Procedure / Set Up:
A small metal ball will be initially at rest in spring loaded gun. Once fired, it will collide with a pendulum/casing that is initially at rest and then swing through some angle ø. The angle will be recorded with a thin metal rod that swings up immediately after the ball collides with the pendulum.
Once the ball was fired, the values needed to determine the initial velocity of the ball were
Mass of ball (m): 0.00763 kg dm = +/- 0.0001kg
Mass of pendulum (M): 0.0809 kg dM = +/- 0.00001 kg
Length of string (L): 0.197 m dL = +/- .001 m
Angle (ø): 17.0º dθ = +/- 0.00873 rad
By first using conservation of momentum, we derived an equation for the initial velocity of the ball. We next used conservation of energy to derive an equation for the final velocity of the ball. Next we substituted the final velocity from our conservation of energy equation into the final velocity of our conservation of momentum equation to find a final equation that would allow us to determine the initial velocity of the metal ball.
We can now plug in our measured values into the derived equation and solve for v0, which equaled 4.765 m/s.
Because there is always some error when making measurements, our initial velocity was not 100% accurate. We therefore needed to calculate the uncertainty in V0.
Below is our derived uncertainty calculation for dv.
dv = 0.02089 m/s
The initial velocity at which the metal ball exited the spring gun was 4.765 +/- 0.2089 m/s
Conclusion:
We were able to calculate the initial velocity of a metal ball fired from a spring loaded gun using conservation of momentum and conservation of energy. Even though we calculated the error in our measurements, there is still other errors to factor in such as the friction from the ball on the spring gun. In general, we derived an equation to find a reasonable speed and reasonable uncertainty for the initial velocity of the metal ball.
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