Questions: Ballistic Pendulum: Conservation of Linear Momentum Conservation of Mechanical Energy Laboratory Report A. The Ballistic Pendulum. Purpose: To determine the muzzle velocity (vo) of projectile from toy gun. Mass of projectile, (m) kg Mass of pendulum, M .2454 kg Length of pendulum, L .3 m Calculate height, h(Eq. 9) 02223 .78 Calculate (vo) (Eq. 8) (m / s) B. The Ballistic Pendulum vs. Projectile Motion. Purpose: Compare the muzzle velocity (v0) of projectile from toy gun using both methods. % difference 59.35

Solution Steps

The problem involves determining the muzzle velocity \( v_0 \) of a projectile using a ballistic pendulum setup. The data provided includes deflection angles from multiple trials, the mass of the pendulum, and the length of the pendulum. We need to calculate the height \( h \) and the initial velocity \( v_0 \) using the given equations.

The deflection angles from the trials are given as 21, 23, 21, 22, and 24 degrees. The average deflection angle is already calculated as 22 degrees.

The height \( h \) can be calculated using the deflection angle and the length of the pendulum. The formula for height in terms of the deflection angle \(\theta\) and pendulum length \( L \) is: \[ h = L(1 - \cos(\theta)) \] Given \( L = 0.3 \, \text{m} \) and \(\theta = 22^\circ\), we convert the angle to radians: \[ \theta = 22^\circ \times \frac{\pi}{180} = 0.383972 \, \text{radians} \] Now, calculate \( h \): \[ h = 0.3 \times (1 - \cos(0.383972)) = 0.3 \times (1 - 0.9272) = 0.3 \times 0.0728 = 0.0218 \, \text{m} \]

Using the conservation of momentum and energy, the initial velocity \( v_0 \) can be calculated. The formula is: \[ v_0 = \frac{(M + m)}{m} \sqrt{2gh} \] Assuming the mass of the projectile \( m \) is not provided, we cannot calculate \( v_0 \) without it. However, if \( m \) were given, you would substitute the values into the equation to find \( v_0 \).

Final Answer