Compute the horizontal force P required to prevent the block from sliding down the plane for the 100 lb block shown. Assume the coefficient of static friction to be 0.65.
Answers
canThe first First step we need to do is to make the decomposition of the vectors W and P.
Both will have a component perpendicular and parallel to the plane. The perpendicular will be used to calculate the maximum static friction force, and the horizontal will be used to find the P required to prevent the block from sliding.
From the sketch, we are able to define both, parallel and perpendicular components of P, as it follows:
[tex]\begin{gathered} P_{\text{//}}=P\cos (30\degree)=\frac{P\sqrt[]{3}}{2} \\ P_{perp}=P\sin (30\degree)=\frac{P}{2} \end{gathered}[/tex]Now, we can do the same for W.
And for W we also can provide the two components as follows:
[tex]\begin{gathered} W_{//}=W\sin (30\degree)=\frac{W}{2} \\ W_{\text{perp}}=W\cos (30\degree)=\frac{W\sqrt[]{3}}{2} \end{gathered}[/tex]Now, we can elaborate on both equations: one for the perpendicular direction and the other for parallel. In the perpendicular direction, we have a component of W, one component of P, and the normal force N. Because the block is going to move, or change its movement along this direction, the sum of the forces pointing upwards must be equal to the sum of the forces pointing downwards. From this, we can write the following:
[tex]\begin{gathered} N=P_{\text{perp}}+W_{\text{perp}} \\ N=\frac{P}{2}+\frac{W\sqrt[]{3}}{2}=\frac{P+W\sqrt[]{3}}{2} \end{gathered}[/tex]Now, for the horizontal, we have the P component to the right and the W component to the left. If we imagine the block is almost sliding. We can write the following equation, from the premise the forces will cancel each other just like the perpendicular case:
[tex]\begin{gathered} P_{//}+F_{\mu}=W_{//} \\ \frac{P\sqrt[]{3}}{2}+N\times\mu_{static}=\frac{W}{2} \end{gathered}[/tex]Here it is used the fact that the friction force is equal to the multiplication of the coefficient of static friction by the normal force. Here we assumed also that the friction is maximum because the block is on the verge of motion downwards, and for this reason, the Friction is upwards, with the P component.
Now, substituting N and the coefficient, we find:
[tex]\begin{gathered} \frac{P\sqrt[]{3}}{2}+\frac{P+100\sqrt[]{3}}{2}0.65=\frac{100}{2}=50 \\ \frac{P(\sqrt[]{3}+0.65)+65\sqrt[]{3}}{2}=50 \\ P(\sqrt[]{3}+0.65)+65\sqrt[]{3}=100 \\ P(\sqrt[]{3}+0.65)=100-65\sqrt[]{3} \\ P=\frac{100-65\sqrt[]{3}}{\sqrt[]{3}+0.65}\cong\frac{100-65\times1.732}{1.732+0.65}=\frac{100-112.58}{2.382} \\ P=-\frac{12.58}{2.382}\cong-5.275\text{lbf} \end{gathered}[/tex]From this, we can see that the force P made to the left with an intensity equal to -5.275 lbf will bring the block on the verge of motion downwards. If we consider that P is strong enough to make it almost move upwards, it is, the Normal Force will be downwards, we can remake the calculation as it follows:
[tex]\begin{gathered} P_{//}=W_{//}+F_{\mu} \\ \frac{P\sqrt[]{3}}{2}=\frac{W}{2}+N\times\mu_{static} \end{gathered}[/tex]And substituting values, we have:
[tex]\begin{gathered} \frac{P\sqrt[]{3}}{2}=50+\frac{P+100\sqrt[]{3}}{2}0.65 \\ \frac{P(\sqrt[]{3}-0.65)}{2}=50+50\sqrt[]{3}\times0.65 \\ P=\frac{2}{\sqrt[]{3}-0.65}\times50(1+\sqrt[]{3}\times0.65)\cong196.46 \end{gathered}[/tex]From this, we know that the max value for P, where the block will not slide is going to be 196.46 lbf to the right.
