VIEWS: 21 PAGES: 31 POSTED ON: 8/7/2011
COLLISION TIME AND COLLISION FORCE Just before collision obstacle fixed to initial velocity the runway (force sensor) trolley 0.505 kg A trolley is moving towards a force sensor fixed to the runway. The force sensor serves as an obstacle hit by the trolley. The velocity of the trolley is measured with a motion sensor. During collision obstacle fixed to the runway (force sensor) trolley 0.505 kg collision force acting on the trolley by the obstacle The collision force is measured by the force sensor. The period during which the collision force is acting is known as collision time. The collision force is not uniform. Just after collision obstacle fixed to final velocity the runway (force sensor) trolley 0.505 kg The front of the trolley and the force sensor are made of very strong material. There is negligible permanent deformation produced by the collision. The collision force - time graph and the velocity - time graph are to be shown. The positive direction is taken as the direction of motion of the trolley before collision. Therefore the collision force is negative. The initial velocity is positive and the final velocity is negative. collision time = 0.03 s maximum magnitude of collision force = 30 N final velocity initial velocity = -0.22 m s-1 = 0.44 m s-1 The collision time is short and the collision force is large. Average collision force on the trolley = mass of the trolley average acceleration of the trolley (-0.22) - (0.44) 0.505 0.03 = -11 N Note that the maximum magnitude of the collision force is much larger than the magnitude of the average collision force. What if the front of the trolley is so designed that it deforms slowly and permanently during collision ? Just before collision obstacle fixed to initial velocity the runway (force sensor) trolley 0.505 kg Bumper (made of paper) Just after collision obstacle fixed to final velocity the runway (force sensor) trolley 0.505 kg Bumper deformed permanently after the collision. This absorbs part of the initial kinetic energy of the trolley. The collision force - time graph and the velocity - time graph are to be shown. collision time = 0.31 s maximum magnitude of collision force = 2.6 N initial velocity final velocity = 0.46 m s-1 = -0.22 m s-1 The collision time is much longer and the collision force is considerably smaller. Average collision force on the trolley = mass of the trolley average acceleration of the trolley (-0.22) - (0.46) 0.505 0.31 = -1 N That’s why the front and back of a car is so designed that it is collapsible during collision. This increases the time of collision and hence reduces the collision force. However the middle portion of the car is still made of strong material so as to protect the passengers inside. velocity Summary u u is the speed before collision. 0 time -v v is the speed after collision. collision force t is the collision time. Fmax is the maximum 0 time magnitude of the collision force. -Favg Favg is the magnitude of the average collision -Fmax force. t velocity Summary u ( -v ) - ( u ) - Favg m time t 0 (-mv) - ( mu) -v t collision force m(u v) Favg t 0 time The collision force increases for -Favg • larger mass of the object -Fmax • higher speed of the object just before collision t • shorter collision time velocity Summary u 0 time -v collision force 0 time Collision force decreases with increase of collision time for the same change in momentum. velocity Summary u 0 time -v v cannot be greater than u. Why ? collision force 0 time -Favg -Fmax t velocity Summary u If there is no kinetic energy loss during collision, 0 time -v v=u This is the case when a gas collision force molecule collides with the wall of the container. The magnitude of the average 0 time collision force is given by -Favg 2mu Favg t -Fmax t Favg a u The fate of a passenger without wearing a safety belt in a car accident Just before the collision between the car and the wall, the car and the passenger moves with the same velocity u. The passenger is at rest relative to the car. u The car hits the wall. Fc is the collision force acting on the car. Fc does not act on the passenger ! There is no horizontal force acting on the passenger to stop him from moving. The friction provided by the seat is negligible. >> Fc Newton’s First Law states that, due to its inertia, an object will maintain its original state of motion unless a resultant force acts on it. Thus the passenger continues to move with the original velocity u towards the front panel of the car. The passenger finally hits the front panel of the car. Fp is the collision force acting on the passenger by the car. Fp is large and stops the passenger in a short period of time ! Fp The area of contact between the passenger and the front panel is small and hence the pressure is very large. This imposes serious injury on the passenger. velocity-time of the car velocity velocity-time of the passenger u 0 time velocity-time of the car velocity velocity-time of the passenger u 0 time The car hits the wall and stops in a short time. velocity-time of the car velocity velocity-time of the passenger u 0 time The passenger continues to move forward after the car stops. velocity-time of the car velocity velocity-time of the passenger u 0 time The passenger hits the front panel and finally stops. Safety Belt Fp safety belt The force exerted by the safety belt on the passenger will depend on the speed with which the safety belt is pulled out. Fp safety belt Functions of safety belt : Provide a force Fp to stop the passenger so that he will not hit the front panel of the car. Achieve a longer collision time between the belt and the passenger so that Fp will be small enough to prevent injury to the passenger. velocity-time of the car velocity velocity-time of the passenger u 0 time Fp An air bag exploded during the collision between the car and the wall serves a similar purpose as a safety belt. What are the disadvantages of using an air bag instead of a safety belt ?
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