The spring shown in the figure is compressed 46 cm and used to launch a 100 kg p

Question

The spring shown in the figure is compressed 46 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 .

Part A

What is the student's speed just after losing contact with the spring?

Express your answer to two significant figures and include the appropriate units.

Part B

How far up the incline does the student go?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

A)

gain in kinetic energy = loss in elastic potential energ

(1/2)mv2= (1/2) K(x)2 gives

v = sqrt(K/m) x = sqrt(80000/100) x (0.46) = 13 m/s.

B)

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 + PE= PE+ U
½kx² + mgh= mgh+ 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
F = Fn
F = mgcos

h= dsin

½kx² + mgh= mgdsin + dmgcos
½kx² + mgh= mgd(sin + cos)
d = [½kx² + mgh] / mg(sin + cos)

d = [½80000(0.46)² + 100(9.81)10] / 100(9.81)(sin30 + 0.10cos30)
d = [8464 + 9810] / 575.46

d = 31.76 m

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