A 10-kg crate is pulled along a horizontal floor by a constant force exerted by a person, Fp = 80N, which acts at a 45◦ angle. The floor is rough and there is a kinetic friction force of 4.1 N acting on the crate as it slides. The crate is pulled for a distance of 10 meters. a) Determine the work done by the pulling force and friction force. b) If the crate starts at rest, what is the final speed of the crate?

Question

A 10-kg crate is pulled along a horizontal floor by a constant force exerted by a person, Fp = 80N, which acts at a 45◦ angle. The floor is rough and there is a kinetic friction force of 4.1 N acting on the crate as it slides. The crate is pulled for a distance of 10 meters. a) Determine the work done by the pulling force and friction force. b) If the crate starts at rest, what is the final speed of the crate?
I have really been struggling with the second part of this problem to find the final speed. If anyone could help that would be awesome! Thank you!

Damon · Answer

Fp horizontal = 80 cos 45 = 56.6 Newtons
Fp up = 56.6 N

normal force = 10 * 9.81 - 56.6 = 41.5 N (not needed but you should know)
friction force = - 4.1 N

Work done by pull = horizontal pull force * distance in direction of pull
= 56.6 * 10 = 566 Joules

Work done by friction horizontal friction force * distance in direction of force
= - 4.1 * 10 = -41 N

final Ke of block = (1/2) m v^2 = 566 Joules - 41 Joules
so
(1/2)(10)v^2 = 525 Joules

Laura · Answer

Thank you so much! I appreciate it!

Damon · Answer

You are welcome.