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Projectile Range Calculation with Ballistic Pendulum and Energy/Momentum Conservation, Schemes and Mind Maps of Physics

Sheffield Hallam University (SHU)Physics

The procedure to calculate the horizontal range of a horizontally fired projectile using a ballistic pendulum and the principles of conservation of energy and momentum. The theory behind the ballistic pendulum, the equations to calculate the velocity and range of the projectile, and the procedure to carry out the experiment. Suitable for students of physics or engineering, and can be used as study notes, lecture notes, summaries, or schemes and mind maps for exam preparation.

Typology: Schemes and Mind Maps

2021/2022

Uploaded on 09/12/2022

rossi46
rossi46 🇬🇧

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OBJECTIVE
To calculate the range of a projectile that is launched horizontally by a ballistic pendulum
by applying Conservation of Energy and Conservation of Momentum.
EQUIPMENT
1. ballistic pendulum
2. carbon paper
3. tape
4. meter stick
5. pan balance
THEORY
Figure 1
The apparatus shown in Figure 1 is called the ballistic pendulum. This device is used to
determine the speed of fast moving projectiles. The projectile is launched horizontally
into a pendulum and then swing together until they reach a maximum vertical height ‘h’.
Conservation of momentum and energy can then be applied to measure the initial speed
of the projectile.
1. You will apply conservation of momentum to the ball + pendulum system
immediately after the ball is fired and immediately after the pendulum catches the
ball. By equating the initial momentum to the final momentum for this complete
inelastic collision you will have an expression for the velocity of the ball
immediately before the collision. The velocity of the ball Vb immediately before
the collision will be in terms of the velocity V of the ball + pendulum system
The Ballistic Pendulum
pf3

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OBJECTIVE

To calculate the range of a projectile that is launched horizontally by a ballistic pendulum by applying Conservation of Energy and Conservation of Momentum.

EQUIPMENT

  1. ballistic pendulum
  2. carbon paper
  3. tape
  4. meter stick
  5. pan balance

THEORY

Figure 1 The apparatus shown in Figure 1 is called the ballistic pendulum. This device is used to determine the speed of fast moving projectiles. The projectile is launched horizontally into a pendulum and then swing together until they reach a maximum vertical height ‘h’. Conservation of momentum and energy can then be applied to measure the initial speed of the projectile.

  1. You will apply conservation of momentum to the ball + pendulum system immediately after the ball is fired and immediately after the pendulum catches the ball. By equating the initial momentum to the final momentum for this complete inelastic collision you will have an expression for the velocity of the ball immediately before the collision. The velocity of the ball Vb immediately before the collision will be in terms of the velocity V of the ball + pendulum system

The Ballistic Pendulum

immediately after the collision, the mass mb of the ball, and the mass mp of the pendulum. That is Vb =Vb (mb ,mp ,V).

  1. The masses mb and mp will be measure directly. We will now apply conservation of energy immediately after the collision and at the point when the ball + pendulum reach the maximum height ‘ h ’. This will allows to find an expression for V in terms of g and h. That is V=V(g,h).
  2. Your expression for Vb can now be expressed in terms of mb , mp, g, and h. That is Vb =Vb (mb ,mp ,g,h).

Figure 2

Knowing the speed of the ball Vb , we can now derive and expression for the horizontal range R of the ball if it was fired horizontally (with the pendulum swung out of the way). See Figure 2 above.

  1. Apply the kinematic equations of motion at the point of launch to obtain an expression for the range R in terms of the velocity of the ball Vb , the height of launch d measured from the floor, and the acceleration of gravity g. That is R=R(Vb , d, g). Substituting the expression for Vb in terms of Vb =Vb (mb ,mp ,g,h) will give our final equation for the range R in terms of R=R(mb ,mp ,d,h).
  2. We will measure mb , mp , d, and h directly and calculate the range R of the ball using our final expression R=R(mb ,mp ,d,h). You will compare this expected value of R to the experimental measured value of R when shooting the ball horizontally.