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

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Answer 1 · 2018-03-29T09:22:37

See below.

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))#