Unit 6: Momentum

Impulse

100

Write out the full equation for impulse.

J=F_nett=(delta)p=m(delta)v

200

A 75-kilogram hockey player is skating across the ice at a speed of 6.0 meters per second. What is the magnitude of the average force required to stop the player in 0.65 second?

692.3 N

300

Calculate the magnitude of the impulse applied to a 0.75-kilogram cart to change its velocity from 0.50 meter per second east to 2.00 meters per second east.

1.13 N*s

400

Explain, in terms of impulse, why air bags are safer during a collision.

Air bags increase the time it takes for a body to come to a stop, which lowers the force experienced by the body.  Less force is safer.

500

If one knows only the constant resultant force acting on an object and the time during which this force acts, one can determine the
a. change in momentum of the object
b. change in velocity of the object
c. change in kinetic energy of the object
d. mass of the object
e. acceleration of the object

a. change in momentum of the object

F_nett = (delta)p

Conservation of Momentum

100

Write out the equation for conservation of momentum for an elastic collision.

m₁v₁ + m₂v₂ = m₁v₁ + m₂v₂

200

A 3.1-kilogram gun initially at rest is free to move. When a 0.015-kilogram bullet leaves the gun with a speed of 500 meters per second, what is the velocity of the gun?

-2.4 m/s

300

A 7.28-kilogram bowling ball traveling 8.50 meters per second east collides head-on with a 5.45-kilogram bowling ball traveling 10.0 meters per second west. Determine the magnitude of the total momentum of the two-ball system after the collision.

7.38 kgm/s 

400

A rubber ball of mass m is thrown horizontally at a vertical wall with a speed v and bounces off elastically and horizontally. What is the magnitude of the change in momentum of the ball?

mv + 0 = -mv + 0

(delta)p = p_final - p_initial 

-2mv

2mv

500

A disc of mass m is moving horizontally to the right with speed v on a table with negligible friction when it collides with a second disc of mass 2m. The second disc is moving horizontally to the right with speed v/2 at the moment of impact. The two discs stick together upon impact. The speed of the composite body immediately after the collision is

(2/3)v

Graphs

100

On a force vs time graph, what does the area under the curve represent?

Impulse

200

In a momentum-time graph, what does the slope represent?

F_net

300

Draw a position vs time graph for an object experiencing a force for 5 seconds.

Since the object is experiencing a force over a period of time, the object has a change in momentum, which means the speed is changing, which means the object is accelerating.

400

Using the force vs. time graph on the white board,

rank the impulse applied to the object during each 2 second interval from greatest to least.

Most area=greatest impulse

Least area=least impulse

500

A student is trying to quickly determine the impulse of an object by analyzing the corresponding force vs. time graph.  The student says that the slope of the graph represents the impulse of the object.  Is this student correct?  Explain why or why not.

No, the impulse would be the area under the curve.

Center of Mass

100

Write the formula for center of mass.

x_CM= (m₁x₁ + m₂x₂ + ...)/(m₁ + m₂ + ...)

200

Determine the location of the center of mass of a barbell with 125 kg on one end and 230 kg 1.5m away.

0.97m from the origin

300

Two particles A and B of equal mass are located at some distance from one another.  Particle A is at rest while Particle B moves away from A at speed v.  What happens to the center of mass of the system of two particles?

It moves away Particle A with speed (1/2)v

400

"Daily Double"

The team that chose this automatically gets 400 points.

The first team that correctly writes down the equation for the velocity of the center of mass will also get 400 points.

v_cm = (m₁v₁ + m₂v₂ + ...) /  (M_total)

500

To weigh a fish, a person hangs a tackle box of mass 4 kg and a cooler of mass 5 kg from the ends of a uniform rigid pole that is suspended by a rope attached to its center.  The system balances when the fish hangs at a point 1/4 of the rod's length from the tackle box.  What is the mass of the fish?

x_CM = L/2

(L/2) = [(4kg*0m) + (m*L/4) + (5kg*L)] / (4kg + m + 5kg)

(L/2) = [(mL/4) + 5L] / (9 + m)

... algebra...

m=2 kg

Random

100

Write out the equation for conservation of momentum in an inelastic collision.

m₁v₁ + m₂v₂ = (m₁ + m₂)v

200

Which situation will produce the greatest change of momentum for a 1.0-kilogram cart?

1. accelerating it from rest to 3.0 m/s
2. accelerating it from 2.0 m/s to 4.0 m/s
3. applying a net force of 5.0 N for 2.0 s
4. applying a net force of 10.0 N for 0.5 s

3. applying a net force of 5.0 N for 2.0s

300

Cart A has a mass of 2 kilograms and a speed of 3 meters per second. Cart B has a mass of 3 kilograms and a speed of 2 meters per second. Compared to the inertia and magnitude of momentum of cart A, cart B has

Cart B has more inertia and the same momentum as Cart A

400

A student says that in a collision between a truck and a car, the car experiences a greater force because the truck has more mass.  Is this student correct?  Explain why or why not.

No, they experience the same force because of Newton's Third Law.

500

An 84 kg student stands on the left end of a 240-kg log which is floating in the water (which you may treat as a frictionless surface). The student and the log are both initially at rest. The student then walks to the far end of the log at a constant speed of 2 m/s. 

1) As the student walks to the right, describe the motion of the log. Provide quantitative values wherever possible.

2) What is the velocity of the center of mass of the log and student?

1) m₁v₁ + m₂v₂ = m₁v₁ + m₂v₂

0 = (84kg*2m/s) + (240kg*v)

v = -0.7 m/s

The log moves to the left with a speed of 0.7 m/s.

2) v_CM = (m₁v₁ + m₂v₂)/m_total

v_cm = [(84kg*2m/s) + (240kg*-0.7m/s)] / (324kg)

v_CM = 0 m/s

(Initial velocity of the log and student was 0m/s, no external forces were applied, conservation of momentum)