Question

Two cars with the same mass and the same acceleration collide (0:00 - 0:22)

Why do they move in different directions with the same acceleration after the collision? Explain using Newton’s Laws. (8 pts)

Answer 1

Answer:

Explanation:Momentum

How hard it is to stop a moving object.

Related to both mass and velocity.

For one particle

p = mv

For a system of multiple particles

P = pi = mivi

Units: N s or kg m/s

Momentum is a vector!

Problem: Momentum (1998)

43. The magnitude of the momentum of the

object is increasing in which of the cases?

(A) II only

(B) III only

(C) I and II only

(D) I and III only

(E) I, II, and III

Ans. Explain your reasoning:

Graph III is the only graph where acceleration is

happening (as evidenced by a curved d vs. t

graph). This means that a net force is being

applied to the object of mass m (by Newton’s

Second Law). In order for momentum to

increase, an impulse (J) needs to be applied (a

Force F over a period of time, t).

p = J = F t

Impulse (J)

The product of an external force and time, which

results in a change in momentum

J = F t

J = P

Units: N s or kg m/s

Problem: Impulse (1984)

56. Two planets have the same size, but different

masses, and no atmospheres. Which of the

following would be the same for objects with

equal mass on the surfaces of the two planets?

I. The rate at which each would fall freely

II. The amount of mass each would balance

on an equal-arm balance

III. The amount of momentum each would

acquire when given a certain impulse

(A) I only

(B) III only

(C) I and II only

(D) II and III only

(E) I, II, and III

Explain your reasoning:

Ans. The gravity would be different on both

planets because gravity depends both on the mass

of the planet and its radius. Since gravity is

different on each planet, they would not fall at the

same rate. But if you put both masses on opposite

sides of an equal-arm balance they would balance

since the masses are equal. Also, since they have

the same mass, the same amount of impulse (J =

F t) should produce the same results. In terms of

momentum increase.

Problem: Impulse (1998)

57. A ball of mass 0.4 kg is initially at rest on the

ground. It is kicked and leaves the kicker's foot

with a speed of 5.0 m/s in a direction 60° above

the horizontal. The magnitude of the impulse

imparted by the ball to the foot is most nearly

(A)

(B)

(C)

(D)

(E)

Show your work:

Ans. The impulse is simply J = mv. The

mass is 0.4 kg and the speed is 5.0 m/s. J = 0.4

kg  5.0 m/s = 2 Ns. The angle is irrelevant

here.

1 Ns

3 N s

2 N s

2

3

Ns

4 N s

1/29/2018 Momentum-2 Krummell

Law of Conservation of Momentum

If the resultant external force on a system is zero,

then the momentum of the system will remain

constant.

The sum of the momentums before a collision is

equal to the sum of the momentums after a

collision.

Pb = Pa

Problem: Conservation of Momentum

(1998)

4. An open cart on a level surface is rolling without

frictional loss through a vertical downpour of

rain, as shown above. As the cart rolls, an

appreciable amount of rainwater accumulates in

the cart. The speed of the cart will

(A) increase because of conservation of

momentum

(B) increase because of conservation of

mechanical energy

(C) decrease because of conservation of

momentum

(D) decrease because of conservation of

mechanical energy

(E) remain the same because the raindrops

are falling perpendicular to the direction

of the cart's motion

Explain your reasoning:

Ans. Mechanical energy is not conserved, in

general. Total energy is, but mechanical energy is

not. Momentum is ALWAYS conserved! So,

suppose you had a cart that has a mass of 10kg

moving at 5 m/s. It has momentum of 50 kg*m/s.

Since friction does not act, the momentum will

remain 50kg*m/s (Newton's law). Suppose at

some later time it has filled up with 10kg of rain,

so now the cart has a mass of 20kg. It still has the

50kg*m/s of momentum, so it must be moving at

2.5m/s, which means it has decreased due to

conservation of momentum.

Collisions

Follow Newton’s Third Law which tells us that

the force exerted by body A on body B in a

collision is equal and opposite to the force

exerted on body B by body A.

During a collision, external forces are ignored.

The time frame of the collision is very short.

The forces are impulsive forces (high force, short

duration).

Collision Types

Answer 2

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