Question

A 193 g block is pressed against a spring of force constant 1.12 kN/m until the block compresses the spring 14.8 cm. The spring rests at the bottom of a ramp inclined at 64.3o to the horizontal.

A) Determine how far up the incline the block moves before it stops if there is no friction between the block and the ramp.

B) How far up the incline does the block move before it stops if the coefficient of kinetic friction is 0.405.

Answer 1

spring const. k = 1.12 kN/m

spring compression x = 14.8 cm

PE of spring   = 0.5kx² = 12.27 J

This energy is trnafered to the mass when the spring is released and it is pushed up the incline.

PE of the mass   = mgh = 12.27 J

h = 12.27/(9.8*0.193) = 6.487 m

The length along the incline = h/sin(64.3) = 7.2 m

b) when the incline has friction part of the energy is used to do work against the frictional force.

Normal force of the mass on the incline = mgCos(p) = 0.193*9.8*Cos(64.3) =0.82 N

frictional force f = 0.82*0.405 = 0.332 N

let x be the length it moved along the incline

work against friction = 0.332x

height raised = xSin(64.3) = 0.9x

0.332x + 0.193*9.8*0.9x = 12.27 J

x = 6.03 m