H2 Physics 4 - Energy and Fields: Work-Energy Theorem on a Rough Surface

Step 1 - Set up the problem

A 3 kg box is pushed across a rough floor by a 20 N force at 15 degrees above the horizontal.

Step 1 - Set up the problem

The coefficient of kinetic friction is 0.25.

Step 1 - Set up the problem

Starting from rest, find the speed after 4 m of travel. Take g = 9.81 m/s squared.

Step 2 - Find the normal reaction

The upward component of the push reduces the normal reaction.

Step 2 - Find the normal reaction

Vertically: N + F sin 15 = mg.

Step 2 - Find the normal reaction

N = 3(9.81) minus 20 sin 15 = 29.4 minus 5.2 = 24.2 N.

Step 3 - Calculate the friction force

Friction equals mu_k times N.

Step 3 - Calculate the friction force

f = 0.25 times 24.2 = 6.06 N.

Step 3 - Calculate the friction force

Friction opposes the motion and reduces the net work done on the crate.

Step 4 - Apply the work-energy theorem

Work-energy theorem: net work = change in KE.

Step 4 - Apply the work-energy theorem

Work by the push's horizontal component minus work by friction = half m v squared.

Step 4 - Apply the work-energy theorem

Horizontal push = 20 cos 15 = 19.3 N.

Step 4 - Apply the work-energy theorem

Net work = 19.3(4) minus 6.06(4) = 77.2 minus 24.2 = 53.0 J.

Step 5 - Solve for the final speed

53.0 = half times 3 times v squared.

Step 5 - Solve for the final speed

v squared = 2(53.0)/3 = 35.3.

Step 5 - Solve for the final speed

v = 5.94 m/s.

Step 5 - Solve for the final speed

The box reaches about 5.9 m/s after 4 m.