1. A hanging mass of 1500 grams compresses a spring 2.0 cm. Find the spring cons

Question

1. A hanging mass of 1500 grams compresses a spring 2.0 cm.   Find the spring constant in N/m.

2. The spring is compressed a total of 3.0 cm, and used to set a 500 gram cart into motion. Find the speed of the cart at the instant it is released, assuming all the elastic potential energy is converted to kinetic energy.

3. Suppose the cart is on a track that is elevated at one end. Find the maximum height h above the plane of the tabletop that the cart will rise to before coming to a stop; assume that all the kinetic energy is converted to gravitational potential energy.

Explanation / Answer

1. F = kx = mg
mass = 1500 g = 1.5 kg

k(0.02) = 1.5 x 9.81

k = 735.75 N/m

2. elastic PE = kx^2 /2

KE = mv^2 /2

735.75 (0.03^2 ) /2 = 0.50v^2 /2

v =1.15 m/s

3.using energy conservation again,

mgh = mv^2 /2

9.81 x h = 1.15^2 /2

h = 0.0675 m

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