 J (answer for part 8)
Part 10)
the kinetic energy of the object increases as it gets closer to ground, since its velocity is increasing in magnitude because is being accelerated in its motion downwards.
You've just put a new wood floor in your house. An object will dent the flooring if the stress--the force divided by the area--exerted by the object is great enough.
A) Find the stress produced by a 50 kg woman in high-heeled shoes (assume a circular heel pad 0.50 cm in diameter) with all of her weight on one heel.
Express your answer with the appropriate units.
B) Find the stress produced by a 5000 kg African elephant (assume a circular contact area of 40 cm in diameter for one foot) standing on all four feet.
Express your answer with the appropriate units.
Answer:
The correct answer will be:
(A) 24955495.07 N/m²
(B) 97482.40 N/m²
Explanation:
(A)
The given values are:
mass,
m = 50 kg
diameter
= 0.50 cm
then,
radius,
r = 0.25 cm
= 0.0025 m
As we know,
⇒ [tex]A = area \ of \ cross \ section[/tex]
[tex]=\pi r^2[/tex]
and,
⇒ [tex]stress = \frac{mg}{A}[/tex]
On substituting the values, we get
[tex]=\frac{(50)(9.8)}{\pi (0.0025^2)}[/tex]
[tex]=24955495.07 \ N/m^2[/tex]
(B)
mass,
m = 5000 kg
radius,
r = 20 cm
= 0.2 m
Now,
⇒ [tex]stress=\frac{\frac{5000}{4} (9.8)}{\pi (0.2^2)}[/tex]
[tex]=97482.40 \ N/m^2[/tex]
please help i will mark brainliest
what does a speedometer measure?
a. accerlation
b. velocity
c. speed
d. average speed.
Answer:
c. speed
Explanation:
Speedometer is a device used to measure the speed of a vehicle. I am pretty sure this is the correct option.
A runaway train car that has a mass of 15,000 kg travels at a speed of 5.4 m/s down a track. Compute the time required for a force of 1500 N to bring it to rest.
(a) 0.019 s
(b) 54s
(c) 4.2Ã106s
(d) 2.4Ã10â7s
Answer:
54 s
Explanation:
Given that,
Mass of a car, m = 15000 kg
Initial speed, u = 5.4 m/s
Final speed, v = 0 (it comes to rest)
Force, F = 1500 N
We need to find time when it comes to rest. Let it is t. Net force is given by :
F = ma, a is acceleration of the car
[tex]F=\dfrac{m(v-u)}{t}\\\\t=\dfrac{m(v-u)}{F}\\\\t=\dfrac{15000\times (0-5.4)}{1500}\\\\t=54\ s[/tex]
So, it will take 54 seconds to come to rest.
The time required to bring the car to rest is 54 s and the right option is (b) 54 s.
To calculate the time required for the force to bring the car to rest, we use the formula below.
Formula:
F = m(v-u)/t............ Equation 1Where:
F = Force applied to the carm = mass of the carv = final velocity of the caru = initial velocity of the cart = time.Make t the subject of the equation
t = m(v-u)/F............. Equation 2From the question,
Given:
F = -1500 N (stopping force)m = 15000 kgv = 0 m/s (to rest)u = 5.4 m/sSubstitute these values into equation 2
t = [1500(0-5.4)]/-1500t = -81000/-1500t = 54 secondst ≈ 54 sHence, The time required to bring the car to rest is 54 s and the right option is (b) 54 s.
Learn more about time here: https://brainly.com/question/4931057
What is the force on a 5-kilogram ball that is falling freely due to the pull of gravity?
Answer:
Force = 49N
Explanation:
Force is given by the multiplication of mass and acceleration.
Mathematically, Force is;
[tex] F = ma[/tex]
Where;
F represents force measured in Newton.
m represents the mass of an object measured in kilograms.
a represents acceleration measured in meter per seconds square.
Given the following data
Mass = 5kg
We know that acceleration due to gravity = 9.8m/s²
To find the Force:
[tex] F = 5*9.8 [/tex]
Force = 49N
2
10 points
Find the total displacement of each of the motions.
a) You walk 45 m W, then 34 mW
b) You drive 5 km N, then 7 km S
c) You cycle 350 m E, then 800 m W, then 200 m E
d) You fly 850 km N then 850 km S
Answer:
a) s = 79 m W
b) s = 2 km S
c) s = 250 m W
d) s = 0 km
Explanation:
We take the following sign convention for the directions:
North (N) ---> positive
South (S) ---> negative
East (E) ---> negative
West (W) ---> positive
a)
45 m W, 34 m W
s = 45 m + 34 m
s = 79 m W
b)
5 km N, 7 km S
s = 5 km - 7 km
s = - 2 km
s = 2 km S
c)
350 m E , 800 m W, 200 m E
s = -350 m + 800 m - 200 m
s = 250 m
s = 250 m W
d)
850 km N, 850 km S
s = 850 km - 850 km
s = 0 km
A displacement vector with a magnitude of 20. meters could have perpendicular components with magnitudes of A. 10. m and 10. m B. 12 m and 8.0 m 12 m and 16 m D. 16 m and 8.0 m
Answer:10.m and 10. M
Explanation:
A displacement vector with a magnitude of 20. m could have perpendicular components with magnitudes of C. 12 m and 16 m.
A displacement vector with a magnitude of 20. meters can be decomposed in 2 perpendicular components.
They would form a right triangle, in which the displacement vector would be the hypotenuse (a) and the components would be the legs (b, c).
Given the magnitude of the legs, we can calculate the magnitude of the hypotenuse using the Pythagorean theorem.
[tex]c = \sqrt{a^{2} + b^{2} }[/tex]
Let's use this formula to calculate the displacement vector for each pair of legs.
A. 10. m and 10. m[tex]c = \sqrt{a^{2} + b^{2} } = \sqrt{(10.m)^{2} + (10.m)^{2} }= 14.1m[/tex]
B. 12 m and 8.0 m[tex]c = \sqrt{a^{2} + b^{2} } = \sqrt{(12m)^{2} + (8.0m)^{2} }= 14.4m[/tex]
C. 12 m and 16 m[tex]c = \sqrt{a^{2} + b^{2} } = \sqrt{(12m)^{2} + (16m)^{2} }= 20m[/tex]
D. 16 m and 8.0 m[tex]c = \sqrt{a^{2} + b^{2} } = \sqrt{(16m)^{2} + (8.0m)^{2} }= 17.9m[/tex]
A displacement vector with a magnitude of 20. m could have perpendicular components with magnitudes of C. 12 m and 16 m.
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Which possible component of initial energy is caused by molecular motion within a material?
Answer: thermal energy
Answer:
Thermal energy
Explanation:
The internal energy of a system is widely known as thermal energy. Now, thermal energy is also called heat energy and it is an internal energy of a component which is produced when an increase in temperature causes atoms and molecules within the component to move faster and start colliding with one other.
Therefore, the more heat the is applied to the component, the hotter the substance and the more its particles move which in turn leads to a higher thermal energy.