As shown in the figure below, a box of mass m = 15.5 kg is released from rest (a

Question

As shown in the figure below, a box of mass m = 15.5 kg is released from rest (at position A) at the top of a 30.0 frictionless incline. The box slides a distance d = 4.20 m down the incline before it encounters (at position B) a spring and compresses it an amount xC = 0.250 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

kinetic energy

elastic potential energy   

gravitational potential energy

total energy

As shown in the figure below, a box of mass m = 15.5 kg is released from rest (at position A) at the top of a 30.0½ frictionless incline. The box slides a distance d = 4.20 m down the incline before it encounters (at position B) a spring and compresses it an amount xC = 0.250 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 kinetic energy elastic potential energy gravitational potential energy total energy

Explanation / Answer

a)
conservation of energy

Ei = Ef

m g h = 1/2 mv^2

9.81*4.2*sin(30 degrees) = 0.5*v^2

v=6.42 m/s

b)

Ei = Ef

m g h = 1/2 kx^2

15.5*9.81*(4.2+0.25)*sin(30 degrees) = 0.5*k*0.25^2
k = 10826 N/m

c) total energy

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