A 5.60 kg of mass is pressed against a spring with a spring constant of 12500 N/

Question

A 5.60 kg of mass is pressed against a spring with a spring constant of 12500 N/m. The spring is compressed 0.250 m, and then the block is released. The block moves on a frictionless surface.

a) what potential energy is stored in the spring before the mass if released?

b) what is the speed of the mass as it leaves the spring?

c) the mass travels up a very long ramp. At a distance 4.40 m above the ground, how fast would the mass be going?

d) how high above the ground does it go before coming to a stop?

Explanation / Answer

the mass is m = 5.60 kg

the spring constant is k = 12500 N/m

the spring is compressed a distance

d = 0.250 m

a)the potential energy stored in the spring is

U = (1/2)k x d^2

b)let v be the speed of the mass

we know that

(1/2)m x v^2 = (1/2)k x d^2

or v^2 = (k/m) x d^2

or v = (k/m)^1/2 x d

c)let v1 be the speed when the mass is at S = 4.40 m

we know that

v^2 - v1^2 = 2gS

or v1^2 = v^2 - 2gS

or v1 = (v^2 - 2gS)^1/2

where g = 9.8 m/s^2

d)let S1 be the distance at which the mass comes to a stop

when the mass stops its final velocity v2 = 0 therefore

v2^2 - v1^2 = 2gS1

or S1 = (v2^2 - v1^2/2g)

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