As shown in the figure below, a box of mass m = 18.8 kg is released from rest (a

Question

As shown in the figure below, a box of mass

m = 18.8 kg

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

d = 3.60 m

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

xC = 0.290 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 =  
How does the total energy of the box at point A compare to the total energy of the box at point B and then at point C? What position did you choose for zero elastic potential energy of the spring? Can you write an expression for the gravitational potential energy of the box at any position on the incline and the spring potential energy for any compression of the spring? N/m

Explanation / Answer

a)
Height difference between A and B , h1= d*sin 30 = 3.6 * sin 30 = 1.8 m

This cause decrease in potential energy and it will increase the kinetic energy by same amount
so,
m*g*h1 = 0.5*m*v^2
g*h1 = 0.5*v^2
9.8*1.8 = 0.5*v^2
v= 5.94 m/s
Answer:5.94 m/s

b)
When the spring is at C, distance moved along the incline,d2 = 3.6 + 0.29 = 3.89 m
Height difference between A and C , h2= d2*sin 30 = 3.89 * sin 30 = 1.945 m

This cause decrease in gravitational potential energy and it will increase the potential energy of spring by same amount
so,
m*g*h2 = 0.5*k*x^2
18.8*9.8*1.945 = 0.5*k*(0.29)^2
k=8522 N/m

Total energy is always conserved. It is same at A,B and C

Zero elstic potential energy is when compression is 0

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