This document discusses the spring mechanism of a tranquilizer gun. It provides the force constant and distance compressed of the gun's spring. It then shows calculations to determine: 1) The amount of potential energy stored in the spring, which is 0.225 Joules. 2) The velocity at which a 1.50g projectile would be ejected from the gun, which is 17.3 meters/second. The calculations neglect friction and the mass of the spring, and equate the initial potential energy to the final kinetic energy of the projectile.

1. L U C Y ( X I A O B I N ) S H E N G
S T U D E N T N U M B E R : 1 2 3 5 1 1 4 5
ENERGY IN SIMPLE
HARMONIC MOTION

2. QUESTION
Jimmy has been much too lively at night, to help him
ease his tantrums his parents bought Tranqoo (a
tranquilizer gun). They wonder how the spring
mechanism works to emit the dart:
1. How much energy is stored in the spring of a
tranquilizer gun that has a force constant of
45.0 N/m and is compressed 0.100 m?
2. (b) Neglecting friction and the mass of the spring,
at what speed will a 1.50 g projectile be ejected
from the gun?

3. OBSERVATIONS

4. OBSERVATIONS
a) When the spring of the gun is not compressed,
there is no work done on the spring so there is no
elastic energy involved with the system.
b) The spring is compressed to distance “x”. Work
must be done by compressing the spring of the gun
to insure that the potential energy stored in the
spring can push the projectile out.
c) The trigger is pulled and the projectile flies out with
velocity “v” as the stored energy in the spring is
converted to kinetic energy.

5. QUESTION 1
Force constant (k): 45.0 N/m
Distance compressed (x): 0.100 m
Amount of energy store when the spring is
compressed is completely composed of potential
energy.
PEel = 1/2kx^2
Plugging in given values:
PEel = 1/2(45.0N/m)(0.100m)^2
=0.225 J

6. QUESTION 2
PEel: 0.225 J
Mass of dart: 1.50g = 0.0015kg
Since friction and mass of the spring is ignored, as
soon as the trigger of the gun is pulled, PE is
completely converted into KE.
KE = PE
KE = 1/2mv^2
0.225J = ½(0.0015g)(v^2)
v = 17.3 m/s

7. Tranq you very much!