SPH4U UNIVERSITY PHYSICS

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1 SPH4U UNIVERSITY PHYSICS ENERGY & MOMENTUM L Momentum & Impulse (P ) Momentum & Impulse The driver of this race car walked away from the crash without a scratch. Luck had little to do with this fortunate outcome, though a practical application of Newton's laws of motion by the engineers who designed the car and its safety equipment protected the driver from injury. October 8, U2 - Momentum & Impulse 1 Momentum When Newton originally formulated his laws of motion, he expressed them in a somewhat different form than you see in most textbooks today. Newton emphasized a concept called a quantity of motion, which is defined as the product of an object s mass and its velocity. Today, we call this quantity momentum. October 8, U2 - Momentum & Impulse 2 1

2 Momentum Since momentum is the product of a vector and a scalar, momentum is a vector quantity. The direction of the momentum is the same as the direction of the velocity. October 8, U2 - Momentum & Impulse 3 Momentum MOMENTUM(p) p =mv where p is the momentum (kg@m/s) m is the mass (kg) v is the velocity (m/s) Momentumdoes not have a unique unit of its own. October 8, U2 - Momentum & Impulse 4 Momentum 1. Determine the momentum of a 0.30 kg hockey puck travelling across the ice at a velocity of 5.6 m/s[n]. p = 1.7 kg@m/s[n] October 8, U2 - Momentum & Impulse 5 2

3 Impulse Newton s first law states that the velocity of an object is constant unless acted on by an external force. So, if a net force is applied to an object, its velocity will change and, therefore, its momentum will also change. Expressed mathematically, his second law, F=ma, can be rewritten as: ma m v m(vf v) i mvf mvi pf pi p p = F October 8, U2 - Momentum & Impulse 6 Impulse IMPULSE()p) is the change in the momentum of a system p = F where )p is the impulse (N@s) 7 N@s = kg@m/s F is the force (N) )t is the time interval (s) 7 during which the force is applied Like momentum, impulse is a vector quantity, and the direction of the impulse is the same as the direction of the force that causes it. October 8, U2 - Momentum & Impulse 7 Impulse 2. If a golf club exerts an average force of 5300 N[W] on a golf ball over a time interval of s, what is the impulse of the interaction? )p = 29 N@s[W] October 8, U2 - Momentum & Impulse 8 3

4 Impulse-Momentum Theory In many collisions, it is exceedingly difficult to make the precise measurements of force and time that you need in order to calculate the impulse. This is because the force changes continually throughout the few milliseconds of contact between the two objects. October 8, U2 - Momentum & Impulse 9 Impulse-Momentum Theory For example, when a golf club first contacts a golf ball, the force is very small. Within milliseconds, the force is great enough to deform the ball. The ball then begins to move and return to its original shape and the force soondrops back to zero. October 8, U2 - Momentum & Impulse 10 Impulse-Momentum Theory You could find the impulse by determining the area under the curve of force versus time (which can be tedious). An alternative and much easier approach is to analyse the momentum before and after the interaction between two objects. October 8, U2 - Momentum & Impulse 11 4

5 Impulse-Momentum Theorem IMPULSE-MOMENTUM THEOREM F = m v = mv -mv where F is the force (N) )t is the time interval (s) m is the mass (kg) )v is the change in the velocity (m/s) f i Sometimes1 and 2 are used as the subscripts instead of i and f. October 8, U2 - Momentum & Impulse 12 Impulse-Momentum Theorem 3. A 0.16 kg puck is travelling at 5.0 m/s[n] when a slapshot changes the puck s velocity to 40 m/s[s]. If the collision lasted s, (a) calculate the impulse imparted by the hockey stick. (b) determine the average force applied by the stick to the puck. (a) )p = 7.2 N@s[S] (b) F avg = 3600 N[S] October 8, U2 - Momentum & Impulse 13 Impulse-Momentum Theorem 4. A student practises her tennis volleys by hitting a ball against a wall. (a) If the kg ball travels at 50 m/s[w] before hitting the wall and then bounces directly backward at 35 m/s[e], what is the impulse of the interaction? (b) If the duration of the interaction is 25 ms, what is the average force exerted on the ball by the wall? (a) )p = 5.1 N@s[E] (b) F avg = 200 N[E] October 8, U2 - Momentum & Impulse 14 5

