Question

A 57 g ice cube can slide without friction up and down a 33 ∘ slope. The ice cube is pressed against a spring at the bottom of the slope, compressing the spring 12 cm . The spring constant is 20 N/m . When the ice cube is released, what distance will it travel up the slope before reversing direction?

Answer 1

The springs stored energy is transferred to the cube as kinetic energy and then by the slop the KE is converted to height energy. 

0.5 . k . x^2 = 0.5 . m . v^2 = m . g . ∆h 

0.5 . 50 . (0.1^2) = 0.05 . 9.8 . ∆h 

∆h = 0.51 m = 51 cm 

This is the height gained 
Distance along the slope = ∆h / sin 60 = 0.589 = 59 cm 

In the second case, the stored spring energy is converted into height energy AND frictional heat energy. 

The height energy is m . g . d sin 60 where d is the distance the cube moves along the slope. 

The Frictional energy converted is F . d 

F ( the frictional force ) = µ . N 

N ( the reaction to the component of the gravity force perpendicular to the surface of the slope ) = m . g . cos60 

Total energy converted 

0.5 . k . x^2 = (m . g . dsin60) + (µ . m . g . cos60 . d ) 

Solve for d 

d = 0.528 = 53 cm