PH212 Lecture 2: Chapter-6-Momentum

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olivedeer219

25 Dec 2018

School

Benjamin Franklin Institute of Technology

Department

Physics

Course

PH212

Professor

Jones

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CHAPTER 6 – MOMENTUM & COLLISIONS

6.1 – MOMENTUM AND IMPULSE

What is momentum?

p = m v = mass x velocity

Vector quantity

What is the SI unit for momentum?

kg x m/s

A 2250 kg truck has velocity of 25 m/s to east. What is its momentum?

p = m v

= 2250 kg  25 m/s

= 5.6x104 kgm/s to the east

True or False: An object with a small mass has less momentum than an object with a large

mass, but same velocity.

False; the object with the bigger mass has more momentum because the velocity is the same

True or False: A small mass object with a large velocity has the same momentum as a large

mass object with a small velocity

True

To change momentum of object, a ____ must be exerted on object over some period of _____

Force, time.

F = ma = ∆p

∆t

What is impulse?

The change of an object’s momentum and

The force applied to an object times the duration of time it was applied (F∆t)

What is the Impulse-Momentum Theorem?

F ∆t = ∆p = mvf - mvi

units kgm/s

Longer applied force in contact with object, the _____resulting change in momentum

Larger

For given stopping force and object velocity what takes longer to stop, heavier objects or

lighter?

Heavier

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Hitting a Baseball

Before

After

p

What is p?

= pf- pi

Impulse = Ft

What has more of an impulse, an object that crashes or an object that bounces?

An object that bounces

In an impulse problem, when asked how far a car travels, use formula:

∆x = ½ (vi + vf) ∆t

Compute ∆t from impulse-momentum

Know velocities, can get ∆x

A 1440 kg car with velocity 15 m/s to west collides with pole & comes to rest in 0.30 s. Force

during collision?

F = Dp / Dt = m(vf – vi) / Dt

= 1400 kg (0 m/s – (-15 m/s)) / 0.30 s

= 7.0 x104 N (to east)

If a truck 1 is traveling at the same velocity as truck 2, but has twice the mass, how much

longer will it take for truck 1 to stop?

Two times longer

What is the most important factor is collisions?

The time it takes person to come to rest

Longer times reduce chance of dying

How are air bags life savers?

Air bag increases time of collision and absorbs some energy from body

You drop egg onto:

1) floor 2) thick piece of foam rubber

In both cases, egg does not bounce

In which case is impulse greater?

A) Floor

B) Foam

C) the same

Answer: C

I = ∆P due to same change in momentum

In which case is average force greater?

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A) Floor

B) Foam

C) the same

Answer: A

∆p = F ∆t

F = ∆p / ∆t

Smaller ∆t = large F

Is impulse a vector or scalar quantity?

Vector

If 2 objects have same KE, is magnitude of the momentum equal?

KE1 = ½ m1v12 = KE2 = ½ m2v22

m1v1 = p1= p1 m2v2 = p2= p2

m1v1v1 = m2v2v2 = p1v1 = p2v2

p1= p2(v2/v1)

No, they are not same unless v1=v2

If v2 is greater than v1, slower object (1) has greater momentum

6.2 – CONSERVATION OF MOMENTUM

What is the conservation of momentum theory?

In a collision there is transfer of momentum and even though each ball’s momentum changes, total

momentum remained constant.

(only when no external forces act on system which we assume in book)

m1v1,i+m2v2,i = m1v1,f + m2v2,f

(initial momentum = final momentum)

What is a collision?

Isolated event in which 2 or more bodies (the colliding bodies) exert relatively strong forces on

each other for a relatively short time

 Only holds true for closed (no mass enters or leaves) and isolated (no external forces)

systems

In a collision, is ∆t the same for both bodies?

Yes

What is the center of mass?

Position at which an extended object’s mass can be treated as point mass

Is the motion of the center of mass of the system only altered by any forces?

Only if they are external to the system

 Collisions of multiple objects & explosion of an object have only internal forces acting so

motion of center of mass is the same before and after event

In collision does momentum remain constant?

