What length would the object have to slide along the ramp? (question 2)

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1 Answer
Mar 29, 2018

See below.

Explanation:

Item 1B)

Object potential energy

E_p = m g h_0

Slide along the ramp

d_0 such that h_0/d_0 = sin theta

Friction force

f =mu m g cos theta

Friction work

E_f = f xx d_0 = mu m g cos theta d_0

Spring accumulated potential energy

E_s = 1/2 K x_0^2

so we have

E_p = E_f + E_s or

m g h_0 = mu m g d_0 cos theta + 1/2 K x_0^2 or

m g d_0 sin theta = mu m g d_0 cos theta + 1/2 K x_0^2

and finally

d_0 = (1/2 K x_0^2)//(m g (sin theta-mu cos theta))