Question

An ice cube of mass 50.0 g can slide without friction up and down a 25.0 degree slope. The ice cube is pressed against a spring at the bottom of the slope,compressing the spring 0.100 m. The spring constant is 25.0 N/m. When the ice cube is released, how far will it travel up the slope before reversing direction?

Identify the initial and final gravitational potential energies.Enter your answers, separated by a comma, in terms of some or all of the variables m, k, x, d, θ,and the acceleration due to gravity g.

Identify the initial and final elastic potential energies.Enter your answers, separated by a comma, in terms of some or all of the variables m, k, x, d, θ, and theacceleration due to gravity, g.

Answer 1

Let, Gravitational potential energy is zero at the maximum compression of spring ,

Then total energy E = U= 1/2 kx²= 1/2 (25 N/m)(0.100 m)² = 0.125 J

Now , at maximum height,

Gravitation potential energy = 0.125 J = mgh [ By conservation of energy]

0.125 J = 0.05 kg× 9.8 m/s²× h

h = 0.255 m

Along the slope, hence distance traveled by ice cube is :

d = 0.255 m/sin25 = 0.604 m