Just as a car tops a 36 meter high hill with a speed of 42 km/h it runs our of g

Question

Just as a car tops a 36 meter high hill with a speed of 42 km/h it runs our of gar and coasts from there, without friction or drag. How high to the nearest meter, will the car coast up the next hill? A 2 kg metal plate slides down a 16-meter high slope. At the bottom its speed is 4.3 m/s. To the nearest Joule, what was the magnitude of the work done by friction? A mass of 3.3 kg is dropped from a height of 3.86 meters above a vertical spring anchored at it lower end to the floor. If the spring constant is 34 N/cm, how far, to the nearest tenth of a cm. is the spring compressed? If the top of the spring in the preceding problem is1. 83 meters above the ground when the mass is released. What is the ball's kinetic energy, to the nearest Joule, just before the mass strikes the spring?

Explanation / Answer

1) On the next high all the energy will be potential (m*g*h)
So m*g*h2 = m*g*h1 + 1/2*m*v^2 ..........(U + K) potential + kinetic
So mass drops out leaving
h2 = h1 + v^2/2g = 36m + (42km/hr*(1000m/km)*(1hr/3600s))^2/(2*9.8) = 42.94 m

2)  Initially, the metal plate was at rest with a gravitational potential energy relative to the ground of...
GPE = mgh
GPE = (2 kg)(9.81 m/s²)(16 m)
GPE = 313.92 J
Then it slides down the slope while losing energy to friction, ending with a kinetic energy of...
KE = ½mv²
KE = ½(2 kg)(4.3 m/s)²
KE = 18.49 J
Without friction, the GPE and KE would be the same. The energy lost from GPE to KE conversion was the work done by friction.
Work = Energy final - Energy initial
W = 18.49 J - 313.92 J
W = -295.43 J
The negative sign just indicates that friction took energy out of the system and dissipated it as heat.

3) The height energy lost goes into spring compression energy
Height energy lost = 3.3*9.8*(3.86 + x)
Spring compression energy = 0.5*3400*x^2
1700*x^2 = 32.34 x + 124.83

x = 0.28065 m = 28.065 cm

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