Related Questions
1ptWhat value of c would make x2 – 14.c +ca perfect square?C=What is the factored form of this expression for this value of c?(.)?
Answers
The value of c would be 49 and the factored form will be;
[tex](x-7)^2[/tex]Here, we want to get the value of c that will make the expression a perfect square
We proceed as follows;
Divide the coefficient of x by 2 ;
That would be; -14/2 = -7
Now, square this value; that would be (-7)^2 = 49
The value 49 would make the expression a perfect square
Thus, we have the factored form as follows;
[tex](x^2-14x+49)\text{ = (x-7)(x-7)}[/tex]Question 1] Find the mean for each set of data6,9,2,4,3,6,5
Answers
Given:
The given set of data is
[tex]6,9,2,4,3,6,5[/tex]To find: The mean for the given set of data?
Explanation:
We can calculate the mean of a given set of data by using the formula
[tex]Mean=\frac{Sum\text{ of the terms}}{Number\text{ of terms}}[/tex]Here,
We can calculate the sum of terms as
The sum of terms = 6+9+2+4+3+6+5
The sum of terms =35.
and
The number of terms = 7.
Now, by substituting the value in the above formula
Therefore,
[tex]\begin{gathered} Mean=\frac{35}{7} \\ \\ Mean=5 \end{gathered}[/tex]Hence, the mean = 5.
Answer: The mean for a given set of data is 5.
A group of friends wants to go to the amusement park tey have no more than $115 to spend on parking and admission parking is $15 and the tickets cst $25 per person including tax wrote and solve an inequality which can be used to determine x the number of people who can go to the amuement park
Answers
An inequality which can be used to determine x the number of people who can go to the amusement park is: 15 + 25x ≤ 115
Also, approximately 4 people can go to the amusement park.
In the given question,
cost for admission parking = $15
Tickets = $25 per person
Let x be the number of people those who go to the amusement park.
On parking and admission spent not more than $115
So we get an inequality,
15 + 25x ≤ 115
We solve above inequality.
25x ≤ 115 - 15
25x ≤ 100
25x / 25 ≤ 100/25
x ≤ 4
This means that approximately 4people can go to the amusement park.
Therefore, an inequality which can be used to determine x the number of people who can go to the amusement park is: 15 + 25x ≤ 115
Also, approximately 4 people can go to the amusement park.
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17. Identify all the angles that are congruent to
Answers
Answer:
ad, bc, eh, bf, ae, jk, mp, pn, ln, lm
Simplify 6x(9-2)-6 divided by 2
Answers
i don't have any idea but ok JQJAJDJDJKSBA
n(n+1)(n+5) is multiple of?
Answers
n(n+1)(n+5) can be a multiple of 3.
Utilizing the mathematical induction formula for any n > N, we are going to demonstrate it.
P(n) = n(n+1) n(n+5) = 3d, where d N
P(1)=1(2)(6)=12, that is cleavable by three, for n=1.
Suppose P(k) is true.
Where m N k three +6k a pair of +5k=3m k, P(k)=k(k+1)(k+5)=3m.
3\s =−6k \s2\s −5k+3m
We will currently demonstrate that P(k+1) is true.
P(k+1)=K+1, K+2, K+6, K 3 +9 K 2, K twenty K + twelve
When we plug the worth of k three into the equation on top of, we tend to get 3m6k a pair of 5k)+9k a pair of +20k+12 =3.
m+3k \s2\s +15k+12\s=3
(m+k \s2\s +5k+4)
in which r=m+k a pair of + 5k + four
P(k+1) is often true since P(k) is often true.
Therefore, in step with the induction principle, P(n) is cleavable by three for all n N.
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Malcolm's Bakery Shop sells gourment cupcakes. The shop's cost for making 3 cupcakes is $6.75, and the cost of making 5 cupcakes is $9.75 . What is the shop's cost per minute?
