1. A 73.0-kg crate is given a push so that it is initially moving at a speed of
ID: 1779173 • Letter: 1
Question
1. A 73.0-kg crate is given a push so that it is initially moving at a speed of 4.30 m/s across the horizontal floor. The coefficient of friction between the crate and the floor is 0.700. The crate eventually comes to rest.
(a) How much mechanical energy is lost due to friction acting on the crate? ___ J
(b) How far does the crate slide? ___ m
2. A 19.0-kg child on a 4.00-m-long swing is released from rest when the ropes of the swing make an angle of 35.0° with the vertical.
(a) Neglecting friction, find the child's speed at the lowest position. ___ m/s
(b) If the actual speed of the child at the lowest position is 3.30 m/s, what is the mechanical energy lost due to friction? ___ J
3. An outfielder throws a 0.150-kg baseball at a speed of 56.0 m/s and an initial angle of 30.0°. What is the kinetic energy of the ball at the highest point of its motion? ___ J
Explanation / Answer
1.
a)
mechanical energy lost = initial kinetic energy = (0.5) m v2 = (0.5) (73) (4.30)2 = 674.885 J
b)
final kinetic energy - initial kinetic energy = work done by friction
0 - 674.885 = - uk mg d
0 - 674.885 = - (0.7) (73) (9.8) d
d = 1.35 m
3.
at the highest point , speed is given as
V = Vo Cos30 = 56 Cos30
so kinetic energy is given as
KE = (0.5) m V2 = (0.5) (0.150) (56 Cos30)2 = 176.4 J
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