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# momentum - 37 Experiment V Conservation of Linear Momentum...

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37 Experiment V: Conservation of Linear Momentum Goals Study the conditions required for the conservation of linear momentum Verify the law of conservation of linear momentum in a collision of two objects with the same mass Use the law of conservation of linear momentum to determine the ratio of the masses of two objects in a collision Introduction and Background Conservation of Momentum : The linear momentum (which we will simply refer to as momentum below), P , of a mass m moving with velocity v is defined as P = m v . For a system consisting of multiple masses, the total momentum of the system is the vector sum P = P 1 + P 2 + P 3 + … , where P 1 , P 2 , P 3 are the momentum of individual masses. Newton’s second law tells us that if, during a time interval t , a net force F acts on the system, the total momentum of the system will be changed by an amount P = F t . Consequently, so long as the net force on the entire system is zero, the total momentum of the system remains constant (conserved). Because F and P are vectors, if the sum of the forces along a particular direction is zero, the component of the total momentum along that direction will be conserved. In other words, it is possible to have a situation in which the total momentum of a system is conserved along some directions but not conserved along others, as in the case of this lab. Collisions : Conservation of momentum is often applied to the analysis of collisions of two (or more) masses. This is particularly useful since the actual collision forces and the resulting accelerations may be impossible to measure directly; but since the collision forces are internal , the momentum is conserved as long as the net external force is zero. To apply momentum conservation in a given direction, x , to a system of two masses undergoing a collision, it is necessary that there be a time interval that includes the collision process but there is no net external force on the system in that direction. Within this time interval, the x -component of the total momentum of the system would remain constant although the individual components P 1x and P 2x are changed during collision. In this lab, we will study glancing collisions between two balls, one of which is initially at rest. We will obtain data that will allow us to check for momentum conservation in the horizontal plane in which there is no external force. Experimental Setup Equipment : Inclined chute, two steel balls and one plastic ball stored in a hollow metal block, large sheets of white wrapping paper, carbon paper, plumb bob, string, meter stick, pan balance, table clamp.

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38 Setup : The experimental setup is shown schematically in Figure 5-1. In an experiment, a target ball is placed on top of a post in front of the inclined chute, while a projectile ball is released from the top of the chute and gain a certain velocity just before the collision. After the collision, the two balls undergo projectile motion with zero initially velocity in the vertical direction and
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momentum - 37 Experiment V Conservation of Linear Momentum...

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