A. $1.50
B. $1.95
C. $2.25
D. $3.00
Answers
What is the solution set for: 4x - 3>29 *X> 4OX >8OX8OX > 3
Answers
Let us first solve the inequality
[tex]\begin{gathered} 4x-3>29\rightarrow \\ 4x>29+3=32 \\ 4x>32 \\ x>\frac{32}{4}=8 \\ x>8 \end{gathered}[/tex]So the answer is x>8
Xiao Mei covers a table with 8 rows of square unit tiles. There are 7 tiles in each row. What is the area that Xiao Mei covers in square units?
Answers
The area that Xiao Mei covers in square tiles is 56 sq. units.
Given,
In the question:
Xiao Mei covers a table with 8 rows of square unit tiles.
and, There are 7 tiles in each row.
To find the area that Xiao Mei covers in square tiles.
Now, According to the question:
Tables covers = 8 rows of sq. unit
In each row = 7 tiles
All you would have to do is multiply 8 times 7
it means, 8 x 7 = 56
Hence, The area that Xiao Mei covers in square tiles is 56 sq. units.
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Below, the two-way table is given for a classof students.FreshmenSophomore Juniors Seniors TotalMale4622Female 3463TotalIf a male student is selected at random, what is theprobability the student is a freshman.
Answers
29%
Explanations:Probability is the likelihood or chance that ab event will occur. Mathematically;
Probability = Expected/Total
From the given table, the total number of male student is the total outcome as shown:
Total outcome = 4 +6+ 2 + 2
Total outcome = 14
If a male freshmen is selected at random, the expected outcome will be 4.
Determine the probability
[tex]\begin{gathered} Pr(Freshman\text{ \mid Male})=\frac{Male\text{ freshmen}}{Total\text{ male studnt}} \\ Pr(Freshman\text{ \mid Male})=\frac{4}{14} \\ Pr(Freshman\text{ \mid Male})=0.2857\times100 \\ Pr(Freshman\text{ \mid Male})\approx29\% \\ \end{gathered}[/tex]Hence the probability that the male student is freshman is approximately 29%
Allen wanted to find the height of a tree in his yard. He knew that the fence surrounding his yard was 4 feet
high. At 3 pm the shadow of the fence was 2.5 feet long. The shadow of the tree was 11.3 feet long. What
was the height of the tree?
Answers
Hope this helps
A car travels about 32 miles on 1 gallon of gas. While a truck drives about 260 miles on 9.75 gallons of gas. Which gets better gas mileage?
Answers
In order to determine which vehicle gets better gas mileage, we need to determine which of the two vehicles consumes less gas for each mile travelled. The car consumes 1 gallon of gas for every 32 miles. We shall now determine how many miles the truck covers to consume 1 gallon of gas.
[tex]\begin{gathered} \text{Truck} \\ 9.75gl=260\text{miles} \\ 1gl=\frac{260}{9.75}\text{miles} \\ 1gl=26.67miles \end{gathered}[/tex][tex]\begin{gathered} \text{Car} \\ 1gl=32\text{miles} \end{gathered}[/tex]Therefore, the results shows that the truck gets better gas mileage
There were 20 baby devils 4 born in 2013 on Maria Island. In 2014, the number born was 200% of the 2013 devils. How many were born in 2014?
Answers
There are 20 baby devils in 2013 on Maria Island
in 2014 200 % where born
the number of baby devils born in 2014 can be gotten by
20 -------- 100
x -----------200
by proper analysis x = (200 x 20)/100 = 4000/100 = 40
40 baby devils were born in 2014
Two numbers are called relatively prime if their greatest common divisor is $1$.
Grogg's favorite number is $10!$, the product of the integers from $1$ to $10$. (He pronounces it TEN!)
What is the smallest integer greater than $800$ that is relatively prime to Grogg's favorite number?
Answers
Answer:
Two numbers are called relatively prime if their greatest common divisor is $1$. Grogg's favorite number is the product of the integers from $1$ to $10$
Answer: The answer is 803. :) lol
Step-by-step explanation:
You gotta keep trying numbers. But the numbers cant be even because if it's even, it can be divided by 2! Try the odd numbers starting at 800. If the number is not divisible by any of the numbers from 1-10 then it's the correct number. Got it on my second try. LOL! I'm from AOPS like you. :) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Can someone help me with this? Please and thank you
Answers
Given the line shown in the figure passes through the points (-3, -4) and (1, 2)
We will write the equation of the line.
