If you dropped a 4.5 kg (10 lb) bowling ball and a 5.4 kg (12 lb) bowling ball from the same height, which would you expect to have more kinetic energy? Why?
Answers
Answer:
Question #97527
A bowler lifts a 5.4-kg (12-lb) bowling ball from ground level to a height of 1.6 m (5.2 ft) and then drops it. (a) What happens to the potential energy of the ball as it is raised? (b) What quantity of work, in J, is used to raise the ball? (c) After the ball is dropped, it gains kinetic energy. If all the work done in part (b) has been converted to kinetic energy by the time the ball strikes the ground, what is the ball’s speed just before it hits the ground? (Note: The force due to gravity is F = m * g, where m is the mass of the object and g is the gravitational constant; g = 9.8 m>s2.
Expert's answer
Mass of the ball = 5.4 Kg
Height = 1.6 m
(a)Let the potential energy of the ball at h=0 is 0.
The potential energy of the ball at h=1.6 is -mgh=-(5.4 ×1.6×9.8) = - 84.672 J−mgh=−(5.4×1.6×9.8)=−84.672J (Ans)
(b) Work done = change in potential energyWorkdone=changeinpotentialenergy
= P.Ef - P.E.i=P.Ef−P.E.i
=(-84.672-0) J=(−84.672−0)J
= - 84.672 J=−84.672J (Ans)
(c)According to conservation of energy, W = changeW=change in Kinetic Energy.
K.E.f - K.E.i = WK.E.f−K.E.i=W
K.E.i = 0 JK.E.i=0J
K.E.f = 1/2 mv2K.E.f=1/2mv2
1/2 mv2 = 84.672 J1/2mv2=84.672J
v2 = 2×84.672/5.4v2=2×84.672/5.4
v = √914.4576 m/sv=√914.4576m/s
v = 30.24 m/sv=30.24m/s (Ans)
Answer:
the one having more mass would have more kinetic energy because earth attracts both of them with same acceleration , hence same velocity also (assuming the time to be very small) kinetic energy
= 1/2mv^2,
where velocity of both balls remains same, only difference is in their mass
so, the ball with greater mass(5.4 kg) would have more kinetic energy