Lvl 3
So What’s Momentum ?
• Momentum is moving inertia which in equation form is: mass x velocity
• This can be abbreviated to : p = mv
• Momentum is a VECTOR quantity.
• So, A really slow moving truck and an extremely fast roller skater can . have the same momentum.
Question : Under what circumstances would the roller skater and the truck
have the same momentum ?
Answer : The roller skater and truck can have the same momentum if the . . ratio of the speed of the skater to the speed of the truck is the . . same as the ratio of the mass of the truck to the mass of the skate.
For Example : A 1000 kg truck moving at 0.01 has the same momentum as a 50 kg
skate moving at 0.2
Truck Roller Skater
p = mv p = mv
p = (1000 kg)(.01) p = (50 kg)(.2)
p = 10 =10Ns p = 10 =10Ns
Notice the momentum of both the skater and the truck are the same!
Impulse and Momentum
• Impulse is defined as a change in momentum
• If momentum changes, it’s because mass or velocity change.
• Most often mass doesn’t change so velocity changes and that is acceleration.
• Recall Force = mass x acceleration (F = ma)
• Applying a force over a time interval to an object changes the momentum
• We can rewrite acceleration at:
• Now rewrite Newtons 2nd Law
F=maàF
• Therefore, if we move the t to the other side of the equation:
Ft=m()
• In simple form: Impulse = F t or Ft = mDv (note: D means change in)
Problems start here and below!
Momentum Practice
1) If you throw a ball horizontally while standing on roller skates, you roll backwards. Will you roll backwards if you go through the motions of throwing the ball, but hold on to it instead? Explain your reasoning.
______
2) 2. Which has the greater change in momentum, a 50 gram clay ball that strikes a wall at 1 m/s and sticks or a 50 gram superball that strikes a wall at 1 m/s and bounces away from the wall at 0.8 m/s? Explain your reasoning.
______
6) An elephant is riding a snowboard down Mammoth Mountain. The velocity of the snowboard (and the elephant – duh!) is 30 m/s and has a momentum of
600,000 kg•m/s. What is the mass of the elephant?
6b) Which would have the greater momentum, a 60,000 kg freight train traveling at 40 m/s or the mammoth snowboard riding elephant? Explain your answer
7) A car with a mass of 850 kg travels with a velocity of 7.0 m/s. The momentum:
7b) The velocity of the car is increased to 9.0 m/s in a time of 2.0 seconds. The new momentum is ______. The change in momentum of the car is ______.
7c) Remember a change in momentum is defined as an IMPULSE. Based on 7b, what is the impulse of the car?
7d) Use the impulse equation to find the force of the motor to change the momentum in the previous problem.
8) A bullet is fired from a gun towards the right with a speed of 700 m/s. It has a mass of 15 grams. The momentum is ______(remember to convert grams to kg)
8b) What is the impulse required to stop the bullet?
8c) The time the bullet is in the barrel is 0.0010 s. Find the impulse on the gun ______.
8d) Find the initial force on the gun. ______
9) A .040-kg bullet slows from 600 to 500 m/sec as it penetrates a can of anchovies.
A) What impulse (change in momentum) is received by the bullet and the can?
B) If the can is .12 m in diameter, how long is the bullet in the can? (Think – what is the average velocity during interaction?) (hint…do we know an equation with d=…)
C) What force is exerted on the bullet during this time?
10 a) A 0.06 kg tennis ball, initially at rest, is hit from a racket with a velocity of 33.6 m/s. If the time that the racket and ball were in contact with each other was 0.06 seconds, then what force was required to move the ball?
10 b) The ball from crossed the net towards the awaiting opponent. The ball reached the opponent with the velocity that it left the original players racket with (33.6 m/s). If the ball was again contacting the racket for 0.06 seconds, what force would the second player now have to impart on the ball to return the ball with a velocity of 27.9 m/s? The second player has the same time of contact.
10 c) Is this similar to the problem we have done with the happy ball and the sad ball? Why do you think this?
10 d) How does the force required to change the direction of an object completely compare to an object that is brought from motion, to a stop? Can this explain why the happy ball knocked over the wooden block, but the sad ball did not?
11) A 0.08 kg baseball is accelerated for 0.28 seconds to a speed of 37.6 m/s. What is the average force applied to the ball during the throwing motion?
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