Question

A jack-in-the-box toy consists of a clown mounted to a spring inside of a box. When the box open the clown pops out and oscillates. Suppose the clown only oscillates vertically and the clown has a mass of 34 kg. The spring it is mounted on has a force constant of 1.61 N/m.

(a) What is the maximum velocity of the clown if the amplitude of the oscillation is 2.00 cm?

Answer 1

To find the maximum velocity of the clown in a jack-in-the-box toy, we need to calculate the angular frequency and multiply it by the amplitude of the oscillation.

Step-by-step explanation:

To find the maximum velocity of the object bouncing on the spring, we can use the equation for simple harmonic motion:

v_max = Aω

where v_max is the maximum velocity, A is the amplitude of the motion, and ω is the angular frequency of the motion.

First, we need to convert the amplitude from centimeters to meters:

A = 2.00 cm = 0.02 m

The angular frequency can be calculated using the equation:

ω = sqrt(k/m)

where k is the force constant of the spring and m is the mass of the object.

Substituting the given values:

ω = sqrt(1.61 N/m / 34 kg) ≈ 0.147 rad/s

Finally, substitute the values of A and ω into the equation for v_max:

v_max = 0.02 m * 0.147 rad/s ≈ 0.003 m/s

Therefore, the maximum velocity of the clown is approximately 0.003 m/s.