Question

A 195-g block is pressed against a spring of force constant 1.30 kN/m until the block compresses the spring 10.0 cm. The spring rests at the bottom of a ramp inclined at 60.0° to the horizontal. Using energy considerations, determine how far up the incline the block moves from its initial position before it stops under the following conditions.

(a) if the ramp exerts no friction force on the block
m

(b) if the coefficient of kinetic friction is 0.366
m

Answer 1

Given data

m = 0.195 kg

k = 1300 N/m

x = 10cm = 0.10 m

= 0.366

initial potential energy of spring = final gravitational potential energy of block

½*k*x² = m*g*h

here

h = d*sin60

½*k*x² = m*g*d*sin60

d = (k*x²) / (2*m*g*sin60)

d = (1300*0.10²) / (2*0.195*9.8*sin60)

d = 3.92 m

b)

initial potential energy of spring = (work done by friction) + (final gravitational potential energy of block)

½*k*x² = mg(d'sin60) + (mgcos60*d')

½*k*x² = m*g*d'(sin60 + cos60)

d' = k*x²/[2*m*g(sin60 + cos60)]

d' = (1300*0.10²)/ [2*0.195*9.8*(0.8666 + 0.183)

d' = 4.97 m