# What is the acceleration of the crate?

• Sylvia
In summary, a 22.0-kg crate is pulled along a horizontal floor by a force of 300 N, with a coefficient of friction of 0.270. The problem involves finding the acceleration of the crate, which can be determined by setting up equations for both the crate and the pulley separately. The crate equation would be -Friction + Tension = ma, while the pulley equation would be F - 2T = 0. By solving these equations, the acceleration is found to be 3.41 m/s^2.
Sylvia
Problem: A 22.0-kg crate is pulled along a horizontal floor by the ideal arrangement
shown in figure below. The force F is 300 N. The coefficient of friction between the crate and
the floor is 0.270. What is the acceleration of the crate?

## Homework Equations

F = ma
Friction = (coefficient)(normal force)[/B]

## The Attempt at a Solution

Welcome to PF! :)

F acts on the pulley, not on the crate. The crate is connected to a rope. What is the force the rope pulls the crate with?
Note that the pulley is ideal, massless. What forces act on it, and what should be the resultant force?

Thank you! :)
That's the tension force, right? So would I set it up as F + T - Friction = ma?
I also wondered this at first, but I got confused because how would you know what the value of T is?

Sylvia said:
That's the tension force, right?
Yes.
Sylvia said:
So would I set it up as F + T - Friction = ma?
No. Consider the pulley and the crate separately. What forces act directly on the crate? (Hint: F does not.) What forces act on the pulley?
You can write a ##\Sigma F_x = m a_x## equation for each, but in the case of the pulley the mass is zero.

Sylvia said:
Thank you! :)
That's the tension force, right? So would I set it up as F + T - Friction = ma?
I also wondered this at first, but I got confused because how would you know what the value of T is?
F does not act on the crate. F is applied at the pulley. So what equations you have both for the crate and for the pulley?

haruspex said:
Yes.

No. Consider the pulley and the crate separately. What forces act directly on the crate? (Hint: F does not.) What forces act on the pulley?
You can write a ##\Sigma F_x = m a_x## equation for each, but in the case of the pulley the mass is zero.

See, that's where I'm confused. For the crate would I have -Friction + Tension = ma? And then for the pulley I would have F + Tension = ma? I'm not sure where the tension is playing a role.

Sylvia said:
See, that's where I'm confused. For the crate would I have -Friction + Tension = ma?

Correct.
Sylvia said:
And then for the pulley I would have F + Tension = ma? .
Think: There are two pieces of the string pulling the pulley. The tension is the same in both pieces. And what is the direction of force one string exerts on the pulley?
And the pulley is massless.

ehild said:
Correct.

Think: There are two pieces of the string pulling the pulley. The tension is the same in both piece.

Since the mass of the pulley is 0 and since the tension in both pieces is the same, I would get F - 2T = 0?

Sylvia said:
Since the mass of the pulley is 0 and since the tension in both pieces is the same, I would get F - 2T = 0?
Exactly! You can solve the problem now. :)

Thank you very much for the help!

You are welcome. What did you get for the acceleration?

I actually had a different version of this question; I googled the question and found this version so I could copy and paste it (the question was the same, just the numbers were different). I had 24 kg and coeff. of friction was 0.290. But I ended up getting the right answer, which was 3.41 m/s^2 :)

Correct! Good work.:)

## What is the acceleration of the crate?

The acceleration of a crate is the rate at which the velocity of the crate changes over time. It is a measure of how quickly the crate is speeding up or slowing down.

## How is acceleration calculated?

To calculate acceleration, you need to know the change in velocity and the time interval over which the change occurs. The formula for acceleration is: acceleration = (final velocity - initial velocity) / time interval.

## What are the units of acceleration?

Acceleration is typically measured in meters per second squared (m/s²) in the metric system or feet per second squared (ft/s²) in the imperial system.

## What factors can affect the acceleration of a crate?

The acceleration of a crate can be affected by various factors such as the force applied to the crate, the mass of the crate, and any opposing forces such as friction or air resistance.

## How does acceleration relate to other concepts in physics?

Acceleration is closely related to other concepts such as velocity, force, and mass. It is a key component in Newton's second law of motion and is also used in equations for calculating work, energy, and power.

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