a mass of 10 kg is pushed off a cliff which is 1000.5 m high above a slid incomp

Question

a mass of 10 kg is pushed off a cliff which is 1000.5 m high above a slid incompressible ground A. calculate the velocity during travel downward at 100.4m height above ground level.

A. Calculate the velocity during travel downward at 100.4 m height above ground level.

B. what is the velocity right before it hits the ground

C. if instead of a solid incompressible wall, the mass hits a spring with spring constant k =15 N/m, what is the max height above ground the mass rises after hitting the spring?

Explanation / Answer

take P.E. = 0 at ground level

(A)
energy conservation

MgH = Mgh + 1/2 Mv^2

10 x 9.8 x 1000.5 = (10 x 9.8 x 100.4) + 1/2 x 10 x v^2

98049 = 9839.2 + 5 x v^2

88209 = 5 x v^2

v = 132.8 m/s

(B)
energy conservation

MgH = 1/2 MV^2

10 x 9.8 x 1000.5 = 1/2 x 10 x V^2

V = 140 m/s

(C)
whole K.E. stored in spring by compression
energy in spring (U) = 1/2 MV^2

U = 1/2 x 10 x (140)^2

U = 98000 J

now

again energy conservation

U = MgH'

H' = 98000 / (10 x 9.8)

H' = 1000 m

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