A mass of 3.8 is placed on a stiff vertical spring, which has a spring constant

Question

A mass of 3.8 is placed on a stiff vertical spring, which has a spring constant of 950n/m The object is then pressed against the spring until it has been compressed a distance of 88.7cm. The mass is then released and is allowed to be thrown up into the air.

a What will be the elastic potential energy stored on the spring just before the mass is released?

b What will be the gravitational potential energy be of this mass when it reaches its highest point?

c how high will this mass be thrown?

d what will be the velocity of the mass just as it leaves the spring?

Explanation / Answer

Here ,

mass , m = 3.8 Kg

spring constant , k = 950 N/m

compression , x = 88.7 cm = 0.887 m

a)

initial potential energy stored in spring = 0.5 * k * x^2

initial potential energy stored in spring = 0.5 * 950 * 0.887^2

initial potential energy stored in spring = 373.71 J

the initial potential energy stored in spring is 373.71 J

b)

at the highest point

gravitational potential energy = m * g * h

gravitational potential energy = 3.8 * 9.8 * 0.887

gravitational potential energy = 33.03 J

c)
let the height is h

m * g * h = initial potential energy of spring

3.8 * 9.8 * h = 373.71

h = 10.04 m

the mass will be throwm 10.04 m higher

d)

let the velocity of mass is v

0.5 * 3.8 * v^2 = 373.71 - 33.03

v = 13.4 m/s

the velocity of mass is 13.4 m/s

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