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# 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.

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?

### 1 Answer by Expert Tutors

Arturo O. | Experienced College Instructor for Physics TutoringExperienced College Instructor for Physi...
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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