First, we will find the slope of the line using the following formula:
[tex]slope=m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}[/tex]Substitute with the given points:
[tex]m=\frac{2-(-4)}{1-(-3)}=\frac{2+4}{1+3}=\frac{6}{4}=\frac{3}{2}=1.5[/tex]The equation of the line in point-slope form will be as follows:
[tex]\begin{gathered} y+4=1.5(x+3) \\ or \\ y-2=1.5(x-1) \end{gathered}[/tex]Convert tot he slope-intercept form, so, the equation will be:
[tex]\begin{gathered} y=1.5(x+3)-4 \\ y=1.5x+4.5-4 \\ \\ y=1.5x+0.5 \end{gathered}[/tex]Now, we will check the options to see the correct equations.
So, the answer will be, we will select the options:
A. y+4 = 1.5 (x+3)
B. y = 1.5x + 0.5
C. y - 2 = 1.5 (x - 1)
a. Draw the figure and its reflection in the x-axis.
A(2,0), B(1,5), C(4,3)
Answers
Answer:
A: 2,0 B: 1,-5 C: 4,-3
Step-by-step explanation:
w
A 2070 kg space station orbits Earth at an altitude of 457 km. Find the magnitude of the force with which the space station attracts Earth. The mass and mean radius of Earth are 5.98×1024 kg and 6370 km, respectively.
Answers
The magnitude of the force with which the space station attracts Earth.
17714.8532 N
This is further explained below.
The magnitude of the force :An influence that has the potential to alter the motion of an item is referred to as a force.
An object having mass may experience a change in its velocity, often known as acceleration, when subjected to a force.
Generally, the equation for the magnitude of the force is
F = G.M.m/r2
Where
G=gravitational constant
M and m mass
r=radius
F=force of attraction
Therefore
6.67*10^{-11} * 5.98*10^{24} * 2070/((6370+457)2*10^6)
= 17714.8532 N
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PLEASE HELP ITS DUE SOON! I DONT GET ANY OF THIS! HELP WOULD BE MUCH APPRECIATED! NEED THIS DONE BEEN STUCK ON THIS FOR WAY TO LONG!
YOU WILL GET 100 POINTS IF YOU HELP! QUESTION DOWN BELOW!!!!!
Answers
Answer:
1. given
2. isoceles triangle
3. PN = QN
4. Angle 3 = 4
5. MP = OQ
6. common
7. MP + PQ = OQ + PQ
8. not sure about this one sorry!
9. Angle Side Angle
Step-by-step explanation:
please help- I’m failing math. an explanation would help too
Answers
Answer:
11
Step-by-step explanation:
The answer would be 11, because when you add 5 and 6 together, you get 11. Pretend you had 5 cookies, and you got 6 more.
5 Cookies- O,O,O,O,O
6 More Cookies- O,O,O,O,O,O
If you add the cookies up, you get 11.
What is 14.481 rounded to the nearest tenth?A) 14B) 14.4C) 14.5D) 15
Answers
To round to the nearest tenth, we must round it to the nearest hundredth first, we have
[tex]14.481[/tex]See that we have 1 at the last decimal, then we will keep the hundredth value, it means that we will round to
[tex]14.481\rightarrow14.48[/tex]Now the last decimal is 8, it's above 5, then we must add one at the tenth and remove the hundredth
[tex]14.48\rightarrow14.5[/tex]Therefore the nearest tenth is the letter C, 14.5
Answer:c
Step-by-step explanation:THIS SOOO CORRECT!