6 Impulse & Auto Safety One of the most practical and important applications of impulse is in the design of automobiles and their safety equipment. When a car hits another car or a solid wall, little can be done to reduce the change in momentum. The mass of the car certainly does not change, while the velocity changes to zero at the moment of impact. Since you cannot reduce the change in momentum, you cannot reduce the impulse. However, since impulse (F)t) depends on both force and time, engineers have found ways to reduce the force exerted on car occupants by extending the time interval of the crash. October 8, U2 - Momentum & Impulse 15 Impulse & Auto Safety In the early days, engineers and designers thought that a very strong, solid car would be ideal. As the number of cars on the road and the speed of the cars increased, the number and seriousness of accident injuries made it clear that the very sturdy cars were not protecting the car occupants. By the late 1950s and early 1960s, engineers were designing cars with very rigid passenger cells that would not collapse onto the passengers, but with less rigid crumple zones in the front and rear, as shown. October 8, U2 - Momentum & Impulse 16 Impulse & Auto Safety When a rigid car hits a wall, a huge force stops the car almost instantaneously. The car might even look as though it was only slightly damaged. However, parts of the car, such as the steering wheel, windshield, or dashboard, exert an equally large force on the passengers, stopping them exceedingly rapidly and possibly causing very serious injuries. October 8, U2 - Momentum & Impulse 17 6

7 Impulse & Auto Safety When a car with well-designed crumple zones hits a wall, the force of the wall on the car causes the front of the car to collapse over a slightly longer time interval than it would in the absence of a crumple zone. Since F)t is constant and )t is larger, the average force, F, is smaller than it would be for a rigid car. Although many other factors must be considered to reduce injury in collisions, the presence of crumple zones has had a significant effect in reducing the severity of injuries in automobile accidents. October 8, U2 - Momentum & Impulse 18 Impulse & Safety Equipment The concept of increasing the duration of an impact applies to many forms of safety equipment. For example, the linings of safety helmets are designed to compress relatively slowly. If the lining was extremely soft, it would compress so rapidly that the hard outer layer of the helmet would impact on the head very quickly. If the lining did not compress at all, it would collide with the head over an extremely short time interval and cause serious injury. Each type of sport helmet is designed to compress in a way that compensatesfor the type of impacts expected in that sport. October 8, U2 - Momentum & Impulse 19 Impulse & Safety Equipment IMPULSE& SAFETY since )p = F)t and )p does not change then 8 )t in order to 9 F important application is in the design of safety equipment crumple zones air bags safety helmets sports equipment Although a car crash seems almost instantaneous, the time taken for the front or rear of the car to crumple is great enough to significantly reduce the average force of the impact and, therefore, the average force exerted on the passenger cell and the passengers. October 8, U2 - Momentum & Impulse 20 7

8 Impulse & Safety Equipment 5. A bungee jumper jumps from a very high tower with bungee cords attached to his ankles. As he reaches the end of the bungee cord, it begins to stretch. The cord stretches for a relatively long period of time and then it recoils, pulling him back up. After several bounces, he dangles unhurt from the bungee cord. Use the concept of impulse to explain the difference in the results of a jump using a proper bungee cord and a jump using an ordinary rope. )p = F)t 7 )p is constant bungee cord (stretches) L as )t 8, F impact 9 regular rope (no stretch) L as )t 9, F impact 8 October 8, U2 - Momentum & Impulse 21 U Check Your Learning TEXTBOOK P.227 Q.3,5,9-11 (Review) P.257 Q.1-4 (PJ: Momentum & The Neutrino) October 8, U2 - Momentum & Impulse 22 8