As shown in the figure below, a box of mass m = 19.3 kg is released from rest (a

Question

As shown in the figure below, a box of mass

m = 19.3 kg

is released from rest (at position A) at the top of a 30.0° frictionless incline. The box slides a distance

d = 5.00 m

down the incline before it encounters (at position B) a spring and compresses it an amount

xC = 0.240 m

(to point C) before coming momentarily to rest. Using energy content, determine the following.

(a) speed of the box at position B

vB =  m/s

(b) spring constant

k =  N/m

(c) the physical quantity that is constant throughout the process

a)kinetic energy

b)elastic potential energy     

c) gravitational potential energy

d)total energy

Explanation / Answer

A) use v^2 - u^2 = 2*a*s

=> speed at B = sqrt(2*9.8*sin(30)*5) = 7 m/s

B) Apply energy conservation

=> between B and C

=> 0.5*19.3*7*7 + 19.3*9.8*0.24*sin(30) = 0.5*k*0.24*0.24

=> k = 17206 N/m

c) Total energy

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