Question

Part A)

A 65 g ice cube can slide without friction up and down a 30∘ slope. The ice cube is pressed against a spring at the bottom of the slope, compressing the spring 10 cm. The spring constant is 22 N/m . When the ice cube is released, what total distance will it travel up the slope before reversing direction?

Express your answer to two significant figures and include the appropriate units

.

Part B) The ice cube is replaced by a 65 g plastic cube whose coefficient of kinetic friction is 0.20. How far will the plastic cube travel up the slope?

Express your answer to two significant figures and include the appropriate units.

Answer 1

Part A)

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

1/2x k x( x²) = m x gx ∆h

0.5 x 22 x (0.1²) = 0.065 x 9.8 x ∆h

∆h = 0.17 m = 17 cm

Therefore the height gained is ∆h = 17 cm

Distance along the slope = ∆h / sin 30 =17/(1/2)=34 cm

part B)

The height energy is mgd sin θ    (where d is the distance the cube moves along the slope.) given θ=30

The Frictional energy is Fxd

F ( the frictional force ) = µ x N

N ( the reaction to the component of the gravity force perpendicular to the surface of the slope ) = m g cos30

Total energy converted

0.5 x k x( x²) = (mxgxdsin30) + (µx m xg xcos30x d )

0.5x22x0.1x0.1=mgd[(√3+μ)/2]

d=1.99x10^-4 m