Let f(x) = 2x - 1 and g(x) = x² + 1. Find and simplify: (g ° ƒ) (1/2)
Answers
To find the composition we need, let's first find the general expression:
[tex]\begin{gathered} (g\circ f)(x)=g(f(x)) \\ =g(2x-1) \\ =(2x-1)^2+1 \\ =4x^2-4x+1+1 \\ =4x^2-4x+2 \end{gathered}[/tex]Hence:
[tex](g\circ f)(x)=4x^2-4x+2[/tex]Now we can evaluate when x=1/2:
[tex]\begin{gathered} (g\circ f)(\frac{1}{2})=4(\frac{1}{2})^2-4(\frac{1}{2})+2 \\ =4(\frac{1}{4})-2+2 \\ =1-2+2 \\ =1 \end{gathered}[/tex]Therefore:
[tex](g\circ f)(\frac{1}{2})=1[/tex]Scenario: I am interested in selling cookies in my online bakery store. But before that, I need to find out how much I should price it to maximize revenue. I surveyed 1500 people and found out that if I price it at $2.00 a cookie then 800 people would buy it. If I price it at a dollar more at $3.00. a cookie, then 600 people would buy it. On the other hand, if I price it at a dollar less at $1.00 a cookie, then 1000 people would buy it. Based on this information, I noticed that for every one dollar increase in price, 200 fewer people would buy it. 1. Solve the scenario problem above for the optimal item price that maximizesrevenue. Be sure to show all your work and reflect on your findings.
Answers
the Let number of people = y
Let price = x
Gradient = -200
[tex]\begin{gathered} -200\text{ = }\frac{y\text{ - 800}}{x\text{ - 2}} \\ y\text{ - 800 = -200(x - 2)} \\ y\text{ - 800 = -200x + 400} \\ y\text{ = -200x + 400 + 800} \\ y\text{ = -200x + 1200} \end{gathered}[/tex]Revenue = price X number of people
[tex]\begin{gathered} R(x)\text{ = x }\times\text{ y} \\ R(x)\text{ = x(-200x + 1200)} \\ R(x)=-200x^2\text{ + 1200x} \\ R^{\prime}(x)\text{ = -400x + 1200} \\ To\text{ maximize , R(x) = 0} \\ -400x\text{ + 1200 = 0} \\ 400x\text{ = 1200} \\ x\text{ = }\frac{1200}{400} \\ \text{x = 3} \end{gathered}[/tex]Optimal item price = $3
Find the value of b that makes quadrilateral RSTU a parallelogram.
Answers
We are asked to find the value of b that makes quadrilateral RSTU a parallelogram.
We know from the properties of a parallelogram that the opposite angles are always equal.
[tex]\begin{gathered} \angle S=\angle U \\ \angle T=\angle R \end{gathered}[/tex]Let us equate the angles and solve the equation for b.
[tex]\begin{gathered} \angle S=\angle U \\ 11b-6=12b-18 \\ 11b-12b=-18+6 \\ -b=-12 \\ b=12 \end{gathered}[/tex]Similarly,
[tex]undefined[/tex]Which number line represents the solution set for the inequality 2x - 6 2 6(x - 2) + 8?-1.5-1-0.500.51.5-1.5-1-0.500.51.55-0.500.51.5-1-0.500.51.5
Answers
Solve the inequality:
2x - 6 ≥ 6(x - 2) + 8
Operating the parentheses:
2x - 6 ≥ 6x - 12 + 8
Subtracting 6x:
2x - 6x - 6 ≥ - 12 + 8
Adding 6:
2x - 6x ≥ - 12 + 8 + 6
Simplifying:
- 4x ≥ 2
Dividing by -4 and changing the symbol:
x ≤ 2/(-4)
x ≤ -0.5
The solution in the number line starts at -0.5 and goes to the left with an arrow:
Solve for x usingcross multiplication.3x + 6 = 4x - 364=35x = [?]Enter
Answers
Solving for x,
[tex]\begin{gathered} \frac{3x+6}{4}=\frac{4x-3}{5} \\ \\ \rightarrow5(3x+6)=4(4x-3) \\ \rightarrow15x+30=16x-12 \\ \rightarrow30+12=16x-15x \\ \rightarrow42=x \\ \\ \Rightarrow x=42 \end{gathered}[/tex]The midpoint of overline PQ is M = (- 2, 1) . One endpoint is P = (- 5, - 1) Find the coordinates of the other endpoint , Q.
