Answer:
E) True. The girl has a larger tangential acceleration than the boy.
Explanation:
In this exercise they do not ask us to say which statement is correct, for this we propose the solution to the problem.
Angular and linear quantities are related
v = w r
a = α r
the boy's radius is r₁ = 1.2m the girl's radius is r₂ = 1.8m
as the merry-go-round rotates at a constant angular velocity this is the same for both, but the tangential velocity is different
v₁ = w 1,2 (boy)
v₂ = w 1.8 (girl)
whereby
v₂> v₁
reviewing the claims we have
a₁ = α 1,2
a₂ = α 1.8
a₂> a₁
A) False. Tangential velocity is different from zero
B) False angular acceleration is the same for both
C) False. It is the opposite, according to the previous analysis
D) False. Angular acceleration is equal
E) True. You agree with the analysis above,
(c) the fraction of energy lost during the impact
By Newton's 2nd law, m*a=sum_of_forces where m is the mass and a the acceleration. Here there are two forces in opposed directions.
Thus 5*a=40-8=32 therefore a=32/5=6.4m^s/2
At 100 km/hr, the car's kinetic energy is
KE = (1/2) (mass) (speed)²
KE = (1/2) (1575 kg) ( [100 km/hr] x [1000 m/km] x [1 hr/3600 sec] )²
KE = (787.5 kg) (27.78 m/s)²
KE = 607,639 Joules
In order to deliver this energy in 2.9 seconds, the engine must supply
(607,639 J / 2.9 sec) = 209,531 watts
<em>Power = 281 HP</em>
