The following questions refer to a pop-up toy with a mass of .35 kg. The toy’s spring compresses .04 m and has a spring constant of 4,500 N.

Question

The following questions refer to a pop-up toy with a mass of .35 kg. The toy’s spring compresses .04 m and has a spring constant of 4,500 N.

 

1. What is the spring potential energy before the pop-up toy pops up?

2. What height will the toy reach?

3. What speed will the pop up toy reach?

4. What is the weight of the object?

 

SHOW WORK FOR ALL PLEASE.

 

Answer 1

The spring constant must have units of force over length, so I assume you meant k = 4500 N/m.  If so, then:

 

(1)

 

U = (1/2) k x^2 = (1/2) (4500 N/m) (0.04 m)^2 = 3.6 J

 

(2)

 

U of the spring would be fully converted to gravitational potential energy when the mass comes to instantaneous rest at maximum height, so

 

U = mgh

 

h = U / (mg) = (3.6 J) / [(0.35 kg) (9.8 m/s^2)] = 1.0496 m

 

(3)

 

Maximum speed is attained when the object passes the equilibrium (i.e. uncompressed/unstretched) point of the spring, where the potential energy of the spring is fully converted to kinetic energy:

 

U = (1/2) m v^2

 

v = sqrt(2U / m) = sqrt [2 (3.6 J) / 0.35 kg)] = 4.536 m/s 

 

(4)

 

W = mg = (0.35 kg) (9.8 m/s^2) = 3.43 N