As shown in the figure below, a box of mass m = 17.0 kg is released from rest (a

Question

As shown in the figure below, a box of mass m = 17.0 kg is released from rest (at position A) at the top of a 30.0° frictionless incline. The box slides a distance d = 4.50 m down the incline before it encounters (at position B) a spring and compresses it an amount xC = 0.300 m (to point C) before coming momentarily to rest. Using energy content, determine the following.

(a) speed of the box at position B

(b) spring constant

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

1) kinetic energy 2)elastic potential energy 3) gravitational potential energy 4)total energy

Explanation / Answer

Here ,

a) speed of the box at position at B

using conservation of energy

0.5 * m * v^2 = m * g * d * sin(theta)

0.5 * v^2 = 9.8 * 4.5 * sin(30)

v = 6.64 m/s

the speed of block at B is 6.64 m/s

b)

let the spring constant is k

0.5 * k * 0.3^2 = 17 * 9.8 * (4.5 + 0.3) * sin(30)

solving for k

k = 8885.3 N/m

the spring constant is 8885.3 N/m

c)

the 4)total energy is conserved

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