Question

A Red Rider bb gun uses the energy in a compressed spring to provide the kinetic energy for propelling a small pellet of mass 0.21 grams. By cocking the lever attached to the stock of the rifle, the spring (k = 2000 N/m) is compressed 9 cm from its equilibrium point.

What is the potential energy energy stored in the compressed spring?

A: 2.5887

B: 3.4429

C: 4.5791

D: 6.0902

E: 8.1000

J

A: 4.9679

B: 5.6137

C: 6.3435

D: 7.1681

E: 8.1000

What is the kinetic energy of the pellet when the spring is released?

J

What is the muzzle velocity of the bb?

A: 132.1027

B: 191.5490

C: 277.7460

D: 402.7317

E: 583.9610

m/s

If the rifle was modified so that the spring could be compressed twice as far, 18 cm, what would be the resultant muzzle velocity of the bb?

A: 264.2055

B: 383.0980

C: 555.4921

D: 805.4635

E: 1167.9221

m/s

Answer 1

a)

spring PE is given as

U = 0.5 k x^2 = 0.5* 2000*0.09^2 = 8.1 J

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b)

kinetic energy = spring potential energy = 8.1 J

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c)

0.5*m v^2 = 8.1

0.5* 0.21*10^-3* v^2 = 8.1

v = 277.746 m/s

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d)

0.5 kx^2 = 0.5 m v^2

v = x sqrt (k/m)

that is velocity is directly proportional to displacement

on increasing the distance to twice

velocity also becomes twice of its initial value

v = 2* 277.7 = 555.49 m/s

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