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Document Summary

What is momentum? p = m v = mass x velocity. What is the si unit for momentum? kg x m/s. A 2250 kg truck has velocity of 25 m/s to east. True or false: an object with a small mass has less momentum than an object with a large mass, but same velocity. False; the object with the bigger mass has more momentum because the velocity is the same. True or false: a small mass object with a large velocity has the same momentum as a large mass object with a small velocity. To change momentum of object, a ____ must be exerted on object over some period of _____ The force applied to an object times the duration of time it was applied (f t) F t = p = mvf - mvi. Longer applied force in contact with object, the _____resulting change in momentum. In an impulse problem, when asked how far a car travels, use formula:

Related Questions

Kinetic energy KE has dimensions kg · m²/s². It can be written in terms of the momentum p (Topic 6) and mass m as

$KE= \frac{p^{2}}{2 m}$

(a) Determine the proper units for momentum using dimensional analysis. (b) Refer to Problem 5. Given the units of force, write a simple equation relating a constant force F exerted on an object, an interval of time t during which the force is applied, and the resulting momentum of the object, p.

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champagnereindeer524

Object A collides on a horizontal frictionless surface with an initially stationary target, object X. The initial and final velocities of object A are shown. The final velocity of object X is not given.

a). At an instant during the collision, is the net force on object A zero or non-zero?

b) [During the collision, is the momentum of object A conserved? Explain. Is the momentum of the system consisting of objects A and X conserved? Explain. On the same horizontal surface, object C collides with an initially stationary target, object Z. The initial speeds of objects C and A are the same, and m_x = m_z > m_A = m_c. After the collisions, object C moves in the direction shown and has the same final speed as object A. In the space below, copy the vectors v_C1 and v_cr with their tails together. Use these vectors to draw the change in velocity vector for glider C, Delta v_c. Is the magnitude of the change in velocity vector of object A greater than, less than, or equal to the magnitude of the change in velocity vector of object C? Explain? Is the magnitude of the change in the momentum vector of object A greater than, less than, or equal to the magnitude of the change in the momentum vector of object C? Explain? Is the final speed of object X greater than, less than, or equal to the final speed of object Z? Explain. Consider the following incorrect statement: Gliders A and C have some change in momentum. They have the same mass, and because they have the same initial speed and same final speed. Delta-v is the same for each of.them." Discuss the error(s) in the reasoning.

sangriaporcupine175

which of the vectors below best represents the direction of the impulse vector j⃗ ?

To learn about the impulse-momentum theorem and its applications in some common cases.

Using the concept of momentum, Newton's second law can be rewritten as

?F? =dp? dt, (1)

where ?F? is the net force F? net acting on the object, and dp? dt is the rate at which the object's momentum is changing.

If the object is observed during an interval of time between times t1 and t2, then integration of both sides of equation (1) gives

?t2t1?F? dt=?t2t1dp? dtdt. (2)

The right side of equation (2) is simply the change in the object's momentum p2??p1?. The left side is called the impulse of the net force and is denoted by J? . Then equation (2) can be rewritten as

J? =p2??p1?.

This equation is known as the impulse-momentum theorem. It states that the change in an object's momentum is equal to the impulse of the net force acting on the object. In the case of a constant net force F? net acting along the direction of motion, the impulse-momentum theorem can be written as

F(t2?t1)=mv2?mv1. (3)

Here F, v1, and v2 are the components of the corresponding vector quantities along the chosen coordinate axis. If the motion in question is two-dimensional, it is often useful to apply equation (3) to the x and y components of motion separately.

( The following questions will help you learn to apply the impulse-momentum theorem to the cases of constant and varying force acting along the direction of motion. First, let us consider a particle of mass m moving along the x-axis. The net force F is acting on the particle along the x-axis. F is a constant force.)

A) The particle starts from rest at t=0. What is the magnitude p of the momentum of the particle at time t? Assume that t>0.

B) The particle starts from rest at t=0. What is the magnitude v of the velocity of the particle at time t? Assume that t>0.

C) The particle has the momentum of magnitude p1 at a certain instant. What is p2, the magnitude of its momentum ?t seconds later?

D) The particle has the momentum of magnitude p1 at a certain instant. What is v2, the magnitude of its velocity ?t seconds later?

E) Find the magnitude of the impulse J delivered to the particle.

F) Which of the vectors below best represents the direction of the impulse vector J??
(Figure 1)

1
2
3
4
5
6
7
8

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PH212 Lecture 2: Chapter-6-Momentum

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