A 25.0 kg block is resting on the edge of 0.800 m tall table. The potential ener

Question

A 25.0 kg block is resting on the edge of 0.800 m tall table.
The potential energy stored in the block is?

and

A spring is compressed 0.20 m. The spring constant is 950 N/m. What is the potential energy stored in the compressed

spring?

If you could explain the procedure to find potential stored energy, I would much appreciate it! :)

Then I was having trouble with:   

A cart at the top of a 32 m high rollercoaster track has an initial velocity of 0 m/s. The cart has a mass of 5.0 x 102

kg. The cart then proceeds down to the bottom of the track. The height of the track is 0.0 m at the bottom.
(Negelect friction)
What was the kinetic energy of the cart at the top of the track?

Even if you don't answer all the questions, only the procedures would be appreciated :)

Explanation / Answer

Gravitational potential energy of a mass m at a height h = mgh (with ground level as reference)

mass m = 25.0 kg

h = 0.800 m

g = 9.80 m/s2

so , Gravitational potential energy U = mgh = 196 J

spring constant k = 950 N/m

compression of spring x = 0.20 m

potential energy stored in the spring U = (1/2) kx2

U = 19 J

in the third part we have to conserve total energy = kinetic energy + potential energy

at the top :

potential energy U = mgh = 5.0 x 102 x 9.8 x 32 = 156800 J

kinetic energy K = (1/2) mv2 = 0 (since the initial velocity is zero)

at the bottom :

potential energy U = mgh = 5.0 x 102 x 9.8 x 0 = 0 J

kinetic energy K = (1/2) mv2

conserving energy :

156800 + 0 = 0 + (1/2) mv2

speed at the bottom v = 25.04 m/s

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