mass i3 Ci 3 SSM A 5.0 g marble is fired vertically upward using a spring 1 gun.

Question

mass i3 Ci 3 SSM A 5.0 g marble is fired vertically upward using a spring 1 gun. The spring must be compressed 8.0 cm if the marble is to just reach a target 20 m above the marble's position on the compressed spring. (a) What is the change Ug in the gravitational potential en- ergy of the marble-Earth system during the 20 m ascent? (b) What is the change Us in the elastic potential energy of the spring during its launch of the marble? (c) What is the spring con- stant of the spring? ·.ritial l cneed must he given the ball so

Explanation / Answer

a) 0.98 J

b) -0.98 J

c) 306.25 N/m

m = 0.005 kg

x = 8.0 cm

= 0.08 m

g = 9.8 m / s2

h = 20 m

(a)

the change in gravitational potential energy willbe

Ug = m g h

= (0.005kg)(9.8 m / s2)(20)

= 0.98 J

(b)

let Ue be the elastic energy ofthe spring, according to the law of conservation ofmechanical

energy we can write

Ug + Ue =0

Ue =- Ug

= -0.98 J

(c)

Spring energy = (1/2)kx^2

0.98 = (1/2)(k)(8/100)^2

Solving for "k"

k = 306.25 N/m

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