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h=h2-h,- M M h2 Before After GL Figure 9.1 Ballistic pendulum parameters. See Experimental Planning text for description. A. The Ballistic Pendulum The ballistic pendulum allows the experimental determination of the velocity of a projectile that is launched horizontally. This is done using two conservation principles and a few simple measurements. The parameters of a ballistic pendulum system are shown in GL Fig. 9.1. A projectile of mass m is fired with velocity v, into a stationary pendulum bob of mass M and becomes embedded. The (horizontal) momentum of the system can be expressed in terms of the variables given in GL Fig. 9.1. What is the momentum of the system immediately after the projectile is fired (that is, just before it hits the pendulum bob)? 1. In terms of the variables given in GL Fig. 9.1, what is the momentum of the system immediately after the mass m becomes embedded in the pendulum bob?

h=h2-h,- M M h2 Before After GL Figure 9.1 Ballistic pendulum parameters. See Experimental Planning text for description. A. The Ballistic Pendulum The ballistic pendulum allows the experimental determination of the velocity of a projectile that is launched horizontally. This is done using two conservation principles and a few simple measurements. The parameters of a ballistic pendulum system are shown in GL Fig. 9.1. A projectile of mass m is fired with velocity v, into a stationary pendulum bob of mass M and becomes embedded. The (horizontal) momentum of the system can be expressed in terms of the variables given in GL Fig. 9.1. What is the momentum of the system immediately after the projectile is fired (that is, just before it hits the pendulum bob)? 1. In terms of the variables given in GL Fig. 9.1, what is the momentum of the system immediately after the mass m becomes embedded in the pendulum bob?

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# Projectile Motion: The Ballistic Pendulum ## Experimental Planning ### GL Figure 9.1 Ballistic Pendulum Parameters The diagram illustrates a ballistic pendulum system. It consists of two stages: - **Before Collision**: A projectile of mass \( m \) is fired with velocity \( v_{\circ} \) towards a stationary pendulum bob of mass \( M \). - **After Collision**: The projectile becomes embedded in the bob, and they move together with velocity \( V \). The combined system then reaches a height \( h_1 \), with the difference in height from the original position to \( h_2 \) being \( h = h_2 - h_1 \). ### A. The Ballistic Pendulum The ballistic pendulum is an experimental device used to measure the velocity of a projectile that is launched horizontally. This measurement relies on two principles of conservation: momentum and energy, alongside basic measurements. The parameters for this experiment as shown in GL Fig. 9.1 include: - A projectile of mass \( m \) impacting and embedding into a pendulum bob of mass \( M \). - The horizontal momentum of the system post-collision is expressed in terms of the parameters in GL Fig. 9.1. To analyze this, consider: 1. **Momentum Calculation**: - Determine the system's momentum immediately after the projectile is embedded in the pendulum bob using the variables from GL Fig. 9.1. 2. **Conservation of Horizontal Momentum**: - If horizontal momentum is conserved, assess the relationship between initial and final momentum based on your earlier calculations. 3. **Conservation of Momentum Equation**: - Derive an equation representing momentum conservation for this collision and designate it as Equation 1. These steps help in determining the initial velocity of the projectile based on the pendulum's subsequent motion.
Transcribed Image Text:# Projectile Motion: The Ballistic Pendulum ## Experimental Planning ### GL Figure 9.1 Ballistic Pendulum Parameters The diagram illustrates a ballistic pendulum system. It consists of two stages: - **Before Collision**: A projectile of mass \( m \) is fired with velocity \( v_{\circ} \) towards a stationary pendulum bob of mass \( M \). - **After Collision**: The projectile becomes embedded in the bob, and they move together with velocity \( V \). The combined system then reaches a height \( h_1 \), with the difference in height from the original position to \( h_2 \) being \( h = h_2 - h_1 \). ### A. The Ballistic Pendulum The ballistic pendulum is an experimental device used to measure the velocity of a projectile that is launched horizontally. This measurement relies on two principles of conservation: momentum and energy, alongside basic measurements. The parameters for this experiment as shown in GL Fig. 9.1 include: - A projectile of mass \( m \) impacting and embedding into a pendulum bob of mass \( M \). - The horizontal momentum of the system post-collision is expressed in terms of the parameters in GL Fig. 9.1. To analyze this, consider: 1. **Momentum Calculation**: - Determine the system's momentum immediately after the projectile is embedded in the pendulum bob using the variables from GL Fig. 9.1. 2. **Conservation of Horizontal Momentum**: - If horizontal momentum is conserved, assess the relationship between initial and final momentum based on your earlier calculations. 3. **Conservation of Momentum Equation**: - Derive an equation representing momentum conservation for this collision and designate it as Equation 1. These steps help in determining the initial velocity of the projectile based on the pendulum's subsequent motion.
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