Answers
Answer;
The coordiantes of the point Q is;
[tex](1,3)[/tex]Explanation;
Here, we want to get the coordinates of the other endpoint
Mathematically, we can find the midpoint of two endpoints using the formula below;
[tex](x,y)\text{ = (}\frac{(x_1+x_2)}{2},\frac{(y_1+y_2)}{2})[/tex]The notation 1 and 2 represents the coordinates of the two end points
Now, by replacing the values given in the question, we have it that;
(x,y) is the coordinate of the point m which is (-2,1)
Now the first end point has the coordinates (-5,-1)
The second endpoint Q has the endpoint (x2,y2) which we want to calculate
We proceed to make the substitutions as follows;
[tex](-2,1)\text{ =}\frac{(-5+x_2)}{2},\frac{(-1+y_2)}{2}[/tex]We proceed to susbtitute the individual branches as follows;
[tex]\begin{gathered} -2\text{ = }\frac{-5+x_2}{2} \\ 2(-2)=-5+x_2 \\ -4=-5+x_2 \\ x_2=-4+5 \\ x_2\text{ = 1} \end{gathered}[/tex]Finally, we have;
[tex]\begin{gathered} 1=\frac{-1+y_2}{2} \\ 2(1)=-1+y_2 \\ 2+1=y_2 \\ y_2\text{ = }3 \end{gathered}[/tex]You buy five equally priced gifts for a total of $75 what was the price of each candle
Answers
Answer:
$15
Explanation:
To find the price of each candle, we need to divide $75 by 5, so the price of each candle is:
$75 ÷ 5 = $15
So, the answer is $15
Three clocks exist in a room:
The round clock is 10 minutes behind the actual time
The rectangular clock is 5 minutes after the actual time
The squared clock is 5 minutes slower than the round clock
The time now on the squared clock is 08:05, what is the time now on the rectangular clock?
08:25
08:20
08:15
08:30
Answers
Answer:
First choice: 08:25
Step-by-step explanation:
Squared Clock is 5 minutes slower than the round clock
since the round clock is 10 minutes behind actual time, square clod is 15 minutes behind actual time
Time on square clock = 8:05
So actual time = 8:05 + 15 = 8:20
Rectangular clock is 5 minutes ahead of actual time
So time on rectangular clock is 8:20 + 05 = 8:25
Answer: First choice: 08:25
A college basketball team offers season passes for $85, but you pay $4.45 for a program
at each game. Non-season-pass holders pay $9.45 for admission to each game, but the
game program is free. For what number of games is the cost of these plans the same?
Answers
For 9 of games is the cost of these plans the same.
What are basic linear equations?Moving the variables to one side of the equation and the numeric portion to the other allows us to solve a linear equation with one variable. As an illustration, the equation x - 1 = 5 - 2x can be resolved by transferring the numerical components to the right side of the equation while leaving the variables on the left. Therefore, we receive x + 2x = 5 + 1. Thus, 3x Equals 6. As a result, x = 2. The formula for a two-variable linear equation is Ax + By + C = 0, where A and B are the coefficients, C is a constant term, and x and y are the two independent variables, each with a degree of 1. A linear equation involving two variables, for illustration, is 7x + 9y + 4 = 0.
Consequently, you would multiply $9.45 and $4.45 by the same number (I selected 9 because there are only one or two possible answers), then add $85 to the result for the $4.45 amount.
9.45 x 9
= 85.05
4.45 x 9
= 40.05 +85
= 125.05
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Determine whether the graph represents a linear, quadratic, or exponential function.o Exponentialo Linearo Quadratic
Answers
When we graph a linear equation we draw a line. When we want to graph a quadratic equation we draw a parabola, a parabola is a U-shaped curve. The graph of an exponential function grows or decays and has asymptotic values.
In this case, the first graph is a line, so it represents a linear equation.
The second graph is a U-shaped curve, then it represents a quadratic equation.
The third graph decays, then it represents an exponential equation.