Momentum and Collisions Review

Chapter 6(all)

OverviewMomentum (p=mv) Vector quantity of motion equal to an object’s mass

times its velocity.

Impulse (p=Ft)- is equal to the change in momentum

Conservation of Momentum Since every action creates an EQUAL and opposite reaction (F12t= -F21t) the total momentum in an isolated system is constant. pinit=pfinal

Collisions-(recognize and give examples of each)

Elastic (both momentum & kinetic energy conserved)

Inelastic (momentum conserved, kinetic energy is not)

Perfectly Inelastic (two objects collide & stick together)

Linear Momentum

Mass x VelocityVector QuantityMeasured in Kg x m/s, direction matches

velocity

Object A, with mass a moves to the right at velocity a

Object A has a momentum of mava

Impulse

Defined as: change in momentum, also Ft

Newton’s Second Law: Originally written as F=p/t, instead of F=ma

Force x Time Graph: On a F x T graph the area between the graph and the x-axis is the impulse.

Reducing Impulse: To reduce force of impact, cars are designed to crumple like an accordion, increasing t and thus reducing the force on the driver in a car crash

Conservation of MomentumMomentum is always conserved: m1v1i + m2v2i = m1v1f +

m2v2f

The total momentum of an isolated system of objects is conserved regardless of the nature of the forces between the objects.

v1i v2im1

m2

Before Collision

m1 m2v1f

v2f

After Collision

CollisionsInelastic-Example: A rubber ball collides with a hard

surface, kinetic energy is lost because ball is deformed during contact with the surface transforming some of the energy into heat.

Elastic-(m1v1i + m2v2i = m1v1f + m2v2f) Example: Billiard balls collide without losing any of their energy.

Perfectly Inelastic- (m1v1i + m2v2i=(m1+m2)vf) (two objects stick together creating single mass) Two snowballs collide, and create one larger snowball and final velocities of snowballs are the same.

Explosions- Something flies apart into two or more pieces. (mvo=m1v1+m2v2) Of course, m1 and m2 will add up to the original mass.

Glancing CollisionsWhen objects do not collide on the same path line, they

make glancing collisions.

To solve this type of problem, break it into components!!

v1i

v2f

v 1f

Before Collision

After Collision

X: m1v1i = m1v1fcos + m2v2fcos

Y: 0 = m1v1fsin - m2v2fsin

What are the two basic types of collisions?

Elastic and InelasticElastic and Inelastic

Explain the formula p=mv, describe what each variable is

Momentum is equal to the mass of the object times the velocity, p=momentum m=mass v=velocity

What was Newton’s second law originally expressed as?

F= F= change in momentum change in momentum = = pp

time intervaltime interval tt

HINT: not F=ma

Why is it safer to bend your knees when you land from a relatively large height?

Bending your knees Bending your knees increases the time in which increases the time in which the impact occurs,thus the impact occurs,thus reducing the force reducing the force

HINT: F= p/t

If ball a is stationary and has a mass of m, what will it’s velocity be when it is hit by ball b (mass 2m, velocity v) assuming a perfectly inelastic collision?

mmaavvaa+m+mbbvvbb=(m=(maa+m+mbb)v)vfinalfinal

0 + 2mv = (m+2m)v0 + 2mv = (m+2m)vfinalfinal

VVfinalfinal= 2/3 v= 2/3 v

The total momentum of an isolated system of objects is _________ regardless of the nature of the forces between the objects.

ConservedConserved

An _________ collision is one in which both momentum and kinetic energy are conserved

ElasticElastic

An __________ collision is one in which momentum is conserved but kinetic energy is not

InelasticInelastic

What is indicated by the area under a graph of force vs. time?

ImpulseImpulse

What are some examples of things that are designed to increase the t of an impact?

Boxing Gloves, Cars, Boxing Gloves, Cars, baseball glovesbaseball gloves

mm11vv1i1i + m + m22vv2i2i = m = m11vv1f1f + m + m22vv2f2f

What does this equation demonstrate?

Conservation of Conservation of Momentum (in one Momentum (in one dimension)dimension)

If a 3000 kg object traveling at 22 m/s collides with a 60 kg object traveling the opposite direction at 30 m/s, which object experiences the most force?

They experience the same They experience the same forceforce

In golf, novice players are often advised to be sure to “follow through” with their swing. Why does this make the ball travel a longer distance?

Following through allows the Following through allows the club to remain in contact with club to remain in contact with the ball longer. This means the ball longer. This means the ball experiences a greater the ball experiences a greater impulse which results in a impulse which results in a larger change of its larger change of its momentum.momentum.

