Question

Susan's 13.0 kg baby brother Paul sits on a mat. Susan pulls the mat across the floor using a rope that is angled 30 (degrees) above the floor. The tension is a constant 28.0 N and the coefficient of friction is 0.170.

Use work and energy to find Paul's speed after being pulled 3.20 m .

Please show your work :)

Answer 1

the work done will equal the change in KE, since the initial KE was zero, the change in KE will be the final KE and that will gives us the velocity

work = force x distance

we know the distance is 3.2 m, so we need to find the force acting on the mat

one force is the horizontal component of the pulling force, which is 28 cos 30 = 24.2 N

the friction force is u N where u is the coeff of friction (=0.17) and N is the normal force...we have to find the normal

force knowing there is no vertical acceleration, so all the vertical forces sum to zero

N - mg + 28 sin30 = 0

N= mg - 28 sin 30 = 13 x 9.8- 28 sin 30 = 113.4 N

and f = 0.17 x 113.4 N = 19.28 N

therefore, the net force on the mat is (24.2N-19.28N) = 4.92N, and we have

work done = change in KE

4.92N x 3.2m = 1/2 m v^2

v = Sqrt [2x 15.74 Nm/13kg] = 1.56 m/s