Solving Physics Homework: Force of Friction & Work Done

[pebbles]

Homework Statement

Joe puts 11400 J of energy to drag crate 25 m across floor with constant speed. Rope makes 48 degree angle with horizontal.
Force exerted by the rope on the crate?
What is the force of friction acting on the crate to impede its motion?
What work is done by the floor through the force of friction between floor and the crate?

Homework Equations

See #3.

The Attempt at a Solution

a. I thought I would need to calculate the horizontal component with the 25 m and 48 degree angle and the cosine function, but got the wrong answer.
b. Ffriction=coefficient of kinetic frictionmg. But I don't know mass, so I'm not sure what equation I'd use.
c. W=Fd...Need to correctly calculate part b.


I'd appreciate any help. I'm not so good at physics, so it'd help if you really explain.

Thanks.

 

[mezarashi]

3a: Can you explain more clearly what exactly you're doing with the horizontal component and the 25m and the 48 degree angle and the cosine function? The hint in the question here is that he's done 11.4kJ of work. Work can only be done where there is displacement (i.e. in the x-direction).

3b-c: I'd consider these somewhat "trick" questions for the answers are not hard to get if you have a good conceptual understanding of work. What conditions in the x-direction must be satisfied for there to be constant velocity (no acceleration)? What does the free body diagram in the x-direction look like?

 

[ogb p]

Hello Joe, great job on attempting to solve the problem. Let's go through each part one by one.

a. To calculate the force exerted by the rope on the crate, we need to use the equation F=ma, where F is the force, m is the mass of the crate, and a is the acceleration of the crate. In this case, the crate is moving at a constant speed, so its acceleration is 0. Therefore, the force exerted by the rope on the crate is also 0.

b. To find the force of friction, we need to use the formula Ffriction=coefficient of kinetic friction * normal force. The normal force is the force exerted by the floor on the crate, which is equal to the weight of the crate (mg). We do not know the mass of the crate, but we can calculate it using the given information about the energy and distance. We know that work done (W) is equal to force (F) multiplied by distance (d), so we can rearrange the equation to find the mass of the crate: m = W/d. Plugging in the values, we get m = 11400 J / 25 m = 456 kg. Now we can calculate the force of friction: Ffriction = 0.25 * 456 kg * 9.8 m/s^2 = 1122.6 N.

c. The work done by the floor through the force of friction is equal to the force of friction multiplied by the distance the crate traveled, so W = Ffriction * d = 1122.6 N * 25 m = 28065 J.

I hope this helps explain the process and equations used to solve this problem. Keep practicing and you'll become more comfortable with physics concepts. Good luck with your homework!