Challenge: To design a system that will use the gravitational potential energy of a raised mass to impart an impulse to a cart. The cart AND impacting mass will then roll across the floor.
Parameters: The system must consist of a raised mass of between 200 grams and 1000 grams, raised exactly 50.0 cm above the “impact point”. This measurement will be taken from the centre of mass point. It must be released from rest and must strike your stationary cart at its rest position. At this point it must be released so that the mass and cart can continue as one object. The cart/mass object must roll freely along the floor and come to a rest without any interference or outside energy source. The distance rolled will be measured.
Scoring: Your system will be scored based on the initial velocity of the mass/cart system after impact (in m/s), plus the distance travelled (in m). (ie. want light, smooth rolling cart)
Score = v0 + d
Highest score will receive highest rank.
Physics: The raised mass provides the energy for your system. (∆Ep = mg∆h) The mass will convert the potential energy into kinetic energy. (We will assume 100% here). (Ek = 0.5mv2) The cart will get an impulse from the mass as it collides with the cart. During the collision, the law of conservation of momentum can be used to describe the changes that occur. (∆psys = 0) The combined cart and mass will have an initial velocity that will decline as the system rolls along the floor. Total kinetic energy is not conserved during the collision because the collision is not elastic. (in fact it is called perfectly inelastic.) Friction will cause your cart/mass system to decelerate to a stop at some distance away. We can use the constant acceleration formulae and Newton’s laws to calculate the coefficient of kinetic friction (µ) acting on your cart.
Extensions: Elasticity of collisions can be expressed mathematically.
Help/Hints: The impacting mass is best designed as a perfect pendulum which should release into your cart without much effort as close to the floor as possible. The cart should be designed to be as low as possible and must “catch” the impacting mass without any rebound. Wheels must spin freely to reduce friction.
Quiz Topics: Energy and Momentum (Review Kinematics and Dynamics too)
Online Text: 7.1 - 7.7, 8.1 - 8.6
Timeline: Day 1 Planning
Day 2 Building
Day 3 Building
Day 4 Testing
Day 5 Contest