Impulse is given by the formula:

Impulse= FImpulse= Ft t

Is momentum conserved in a glancing collision?

Yes!!! It is conserved in Yes!!! It is conserved in both the x and y both the x and y directions. Break problem directions. Break problem into components to solve!into components to solve!

Momentum is conserved in all collisions when no _____________ are acting.

External ForcesExternal Forces

The time rate of change of momentum of an object is equal to the ____________ acting on the object

Net ForceNet Force

When holding a hose fire-fighters need to ensure that they are not pushed backwards, especially if the water is ejected at a high speed.

Explain why the fire-fighters experience a backwards force.

The water is pushing against the firefighters so that it The water is pushing against the firefighters so that it can project in the opposite direction. This is a good can project in the opposite direction. This is a good example of Newton’s third Law (action-reaction), but example of Newton’s third Law (action-reaction), but can also be explained in terms of conservation of can also be explained in terms of conservation of momentum. momentum.

Is momentum a vector or scalar quantity?

Vector. (So always pay Vector. (So always pay attention to DIRECTION attention to DIRECTION when working with when working with momentum!)momentum!)

Which has more momentum; a semi-truck or a Mini Cooper, if they are both going 10 mph?

The semi-truckThe semi-truck

Which has more momentum; a parked semi-truck or a Mini Cooper moving at 10 mph?

The Mini CooperThe Mini Cooper

What units are used to define momentum?

Kg m/s (also N s)Kg m/s (also N s)

If a force of 12 N is applied to a 66 kg object for 11 seconds, what is the impulse?

If the object was originally traveling in the positive direction at 1.0 m/s, what is its speed at the end of this time?

Impulse=Ft =12x11=132 Ns

Pinit=mv=66Ns

p=impulse=132Ns

Pfinal=pinit+p=198Ns

vfinal=pfinal/m=3.0 m/s

An object experiences an impulse of 40.51 N-s for a time period of 19.32 s. What was the average force on the object during this time?

A) 782.65 N B) 0.47 N C) 0.62 N D) 3.76 N E) 2.09 N

E) 2.09 NE) 2.09 N

Could you select the correct answer Could you select the correct answer without a calculator? Estimate!! (answer without a calculator? Estimate!! (answer ~40/20=2 only one answer is close to this)~40/20=2 only one answer is close to this)

A squid propels itself by expelling water at a high velocity. How is this possible?

The squid increases the The squid increases the momentum of the water in momentum of the water in the backward direction, the backward direction, therefore increasing the therefore increasing the momentum of the squid in momentum of the squid in the forward directionthe forward direction

Four billiard balls, each of mass .5 kg, all are traveling in the same direction on a billiard table, with speeds 2 m/s, 4 m/s, 8 m/s and 10 m/s. What is the linear momentum of this system?

What is the linear momentum if the last ball was traveling in the OPPOSITE direction at 10m/s?

12 kg m/s12 kg m/s2 kg m/s2 kg m/s

Two balls, each with mass 2 kg, and speeds of 2 m/s and 3 m/s collide head on. They rebound at speeds of 2 m/s and 1 m/s, respectively. Is this collision elastic or inelastic?

Inelastic. Inelastic. KKinitinit=½(2)2=½(2)222+½(2)3+½(2)322=13Joul=13JoulesesKKfinalfinal=½2=½222+½(2)1+½(2)122=5Joules=5Joules8Joules of energy was lost.8Joules of energy was lost.

A car of 500 kg, traveling at 30 m/s rear ends another car of 600 kg, traveling at 20 m/s. in the same direction The collision is great enough that the two cars stick together after they collide. How fast will both cars be going after the collision?

24.5 m/s use 24.5 m/s use mm11vv1i1i + m + m22vv2i2i = (m = (m11+ m+ m22)v)vff

A bat exerts a force on a ball of 100 N for a period of .1 seconds. What is the impulse provided by the bat?

Impulse=FImpulse=Ft=100(.1)=10 t=100(.1)=10 NsNs

What is the momentum of a 4.0 kg object that has a kinetic energy of 50 J?

K = ½mvK = ½mv22 v=5m/s v=5m/sp = mv = 20 kg m/sp = mv = 20 kg m/s

What is the linear momentum of a system of two particles with equal mass m traveling in opposite directions with speed v?

ZeroZero

Two cars of equal mass collide head on and both come to a stop. What can be said about the cars before the crash?

They were moving with They were moving with equal speeds in opposite equal speeds in opposite directionsdirectionsCould you conclude the same thing if the

cars were not of equal mass?