1-The spring shown in the figure is compressed 54 cm and used to launch a 100 kg

Question

1-The spring shown in the figure is compressed 54 cm and used to launch a 100 kg physics student. The track is frictionless until it starts up the incline. The student's coefficient of kinetic friction on the 30 incline is 0.10 . v=15    How far up the incline does the student go?

2- A 25 kg box slides 4.0 m down the frictionless ramp shown in the figure(Figure 1) , then collides with a spring whose spring constant is 140 N/m. maximum compression =3.7 m

At what compression of the spring does the box have its maximum speed?

Explanation / Answer

1]  The total energy of the body is at a maximum at the bottom of the slope. It will be equal to the spring potential energy and the potential energy of the drop.

That total energy will be exchanged for an increase in potential energy and friction energy.

PS + PE1 = PE2 + U

0.5kx^2 + mgh1= mgh2+ Fd

F is the friction force and is equal to the Normal force Fn of the ramp on the body times the coefficient of friction

Fn = mgcos theta

F = uFn

F = umgcos theta

h2 = dsin theta

0.5kx^2 + mgh1 = mgdsin theta + dumgcos theta

0.5kx^2 + mgh1 = mgd(sin theta + ucos theta)

d = [0.5kx^2 + mgh1] / mg(sin theta + ucos theta)

d = [0.5*80000*(0.54)^2 + 100*(9.81)*10] / {100*(9.81)*(sin30 degree + 0.1*cos30 degree)}

d = 37.32

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