![Picture](/uploads/4/7/6/6/47660241/3442920.png?315)
Key Terms
p = mv
F * t = Δp = mΔ
Via - Vib = -Vfa + Vfb (only used in an elastic 1D collision)
Section 1: Momentum and Impulse
-Momentum: a vector quantity defined as the product of an object's mass and velocity.
-p = mv (momentum = mass X velocity)
-Impulse: for a constant external force, the product of the force and the time over which it acts on an object.
-FΔt = Δp (force X time interval = impulse)
-Δp = mvf-mvi (impulse = mass X final velocity + mass X initial velocity)
-This means that a collision of a set impulse happening over a shorter period of time has greater force. To increase the force of a collision, one must increase the impulse or decrease the time interval over which the collision occurs.
Section 2: Conservation of Momentum
-Momentum is conserved when no net force is applied to the system.
-m1v1i + m2v2i = m1v1f + m2v2f
Section 3: Elastic and Inelastic Collisions
-Perfectly inelastic collision: a collision in which two objects stick together and move with a commo velocity after colliding.
-m1v1i + m2v2i = (m1+ m2)vf
-Perfectly elastic collision: a collision I which the total momentum and the total kinetic energy remain constant.
-0.5m1(v1i ^2) + 0.5m2(v2i ^2) = 0.5m1(v1f ^2) + 0.5m2(v2f ^2)
-Most collisions are neither perfectly elastic or perfectly inelastic.
Practice
Multiple Choice Questions:
1. A 740 kg car traveling 19 m/s comes to a complete stop in 2.0 s. What is the force exerted on the car during this stop?
a. 85 N b. 850 N
c. 7000 N d. 9200 N
2. In a collision...
a. total momentum is not conserved b. total kinetic energy is conserved
c. total momentum is conserved d. total impulse is conserved
e. total potential energy is conserved
3. A 4.00 kg object is moving at 5.00 m/s EAST. It strikes a 6.00 kg that is at rest. The objects have an elastic collision. The velocity of the 4.00 kg object after the collision is at an angle of 30.0 degrees SOUTH of EAST. The velocity of the 4.00 kg mass after the collision is
A. 5.78 m/s. B. 4.56 m/s.
C. 3.55 m/s. D. 1.67 m/s. E. 2.66 m/s.
4. A 30.00 kg mass falls from a height of 4.000 m. The momentum of the mass just before it hits the ground is...
A. 144.2 kg m/s. B. 187.8 kg m/s.
C. 320.0 kg m/s. D. 442.4 kg m/s. E. 502.1 kg m/s.
5. Two objects of equal mass hit a wall with the same velocity. They both rebound with the same velocity. Both objects experience the same momentum change but one experiences twice the force as the other. Which of the following statements is true?
A. the contact time between the object and the wall of one is twice the contact time of the other
B. the contact time between the object and the wall of one is equal to the contact time of the other
C. the contact time between the object and the wall of one is one-half the contact time of the other
D. the change in the kinetic energy is the same for the two objects
E. the contact time between the object and the wall of one is 1/3 the contact time of the other
6. A 3.0 kg object is moving to the right at 4.0 m/s. It collides in a perfectly inelastic collision with a 6.0 kg object moving to the left at 2.0 m/s. What is the total kinetic energy after the collision?
A. 62 J B. 25 J
C. 12 J D. 0.0 J E. 36 J
Open-Ended Questions
1. A white pool ball (m1 = 0.3 kg) moving at a speed of 3 m/s collides head-on with a red pool ball (m2 = 0.4 kg) initially moving at a speed of 2 m/s. Neglecting friction and assuming the collision is elastic, what is the velocity of each ball after the collision?
2.A 300 kg snowmobile is traveling at 30 m/s. How fast would a 200 kg snowmobile need to travel to have the same momentum?
3. A 2 kg ball traveling to the right at 10 m/s makes a glancing collision with a 3 kg ball initially at rest. After the collision the 2 kg ball travels with speed 8.4 m/s at an angle 37o above the initial direction. What is the speed and direction of the 3 kg ball after the collision?
4. A car slams on its brakes while traveling at 8 0 kph. If the coefficient of friction between the tires and the pavement is 0.6, for how much time does the car skid? What if the pavement is wet, reducing the coefficient to 0.3? What if the road is snow-covered, reducing the coefficient to 0.12?
Video links
https://www.youtube.com/watch?v=XFhntPxow0U
This explains the basics of momentum, some equations and goes through a simple practice problem.
https://www.youtube.com/watch?v=ph48Xwj_eS8
This video explains what impulse is, how it relates to momentum, and uses a few examples to strengthen understanding.
https://www.youtube.com/watch?v=zj4DZYou-1s
- Impulse: measure of change in momentum
- Momentum: the property or tendency of a moving object to continue moving
- Isolated System: system that does not interact with its surroundings, that is, its total energy and mass stay constant
- Conservation of Momentum: for a collision occurring between object 1 and object 2 in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision
- Elastic Collision: is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total kinetic energy before the encounter, and can occur only if there is no net conversion of kinetic energy into other forms
- Perfectly Inelastic Collision: collision in which there is no loss of kinetic energy, which is changed to some other form of energy
- Inelastic Collision: a collision in which the total kinetic energy of the colliding bodies or particles is not the same after the collision as it was before
- Ballistic Pendulum: device for measuring a bullet's momentum, from which it is possible to calculate the velocity and kinetic energy
p = mv
F * t = Δp = mΔ
Via - Vib = -Vfa + Vfb (only used in an elastic 1D collision)
Section 1: Momentum and Impulse
-Momentum: a vector quantity defined as the product of an object's mass and velocity.
