A mass is connected to a spring resting on an inclined surface. Thespring is str

Question

A mass is connected to a spring resting on an inclined surface. Thespring is stretched by pulling the mass downward a distance x alongthe incline and released from rest. The spring constant is k=861n/m, the mass is 134 kg, the incline makes an angle theta = 18degrees with the horizontal, and the stretch distance x is 84m. (a) using he lowest location of the mass on the incline as thezero of gravitational potential energy, write the initial potentialenergy of the system in symbolic form here. (b) Write the final potential energy of the system in symbolicform using d as the distance the blocks travel from the lowestlocation to the highest point where it stops. (c) how far back up the incline does the mass travel before itstops. (a) using he lowest location of the mass on the incline as thezero of gravitational potential energy, write the initial potentialenergy of the system in symbolic form here. (b) Write the final potential energy of the system in symbolicform using d as the distance the blocks travel from the lowestlocation to the highest point where it stops. (c) how far back up the incline does the mass travel before itstops.

Explanation / Answer

if the mass reach resting postion where the potentialenergy = 0 , then the intial potential energy U = kx^2 / 2 =mgh           h =verticle height of the mass from the reference point of zeropotential energy   k = spring constant x = expanded length the block will stop at a distance at which the change inthe gravitational potential energy is equal to the springpotntential energy after sliding a distance d on the incline plane the dropin the gravitational potential enrgy of the mass              U =  mg(d tan) and change in potential eneregy of the spring               U = kd^2 /2 = mg(d tan). if the block travell back a distance dbefore it come to rest                   kd^2 /2 = mgdtan   

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