Momentum in 1-Dimension Level : Physics I Date : Warm-up Questions If you were in a car that was out of control and had to choose between hitting a concrete wall or a haystack to stop, which would you choose? If you were shot by a bullet, how far would you recoil due to the impact of the speeding bullet? 1. What is Momentum? - Momentum is simply an object in motion => momentum = ( ) ( ) - The symbol for momentum is ( ) - The unit for momentum is kg m/s => ( ) = ( ) ( ) Q1) Does a slowly moving bus have a lot of momentum or little momentum? Explain!! Q2) Does a high speed bullet have a lot of momentum or little momentum? Explain!! Q3) What is the momentum of a huge elephant at rest? 2. Change in Momentum - If you apply an external force over a certain period of time on a moving object, the momentum will change mv i + F t = mv f - A greater force will produce more change in momentum, but how long the force acts on an object is also plays an important role in changing the momentum. That is, a force over an extended period produces greater change in momentum compared to brief force Force time = change in momentum - F t = Impulse, and the symbol is I => F t = m v => I = ( m v )
mv i + F t = mv f or F t = m v Q4) If you were in a car that was out of control and had to choose between hitting a concrete wall or a haystack, which would you choose? Explain using Ft= m v Q5) What is the momentum of an 8kg bowling ball rolling at a speed of 2.5m/s? a) 16g m/s b) 20kg m/s c) 28kg m/s d) 36kg m/s Q7) What is the momentum of a 50kg carton sliding on a frictionless icy surface at a speed of 0.8m/s? a) 100kg m/s b) 80g m/s c) 60kg m/s d) 40kg m/s Q8) Which two cases below has a greater momentum? Case-1 : A bowling ball of mass 7.5kg is moving with a speed of 4m/s Case-2 : A speeding bullet of mass 0.02kg with a speed of 1100m/s Q9) A 50kg carton is sliding with a speed of 4m/s on a frictionless icy surface. If you apply 4N of force over a time of 4s, then what is the new speed v f? a) 4.32m/s b) 7.45m/s c) 9.21m/s c) 13.56m/s
mv i + F t = mv f or F t = m v Q10) A basketball of mass 0.6kg is rolling towards you at a speed of 5m/s. If you are using your foot to stop it, how much force is needed to stop the basketball in 0.2 seconds? a) 60N b) 45N c) 30N d) 15N Q11) A bus of mass 10000kg is moving towards Superman at a speed of 30m/s. How much force must Superman assert on the bus so that the bus will stop in 20 seconds? a) 10000N b) 15000N c) 20000N d) 25000N Q12) A 0.065kg tennis ball moving to the right with a speed of 15m/s is struck by a tennis racket, causing it to move to the left with a speed of 15m/s. If the ball remains in contact with the racket for 0.02s, what is the magnitude and direction of the force experienced by the ball? a) 98N right b) 98N left c) 160N right d) 160N left Q13) When people jump off from a certain height, we naturally bend our knees when we land so that we increase the stopping time. Let's say Jack, who s mass is m=60kg, is playing on top of the kitchen table which is 1m above the floor. He jumps down and when he lands on the floor he bends his knees. If the stopping time is 0.8s, then how much force did the floor exert on Jack? If he unwisely lands with his leg stiff, he would stop at 0.01s. How much force will the floor exert on Jack in this case?
