Consider a father pushing a child on a playground merry-go-round. the system has a moment of inertia of 84.4 kg · m². the father exerts a force on the merry-go-round perpendicular to its 1.50 m radius to achieve a torque of 375 n · m.
(a) calculate the rotational kinetic energy (in j) in the merry-go-round plus child when they have an angular velocity of 14.8 rpm. j
(b) using energy considerations, find the number of revolutions the father will have to push to achieve this angular velocity starting from rest. revolutions
(c) again, using energy considerations, calculate the force (in n) the father must exert to stop the merry-go-round in four revolutions. n

Part a)

Part b)

Part c)

F = 2.7 N

Explanation:

Part a)

As we know that the rotational kinetic energy of the merry go round is given as

here we know that

Now we have

Part b)

Now we know that work done due to torque = change in kinetic energy

Part c)

In order to stop it in four revolutions we have

F = 2.7 N

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s

i think the answer is tomato juice? not entirely sure though