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1 of 28 © Boardworks Ltd 2010 2 of 28 © Boardworks Ltd 2010 What is momentum? Momentum is a property of objects with mass and velocity. It is a vector quantity with the same direction as the velocity of the object. What is the equation for momentum? momentum = mass × velocity p = mv If mass is measured in kg and velocity in m s–1, what are the units of momentum? The units are kg m s–1. (This can also be expressed as N s). 3 of 28 © Boardworks Ltd 2010 Momentum as a vector 4 of 28 © Boardworks Ltd 2010 Force and momentum In order to change the momentum of an object, a force must be applied (from Newton’s first law). The rate of change of momentum of an object is proportional to the resultant force acting on the object. This is an alternative way of stating Newton’s second law in terms of momentum. In a tennis match, when a player exerts a force on the ball, it changes momentum. This means the ball can change speed, direction, shape or size, etc. 5 of 28 © Boardworks Ltd 2010 Rate of change of momentum Stated mathematically, Newton’s second law is: For constant masses this becomes Δ(mv) F= Δt m Δv F= = ma Δt It can therefore be seen that the familiar equation F = m a is a special case of the more general equation for Newton’s second law in terms of momentum. The more general form of the equation is necessary when mass is not constant, for example for a space shuttle taking off. The mass decreases as fuel is burned. 6 of 28 © Boardworks Ltd 2010 True or false? 7 of 28 © Boardworks Ltd 2010 Using the momentum equations 8 of 28 © Boardworks Ltd 2010 9 of 28 © Boardworks Ltd 2010 Conservation of linear momentum The principle of conservation of linear momentum states: The total linear momentum of a system of interacting bodies is constant, providing no external forces act. This applies to collisions, where objects move together and hit one other, and to explosions, where objects fly apart from one another after initially being at rest. collision 10 of 28 explosion © Boardworks Ltd 2010 Collisions 11 of 28 © Boardworks Ltd 2010 Explosions 12 of 28 © Boardworks Ltd 2010 Calculations: conservation of momentum 13 of 28 © Boardworks Ltd 2010 Elastic and inelastic collisions 14 of 28 © Boardworks Ltd 2010 Momentum and energy When one ball is swung on Newton’s cradle, one ball moves out at the other end. If two balls are swung, two balls move out. Two balls have double the mass, and double the momentum. In each collision, momentum is conserved. Total energy is also conserved in each collision because energy cannot be created or destroyed. Therefore, why do the balls eventually come to rest? Because kinetic energy is not always conserved, but is converted to other forms, in this case sound and heat. The collisions are therefore inelastic. 15 of 28 © Boardworks Ltd 2010 Equation for kinetic energy An equation for kinetic energy, Ek, in terms of momentum can be derived for a non-relativistic particle. m v2 Ek = 2 p = mv therefore p v= m Substituting in for v in the equation for Ek: p m m Ek = 2 2 ( ) Ek = 16 of 28 = m p2 2 m2 p2 2m © Boardworks Ltd 2010 Fill in the missing words 17 of 28 © Boardworks Ltd 2010 18 of 28 © Boardworks Ltd 2010 What is impulse? The impulse of a force is defined as: impulse = F Δt Impulse is a vector quantity with the same direction as the force. It is measured in newton seconds (N s). Newton’s second law in the form F = Δ(mv) / Δt can be rearranged to give: F Δt = Δ(mv) The quantity F Δt is the impulse of the force, so it can be seen that impulse = change in momentum Note that N s are the same as kg m s–1 as expected since impulse = Δ(mv), but N s are usually used for impulse. 19 of 28 © Boardworks Ltd 2010 Force–time graphs 20 of 28 © Boardworks Ltd 2010 Impulse and collisions F Δt = Δ(mv) Look at the equation for impulse. What determines how much damage is done in a collision, and how can it be reduced? The size of force controls how much damage there is. Momentum is conserved in a collision, so impulse is constant. To reduce the force, the time over which the collision takes place should be increased. 21 of 28 © Boardworks Ltd 2010 Applications In a car crash, force and therefore damage is reduced by increasing the amount of time over which a collision occurs. Measures such as seat belts can help with this. The seat belt stretches slightly to prolong the passenger’s impact with it. Crumple zones also increase the time over which the collision takes place, due to the time it takes them to crumple. 22 of 28 © Boardworks Ltd 2010 How much do you know about impulse? 23 of 28 © Boardworks Ltd 2010 Impulse and force–time graphs 24 of 28 © Boardworks Ltd 2010 25 of 28 © Boardworks Ltd 2010 Glossary 26 of 28 © Boardworks Ltd 2010 What’s the keyword? 27 of 28 © Boardworks Ltd 2010 Multiple-choice quiz 28 of 28 © Boardworks Ltd 2010