3. Conservation of Momentum - If any quantity in physics that does not change, that quantity is conserved *~In an isolated system, when two or more objects collide, the total momentum before the collision and after the collision is conserved if there is no external force acting on the system!! m1v1i m2v2i Total momentum before collision : m1v1i + m2v2i m1v1f m2v2f Total momentum after collision : m1v1f + m2v2f total momentum before collision = total momentum after collision m 1v 1i + m 2v 2i = m 1v 1f + m 2v 2f 1. Elastic Collision(perfect bounce with no lost in energy) Case1) Mass of object-2 is equal to object-1 (m 1= m 2) Object-1(m 1=2kg) is standing still and object-2(m 2=2kg) with speed of 4m/s collided with object- 1. After the collision, if object-2 stands still, what is the speed of object-1? object-2(m2) object-1(m1) Object-2(m2) Object-1(m1) Case2) Mass of object-2 is greater than object-1(m 1< m 2) Object-1(m 1=2kg) is standing still and object-2(m 2=4kg) collided with object-1 with speed of 6m/s. After the collision, if the speed of object-2 is 2m/s, what is the velocity of object-1? object-2(m2) object-1(m1) Object-2(m2) Object-1(m1)
m1v1i + m2v2i = m1v1f + m2v2f Case3) Mass of object-2 is less than object-1 (m 1> m 2) Object-1(m 1=4kg) is standing still and object-2(m 2=2kg) collided with object-1 with speed of 4m/s. After the collision, if the velocity of object-1 is 3m/s, what is the speed of object-2? object-2(m2) object-1(m1) Object-2(m2) Object-1(m1) 2. Inelastic Collision(not a perfect bounce. Energy lost to heat ex; sticking together after collision) Case4) Object-1 is standing still and object-2 collided with object-1 with speed of 4m/s. If the mass of object-2 and object-1 are identical, and the two objects combine after the collision, what will be the speed of the combined mass? object-2(m2) object-1(m1) (m2+ m1) Case5) Object-1 has a spring attached and is pushed together with object-2. Initially the combined two masses are at rest. If they are released, they push each other away. If the mass of object-1 is 4kg and object-2 is 2kg and the speed of object-1 was 4.3m/s, what is the speed of the object-2? (m1 + m2 ) m1 m2
m1v1i + m2v2i = m1v1f + m2v2f Additional Questions Q14) A 3kg cart moving to the right with a speed of 1m/s has a head-on collision with a 5kg cart that is initially moving to the left with a speed of 2m/s. After the collision, the 3kg cart is moving to the left with a speed of 1m/s. What is the final velocity of the 5kg cart? a) 0.8m/s to the right b) 0.8m/s to the left c) 2m/s to the right d) 2m/s to the left Q15) A 0.05kg lump of clay moving horizontally at 12m/s strikes and sticks to a stationary 0.1kg cart that can move on a frictionless surface. Determine the speed of the cart and clay after the collision. a) 2m/s b) 4m/s c) 6m/s d) 8m/s Q16) A cannon+ball system is stationary. The cannon of mass M=100kg shoots a cannon-ball. If the mass of cannon-ball is m=10kg and the speed of the cannonball was 90m/s, what is the speed of the cannon after the shot? Before shot cannon-ball! After the shot Cannon-ball! (a) 4.5m/s (b) 9m/s (c) 45m/s (d) 90m/s Q17) A boy of mass 80kg on a roller-skater is holding a ball of mass 2kg. The boy+ball is initially at rest. If the boy pushes the ball, producing a speed 10m/s, what is the recoil speed of the boy? a) 0.25m/s b) 0.5m/s c) 0.75m/s d) 1m/s
K= 1 2 mv2 U g=mgh K i+u gi = K f +U gf mv i +F t =mv f m 1v 1i +m 2v 2i = m 1v 1f +m 2v 2f Q18) Ballistic Pendulum A ballistic pendulum is sometimes used in laboratories to measure the speed of a projectile, such as a bullet. The ballistic pendulum shown consists of a block of wood(m 2=2.5kg) suspended by a wire of negligible mass. A bullet of mass m 1=0.01kg is fired with a speed v 1i. Just after the bullet collides with it, the block (with the bullet in it) has a speed of v f and then swings to a maximum height of 0.65m above the initial position. Find the speed v 1i of the bullet, assuming that air resistance is negligible. a) 896m/s b) 754m/s c) 545m/s d) 435m/s (a) v1i (b) m1 m1+m2 m2 vf h=0.650m hint : use K i+u gi = K f +U gf to find v f, then use m 1v 1i +m 2v 2i = m 1v 1f +m 2v 2f to find v 1i.