-p = mv (momentum = mass X velocity)
-Impulse: for a constant external force, the product of the force and the time over which it acts on an object.
-FΔt = Δp (force X time interval = impulse)
-Δp = mvf-mvi (impulse = mass X final velocity + mass X initial velocity)
-This means that a collision of a set impulse happening over a shorter period of time has greater force. To increase the force of a collision, one must increase the impulse or decrease the time interval over which the collision occurs.
Section 2: Conservation of Momentum
-Momentum is conserved when no net force is applied to the system.
-m1v1i + m2v2i = m1v1f + m2v2f
Section 3: Elastic and Inelastic Collisions
-Perfectly inelastic collision: a collision in which two objects stick together and move with a commo velocity after colliding.
-m1v1i + m2v2i = (m1+ m2)vf
-Perfectly elastic collision: a collision I which the total momentum and the total kinetic energy remain constant.
-0.5m1(v1i ^2) + 0.5m2(v2i ^2) = 0.5m1(v1f ^2) + 0.5m2(v2f ^2)
-Most collisions are neither perfectly elastic or perfectly inelastic.
Practice
Multiple Choice Questions:
1. A 740 kg car traveling 19 m/s comes to a complete stop in 2.0 s. What is the force exerted on the car during this stop?
a. 85 N b. 850 N
c. 7000 N d. 9200 N
2. In a collision...
a. total momentum is not conserved b. total kinetic energy is conserved
c. total momentum is conserved d. total impulse is conserved
e. total potential energy is conserved
3. A 4.00 kg object is moving at 5.00 m/s EAST. It strikes a 6.00 kg that is at rest. The objects have an elastic collision. The velocity of the 4.00 kg object after the collision is at an angle of 30.0 degrees SOUTH of EAST. The velocity of the 4.00 kg mass after the collision is
A. 5.78 m/s. B. 4.56 m/s.
C. 3.55 m/s. D. 1.67 m/s. E. 2.66 m/s.
4. A 30.00 kg mass falls from a height of 4.000 m. The momentum of the mass just before it hits the ground is...
A. 144.2 kg m/s. B. 187.8 kg m/s.
C. 320.0 kg m/s. D. 442.4 kg m/s. E. 502.1 kg m/s.
5. Two objects of equal mass hit a wall with the same velocity. They both rebound with the same velocity. Both objects experience the same momentum change but one experiences twice the force as the other. Which of the following statements is true?
A. the contact time between the object and the wall of one is twice the contact time of the other
B. the contact time between the object and the wall of one is equal to the contact time of the other
C. the contact time between the object and the wall of one is one-half the contact time of the other
D. the change in the kinetic energy is the same for the two objects
E. the contact time between the object and the wall of one is 1/3 the contact time of the other
6. A 3.0 kg object is moving to the right at 4.0 m/s. It collides in a perfectly inelastic collision with a 6.0 kg object moving to the left at 2.0 m/s. What is the total kinetic energy after the collision?
A. 62 J B. 25 J
C. 12 J D. 0.0 J E. 36 J
Open-Ended Questions
1. A white pool ball (m1 = 0.3 kg) moving at a speed of 3 m/s collides head-on with a red pool ball (m2 = 0.4 kg) initially moving at a speed of 2 m/s. Neglecting friction and assuming the collision is elastic, what is the velocity of each ball after the collision?
2.A 300 kg snowmobile is traveling at 30 m/s. How fast would a 200 kg snowmobile need to travel to have the same momentum?
3. A 2 kg ball traveling to the right at 10 m/s makes a glancing collision with a 3 kg ball initially at rest. After the collision the 2 kg ball travels with speed 8.4 m/s at an angle 37o above the initial direction. What is the speed and direction of the 3 kg ball after the collision?
4. A car slams on its brakes while traveling at 8 0 kph. If the coefficient of friction between the tires and the pavement is 0.6, for how much time does the car skid? What if the pavement is wet, reducing the coefficient to 0.3? What if the road is snow-covered, reducing the coefficient to 0.12?
Video links
https://www.youtube.com/watch?v=XFhntPxow0U
This explains the basics of momentum, some equations and goes through a simple practice problem.
https://www.youtube.com/watch?v=ph48Xwj_eS8
This video explains what impulse is, how it relates to momentum, and uses a few examples to strengthen understanding.
https://www.youtube.com/watch?v=zj4DZYou-1s