How Is Work Done by Friction Calculated for a Crate Pulled at a Constant Speed?

[JSmith2009]

Homework Statement

A rope that is 30° to the horizontal has a tension of 150 N. It is used to pull a 40kg packing crate on a rough sruface through a distance of 6 m. If the crate moves at a constant speed, find the work done by friction.

Homework Equations

Energy formulas, not kinematic.

The Attempt at a Solution

I'm at a loss for what step to take after drawing my F-B-D. I've got it set up, but just brain-farting what next. I've thought over this problem, and I know it's a very simple one, but I just can't comprehend it or something.

 

[heth]

"constant speed" is question-code for something...

 

[thomate1]

I would approach this problem by first identifying the key variables and equations that are relevant to the situation. In this case, the key variables are the tension in the rope, the angle of the rope, the mass of the crate, the distance it is being pulled, and the coefficient of friction of the surface.

The first equation that comes to mind is the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy. In this case, the crate is moving at a constant speed, so its kinetic energy is not changing. Therefore, the work done on the crate must be equal to zero.

Next, I would consider the forces acting on the crate. The tension in the rope is pulling the crate forward, while the force of friction is opposing its motion. The angle of the rope can be used to determine the horizontal and vertical components of the tension force. The horizontal component is responsible for accelerating the crate, while the vertical component is counteracted by the normal force of the surface.

Using the equation for work (W = Fd), we can see that the work done by the tension force is equal to the horizontal component of the tension force multiplied by the distance the crate is being pulled. Since the crate is moving at a constant speed, the work done by the tension force must be equal to the work done by the force of friction, which is equal to the force of friction multiplied by the distance the crate is being pulled.

Therefore, to find the work done by friction, we need to determine the force of friction. This can be done using the equation for friction (Ff = μN), where μ is the coefficient of friction and N is the normal force. The normal force can be found by considering the vertical forces acting on the crate. Once we have the force of friction, we can use it to calculate the work done by friction using the equation mentioned earlier.

In summary, as a scientist, I would approach this problem by first identifying the relevant variables and equations, and then using them to analyze the forces acting on the crate and the work done by each force. By setting up and solving the relevant equations, we can determine the work done by friction in this situation.