Help Needed: Physics Homework Problem with Angle Theta & Acceleration

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In summary, the box slides down the board at an angle theta, which is held constant. The acceleration of the box is found to be 4.02m/s^2.
  • #1
piper210_355
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Homework Statement



Okay so this is probably a really easy problem, but my teacher literally doesn't teach us any thing, so can someone please help me.

The coefficient of static friction between a 2.5kg box and a wooden board is .45 and the coefficient of kinetic friction between the box and the board is .28. The box is placed on the board, which is slowly lifted at one end until the box starts to slide down the board, at which point the angle theta of the board is held constant. Determine the angle theta of the board and the acceleration of the box as it slides down the board.

Homework Equations


ok for finding theta i know I can use tan(theta)=F(x)/F(normal)

for acceleration i can use a=(mass)(gravity)(sin(theta))


The Attempt at a Solution


tan(theta)=.45/F(normal)
i don't know how to find the normal force.
 
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  • #2
Welcome to PF!

piper210_355 said:
The coefficient of static friction between a 2.5kg box and a wooden board is .45 and the coefficient of kinetic friction between the box and the board is .28. The box is placed on the board, which is slowly lifted at one end until the box starts to slide down the board, at which point the angle theta of the board is held constant. Determine the angle theta of the board and the acceleration of the box as it slides down the board.

i don't know how to find the normal force.

Hi piper210_355! Welcome to PF! :smile:

Hint: the acceleration perpendicular to the board is obviously zero. :smile:
for acceleration i can use a=(mass)(gravity)(sin(theta))

No … apply Newton's second law to all the forces along the board.
 
  • #3
ok so i used these equations

F(f) = u*F(n)

F(f) = F(x)

tan(theta) = F(x)/F(n)

and i rearranged them like so to find theta

tan(theta)=F(x)/F(n)
tan(theta)=F(f)/[F(f)/u)]

Here is where I'm not sure if I'm over simplifying(since in the other one i am dividing by a fraction i then change it by multipling by the reciprical)
tan(theta)=F(f)*[u/F(f)]

This cancels out the F(f) leaving...
tan(theta)=u

so then
(theta)=tan^(-1) .45
(theta)=24.23


is that right or am i off?
 
  • #4
Hi piper210_355! :smile:

(have a theta: θ :wink:)
piper210_355 said:
tan(theta)=u

so then
(theta)=tan^(-1) .45
(theta)=24.23

is that right or am i off?

No, that's fine!

Carry on … :smile:
 
  • #5
Ok I got the rest of these steps from a video on youtube, but I just want to make sure it's right.

First it said to get the force of gravity:
F(g)=(gravity)(mass)
F(g)=(9.81)(2.5)
F(g)=24.5N

Then I found the Force of the parallel (that's what they called the line in between F(n) and F(g) in the video).
F(p)= F(g)sin(24.23)
F(p)=(24.5)(sin 24.23)
F(p)= 10.05

After that I used Newton's second law to find the acceleration.
a=F/m
a=(10.05)/2.5
a=4.02m/s^2
 
  • #6
piper210_355 said:
Ok I got the rest of these steps from a video on youtube, but I just want to make sure it's right.

Then I found the Force of the parallel (that's what they called the line in between F(n) and F(g) in the video).

F(p)= 10.05

After that I used Newton's second law to find the acceleration.
a=F/m
a=(10.05)/2.5
a=4.02m/s^2

Hi piper210_355! :smile:

Using the web is not a good idea. :frown:

Use your books, or lecture notes, and work everything out from basic principles, or you won't be able to do it in the exam.

4.02 would be fine if there was no friction.

Use Newton's second law in the "parallel" direction, and try again! :smile:
 

1. What is angle theta in this physics homework problem?

Angle theta is the symbol used to represent an angle in trigonometry and physics. In this specific problem, it refers to the angle between the horizontal and the acceleration vector.

2. How do I calculate acceleration in this problem?

To calculate acceleration, you will need to use the formula a = Δv/Δt, where a is acceleration, Δv is the change in velocity, and Δt is the change in time. Plug in the given values for velocity and time to solve for acceleration.

3. What is the relationship between acceleration and angle theta?

The relationship between acceleration and angle theta can be explained using trigonometry. The magnitude of acceleration can be calculated using the formula a = g*sin(theta), where g is the acceleration due to gravity (9.8 m/s²). This means that as the angle theta increases, the acceleration decreases.

4. Why is angle theta important in this problem?

Angle theta is important in this problem because it affects the magnitude and direction of the acceleration. It determines how much of the acceleration is acting in the horizontal direction and how much is acting in the vertical direction.

5. How can I use the given information to solve for the unknown variables in this problem?

To solve for the unknown variables in this problem, you will need to use the equations of motion and the given information to create a system of equations. From there, you can use algebraic manipulation to solve for the unknown variables. It is also important to pay attention to units and use proper unit conversions when necessary.

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