Question

# 1) You wish to accelerate a small merry-go-round from rest to a rotational speed of one-fourth...

1)

You wish to accelerate a small merry-go-round from rest to a rotational speed of one-fourth of a revolution per second by pushing tangentially on it. Assume the merry-go-round is a disk with a mass of 300 kg and a radius of 2.00 m .

Ignoring friction, how hard do you have to push tangentially to accomplish this in 6.00 s ? (Use energy methods and assume a constant push on your part.)

F=?

2)

A person opens a door by applying a 13-N force perpendicular to it at a distance 0.70 m from the hinges. The door is pushed wide open (to 120 ? ) in 2.3 s .

How much work was done?

W=?

What was the average power delivered?

p=?

First Question -

(1) First convert the units of required rotational speed into radian/sec –

w = 0.25 x 2 x pi = 1.5708 rad/s

given that, requisite time to accomplish the speed, t = 6 s

So, the required rotational acceleration in rad/s^2:
a = w / t = 1.5708 / 6 = 0.262 rad/s^2

Moment of inertia for the disc, I = 0.5 x m x r^2 = 0.5 x 300 x 2^2 = 600 kgm^2

So, the torque required to accelerate disc -
T = I x a = 600 x 0.262 = 157.2 Nm

Therefore, the requisite force -
F = T / r = 157.2 / 2 = 78.6 N

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