Challenge: To design a quantitative system that will use the gravitational potential energy of a raised mass to impart a measurable impulse to a target ball, launching it horizontally off the table.
Parameters: You must design a system that will allow you to obliquely strike a target ball with a steel pendulum bob so that the target ball flies horizontally off the table at least 20° away from a line perpendicular to the bob’s striking velocity. You can measure, in any way you like, any parameter of your system, and the motion of the objects before and after the collision EXCEPT the mass of the target ball.
Scoring: You will be scored on the accuracy of your estimate for the mass of the target ball.
Score = % difference in mass
Lowest score will receive highest rank.
Physics: The raised mass provides the energy for your system. (∆Ep = mg∆h) The striker will gain kinetic energy as it falls. You want it to strike the target ball slightly off centre so that the collision is ≥ 20° oblique, but perfectly in the plane of the target’s centre of mass so that it flies off with no initial vertical component to its velocity. The kinetic energy of the system will be entirely the striker before, and the sum of both objects kinetic energy after. (Ek = 0.5mv2) The elasticity of the collision is the ratio of these. During the collision, the law of conservation of momentum can be used to describe the changes that occur for each object. (∆psys = 0) The velocity of the target ball can be estimated from its projectile motion after the collision, but the final velocity of the striker must be found from video analysis.
Extensions: Any friction will produce waste energy as heating of surfaces in contact. The conservation laws apply to rotation as well as linear motion. Energy is not a vector quantity. Any motion of the striker after contact with the target may not be linear if it is suspended by a string, for example.
Help/Hints: It would be helpful to design your system to be easy to adjust and measure. For example, ∆h is critical to measure. A slow motion video from directly above the contact point is necessary. Likewise, a grid or something for easy position measurements. Think about the motion of the target afterwards. How are you going to ensure it has no vertical component to its velocity? How are you going to measure dx and dy and the obliqueness of the collision?
Quiz Topics: Energy and Momentum
Online Text: 7.1 - 7.7, 8.1 - 8.6