Momentum and Collisions Review Chapter 6(all)

Overview Momentum (p=mv) Vector quantity of motion equal to an object’s mass times its velocity. Impulse (Dp=FDt)- is equal to the change in momentum Conservation of Momentum Since every action creates an EQUAL and opposite reaction (F12Dt= -F21Dt) 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 Velocity Vector Quantity Measured 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 FDt Newton’s Second Law: Originally written as F=Dp/Dt, 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 Dt and thus reducing the force on the driver in a car crash

Conservation of Momentum Momentum 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. v2f v1i v2i v1f m2 m1 m2 m1 Before Collision After Collision

Collisions Inelastic-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 Collisions When objects do not collide on the same path line, they make glancing collisions. To solve this type of problem, break it into components!! v1f v1i q f After Collision Before Collision v2f X: m1v1i = m1v1fcosq + m2v2fcosf Y: 0 = m1v1fsinq - m2v2fsinf

What are the two basic types of collisions? Elastic 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? HINT: not F=ma F= change in momentum = Dp time interval Dt

Why is it safer to bend your knees when you land from a relatively large height? HINT: F= Dp/Dt Bending your knees increases the time in which the impact occurs,thus reducing the force

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? mava+mbvb=(ma+mb)vfinal 0 + 2mv = (m+2m)vfinal Vfinal= 2/3 v

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

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

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

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

What are some examples of things that are designed to increase the Dt of an impact? Boxing Gloves, Cars, baseball gloves

Conservation of Momentum (in one dimension) m1v1i + m2v2i = m1v1f + m2v2f What does this equation demonstrate? Conservation of Momentum (in one dimension)

They experience the same force 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 force

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

Impulse is given by the formula: Impulse= FDt

Is momentum conserved in a glancing collision? Yes!!! It is conserved in both the x and y directions. Break problem into components to solve!

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

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

Explain why the fire-fighters experience a backwards 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 can project in the opposite direction. This is a good example of Newton’s third Law (action-reaction), but can also be explained in terms of conservation of momentum.

Is momentum a vector or scalar quantity? Vector. (So always pay attention to DIRECTION when working with momentum!)

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

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

What units are used to define momentum? 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=FDt =12x11=132 Ns Pinit=mv=66Ns Dp=impulse=132Ns Pfinal=pinit+Dp=198Ns vfinal=pfinal/m=3.0 m/s

An object experiences an impulse of 40. 51 N-s for a time period of 19 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 N Could you select the correct answer without a calculator? Estimate!! (answer ~40/20=2 only one answer is close to this)

A squid propels itself by expelling water at a high velocity A squid propels itself by expelling water at a high velocity. How is this possible? The squid increases the momentum of the water in the backward direction, therefore increasing the momentum of the squid in the forward direction

Four billiard balls, each of mass 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/s 2 kg m/s

Kinit=½(2)22+½(2)32=13Joules Kfinal=½22+½(2)12=5Joules 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. Kinit=½(2)22+½(2)32=13Joules Kfinal=½22+½(2)12=5Joules 8Joules of energy was lost.

24.5 m/s use m1v1i + m2v2i = (m1+ m2)vf 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 m1v1i + m2v2i = (m1+ m2)vf

A bat exerts a force on a ball of 100 N for a period of. 1 seconds 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=FDt=100(.1)=10 Ns

K = ½mv2  v=5m/s p = mv = 20 kg m/s What is the momentum of a 4.0 kg object that has a kinetic energy of 50 J? K = ½mv2  v=5m/s p = 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? Zero

They were moving with equal speeds in opposite directions 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 equal speeds in opposite directions Could you conclude the same thing if the cars were not of equal mass?