A 3 kg block slides down a 1.2 m long ramp tilted at 20 degrees from horizontal. Without friction, its kinetic energy at the bottom is 12 J (choice d). With a kinetic friction coefficient of 0.15, its kinetic energy is 7 J (choice d). A 3 kg hollow ball rolls down the same ramp without slipping. Its rotational kinetic energy at the bottom is 12 J (choice c).

1. 9. A 3 kg block, initially at rest, slides down a ramp that is 1.2 m long and tilted at an angle of 20
from horizontal. If there is no friction, what is the kinetic energy of the block at the bottom of the
ramp? a. 35 b. 33J c. 20 J d. 12J e. oJ 40. A 3 kg block, initially at rest, slides down a ramp that
is 1.2 m long and tilted at an angle of 20 from horizontal. If there is kinetic friction coefficient of
o.15, what is the kinetic energy of the block at the bottom of the ramp? a. 35 b. 33J c. 12J d. 1.8J
e. o J (or the block never moves) 41. A 3 kg hollow ball ( mR2), initially at rest, rolls without
slipping down a ramp that is 1.2 m long and tilted at an angle of 20° from horizontal. What is
the rotational kinetic energy of the ball at the bottom? a. 35 b. 14J c. 12 J d. 7J e. 5J
Solution
The central concept through thilese questions is
Work done by all forces = change in kinectoc energy
Initial K.E. = 0 (in all cases)
39. Work done by gravity = final KE = mgh = mglsin(theta) = 3*9.8*1.2*sin(20) = 12.06 J-------
----------d
40. No option matches.
Work done =12.06(gravity) - 0.15*3*9.8*cos(20)*
1.2 = 7 J = final KE
Along ramp, F(gravity) = mgsin(theta) = 3*9.8*sin(20) = 10.05 N
F(friction) = 0.15*3*9.8*cos(20) = 2.83 N
41. Work done = work by gravity = 12 J------c
(Work done by friction is zero as the friction is static due to rolling)