Experiment 5. Momentum and Energy conservation in collisions.pdf

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Ken Seaman

5-1 Experiment 5: Momentum and Energy Conservation in Collisions The object of this experiment is to use vectors and components to confirm a) the conservation of linear momentum in a collision and b) to determine whether the kinetic energy is conserved in the collision. A. Introduction Vector Addition A quantity which has direction as well as magnitude is called a vector. Examples of vectors are velocity, displacement, force and momentum. When the directions of vectors are not all along the same straight line, then these vectors cannot be added using simple arithmetic. One way of adding two vectors is to make a closed vector trianglesing the tail-to-tip method. On a diagram, one of the vectors, call it 1 , is drawn to scale and then the second vector, b , is drawn to scale placing its tail at the tip of the first vector and being sure its 2 relative direction is correct. Then, the arrow drawn from the tail of the first vector to the tip of the second represents the sum or resultant of the two vectors. See Fig. 5.1. Vector triangles can be used directly, by drawing to scale and measuring angles with a protractor. But rough sketches of vector triangles can also be usefully employed in solving problems analytically to keep the various angles, etc. clear in your mind. The method of tip-to-tail vector triangles can be extended to vector polygons when more than two vectors must be added. b1+ b 2 b b b 1 2 1 b 2 Fig. 5.1 Closed Vector Triangle Method of Adding Vectors 5-2 Another common way to add vectors is first to resolve each vector into its components along a set of x, y coordinate axes. The steps in resolving a vector into its components are as follows: a) Start with vector b. b) Establish a set of coordinate axes thereby defining the angle between the vector and either the y-axis (β) or the x-axis (α). The components of the vector b resolved along the x and y Y axis in terms of angles α or β b respectively are by [1] b x b sin β or b cos α [2] b = b cos β or b sin α y Note that if b falls on the left-hand β side of the y-axis then the α bx X x-component will be negative, similarly if y falls below the x-axis then the y-component will be negative. After each of theb , b , ...,b to be added have been resolved into their x-components 1 2 n b1x b x ..., nx; and their y-components b 1yb 2y... bny the x-component b Rx of the resultant vector bRcan be found simply by adding up all of the x-components b , 1 , 2..., b ;nxnd the y-component b of the resultant vector b can be found by adding up all of the y-components Ry R b1y b 2y..., ny. The magnitude of the resultant is then 2 2 [3] b R b b Rx Ry and the direction is given by [4] tan θ = bRy /Rx where θ is the angle from the x-axis. See Fig. 5.2. 5-3 Y bRY bR θ bRX X Fig. 5.2 Obtaining a Vector from its Components Conservation of Momentum The momentum of a body is defined as the product of its mass and velocity. It is a vector quantity with the direction of the momentum the same as the direction of the velocity. A force is required to change the momentum of an object and, in the absence of outside forces, the total momentum of a closed system remains the same - momentum is conserved. For example, in the absence of outside forces momentum is conserved in a collision between two objects. The direction and magnitude of the momentum of each object may be changed in the collision but the total momentum before and after the collision is the same. B. Conservation of Momentum (Procedure) NOTE: Each person will have their own trace and must hand it in with their report. We will demonstrate the conservation of momentum by studying the collision of two pucks on the air table. The air table is the same as that used in Experiment 1. You may wish to reread the introduction to that experiment. We will have one puck stationary near the center of the paper and then hit it with another moving puck so that both will go off at an angle. The speeds before and after are found by measuring the distance between dots along the paths. (i) Assumptions Several implicit assumptions will be made in the course of this experiment and we must be careful that these assumptions are justified. For example: (a) We assume that the force of friction is negligible. If this were not so, the calculation of the puck’s speed using a large number of dots would not be valid. As long as the air table is functioning properly, we are justified in making this assumption. (b) We assume that the force of gravity has no effect on the motion of the pucks, hence the requirement that the air tables be very carefully levelled. 5-4 (c) We assume that one puck is stationary. (ii) Getting the trace Now prepare to make your trace. The air table will have been levelled before the lab period started and will stay level as long as it IS NOT MOVED. However, you must check that it is still level. Place your paper on the table, smoothing it out. Placing weights at the corners may help to keep it smooth. Now to check the level, turn on the compressor and place one puck carefully in the centre of the paper. Ideally the puck should not move at all but we shall be satisfied if it moves only very slowly (it would be best if any movement that does take place is along the y-axis of the air table). If the puck moves, of its own accord, easily and consistently in one direction then the air table will have to b
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