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 0.29 grams. By cocking the lever attached to the stock of the rifle, the spring (k = 1800 N/m) is compressed 10 cm from its equilibrium point.

IT IS MULTIPLE CHOICE!!!!

1.What is the potential energy energy stored in the compressed spring? A: 9 B: 11.9700 C: 15.9201 D: 21.1737 E: 28.1611 J Submit Answer Tries 0/1

2.What is the kinetic energy of the pellet when the spring is released? A: 5.6193 B: 6.5746 C: 7.6923 D: 9 E: 10.5300 J Submit Answer Tries 0/1

3.What is the muzzle velocity of the bb? A: 195.1104 B: 220.4747 C: 249.1364 D: 281.5242 E: 318.1223 m/s Submit Answer Tries 0/1

4.If the rifle was modified so that the spring could be compressed twice as far, 20 cm, what would be the resultant muzzle velocity of the bb? A: 398.6183 B: 498.2729 C: 622.8411 D: 778.5514 E: 973.1892

Answer 1

Mass of the pellet = m = 0.29 g = 0.29 x 10^-3 kg

Spring constant = k = 1800 N/m

Compression of the spring = X₁ = 10 cm = 0.1 m

Potential energy of the spring = P

P = kX₁²/2

P = (1800)(0.1)²/2

P = 9 N

Muzzle velocity of the bb = V₁

Kinetic energy of the pellet when the spring is released = K

The potential energy of the spring is converted into kinetic energy of the pellet when the spring is released.

K = P

K = 9 N

K = mV₁²/2

9 = (0.29x10^-3)V₁²/2

V₁ = 249.1364 m/s

If the spring was compressed twice as far that is to 20 cm.

New compression of the spring = X₂ = 20 cm = 0.2 m

New muzzle velocity of the bb = V₂

kX₂²/2 = mV₂²/2

(1800)(0.2)²/2 = (0.29x10^-3)V₂²/2

V₂ = 498.2729 m/s

1) Potential energy of the compressed spring = 9 N (Option A)

2) Kinetic energy of the pellet when the spring is released = 9 N (Option D)

3) Muzzle velocity of the bb = 249.1364 m/s (Option C)

4) Muzzle velocity of the bb is the spring was compressed 20 cm = 498.2729 m/s (Option B)