Momentum Physics
perfect inelastic collisions:
two objects collide, stick together and move as one mass after the collision, transferring some of the kinetic energy into other forms of energy.
for all elastic collisions - independent of each object's mass - the magnitude of the relative velocity of the objects is ........................
the same before and after the collision.
from p(0) - · by deltap - · to p(f) - The equation for momentum change is:
the initial momentum (just before the event) the change in momentum the final momentum (just after the event) P(0) +deltap = p(f)
F, in car air bags, represents the
Force delivered to the passenger due to the accident.
explosion equation
(A m + B m) v = A mv (prime) + B mv (prime)
Determine the momentum of a system of two objects: m1, has a mass of 6 kg and a velocity of 13 m/s towards the east and m2, has a mass of 14 kg and a velocity of 7 m/s towards the west.
-20 kgm/s
perfect inelastic collision formula
A mv + B mv = (A m + B m) v (prime)
conservation of momentum equation
A mv + B mv =A mv (prime) + B mv (prime)
elastic equation conservation of momentum conservation of KE
A p + B p = A p (prime) + B p (prime) A mv + B mv =A mv (prime) + B mv (prime) A KE + B KE = A KE (prime) + B KE (prime) A 1/2mv^2 + B 1/2mv^2 = A 1/2mv^2 (prime) + B 1/2mv^2 (prime)
From which law or principle is the Impulse-Momentum equation derived from? A Conservation of Energy. B Newton's First Law. C Newton's Second Law. D Conservation of Momentum. E I need help
C
If there is no net external force on the system, then __________, and since _____________, I = ____________
F = 0 I = FΔt I = 0
momentum with newton's first law delta p =
F times delta t
Impulse-Momentum equation:
I = F delta t = delta p
A good example of a collision of the same mass particles
The cue ball and the striped and solid balls are all the same mass.
Why don't the internal forces of a system change the momentum of the system?
The internal forces result from the interaction of the objects within the system. By Newton's Third Law, these are all action-reaction pairs, and viewed from outside the system, all cancel out. There is no net force acting on the system and the momentum is conserved.
explosions:
an object or objects breaks apart because potential energy stored in one or more of the objects is transformed into kinetic energy.
Conservation laws: · apply to _____________systems - where the objects only ................................................. · enable us to solve problems without worrying about the __________ of an event.
closed, interact with each other and nothing else details
momentum is a ________________property of nature.
conserved
During a collision or an explosion, measurements show that the total momentum of a closed system .........................
does not change.
momentum of an object changes when it experiences an ____________________ a ___________________ occurs when a ....................................
impulse non-zero external force acts on the object. p(0) + I = p(f)
general inelastic collisions:
two objects collide and bounce off each other, transferring some of the kinetic energy into other forms of energy.
Newton's First Law tells us that
objects remain in motion with a constant velocity unless acted upon by an external force (Law of Inertia).
symbol for momentum
p
when I = 0, _____________________ Since psystem, 0 = psystem, f, the momentum of the system is _____________, that is, it does not change.
p(0) = p(f) conserved
Car Air Bags: seat belt vs. air bag with increasing time
-seat belt increases time interval that it takes a passenger to slow down -air bag will increase that time interval much more than the seat belt by rapidly expanding, letting the passenger strike it, then deflating.
There is a bowling ball (m1) with momentum 20.0 kg-m/s that strikes a stationary bowling pin (m2) and then the bowling ball and pin take off as shown above. What is the final momentum of the pin? page 164 for picture
17.4 kgm/s at 37 degrees south of east
What is the momentum of a 20 kg object moving to the right with a velocity of 5 m/s? A 4 kgm/s B 5 kgm/s C 20 kgm/s D 100 kgm/s E I need help
D
mass is a __________quantity · velocity is a _____________quantity · the product of a ___________ and a _______________is a ____________
scalar vector vector
A 50,000 N force acts for 0.030 s on a 2.5 kg object that was initially at rest. What is its final velocity? A 600 m/s B 1200 m/s C 1400 m/s D 1800 m/s E I need help
A
A tennis ball of mass m strikes a wall at an angle θ relative to normal then bounces off with the same speed as it had initially. What is the change in momentum of the ball in the y direction? A 0 B -2mv C -mv cosθ D -2mv cosθ E I need help page 191
A
Kinetic Energy is conserved in which of the following situations (assume no external forces)? A Elastic collisions only. B Inelastic collisions only. C Explosions only. D Elastic and Inelastic collisions and explosions. E I need help
A
Object A with mass 20.0 kg travels to the east at 10.0 m/s and object B with mass 5.00 kg travels south at 20.0 m/s. They collide and stick together. What is the velocity (magnitude and direction) of the objects after the collision? A 8.9 m/s 26.6o South of East B 5.4 m/s 34.9o East of South C 3.4 m/s 49.2o North of East D 2.1 m/s 55.8o South of East
A
What is the mass of an object that has a momentum of 35 kg-m/s with a velocity of 7 m/s? A 5 kg B 7 kg C 15 kg D 21 kg E I need help
A
What is the velocity of a 5 kg object whose momentum is -15 kg-m/s? A -3 m/s B -5 m/s C -15 m/s D -60 m/s E I need help
A
Which object or objects have the greatest momentum? A A large trailer truck moving at 30 m/s. B A motorcycle moving at 30 m/s. C The Empire State Building. D Choices A and B have the same momentum. E I need help
A
There is a battery powered wheeled cart moving towards you at a constant velocity. You want to apply a force to the cart to move it in the opposite direction. Which combination of the following variables will result in the greatest change of momentum for the cart? Select two answers. A Increase the applied force. B Increase the time that the force is applied. C Maintain the same applied force. D Decrease the time that the force is applied. E I need help
A, B
In order to increase the final momentum of a golf ball, the golfer should: Select two answers: A maintain the speed of the golf club after the impact (follow through). B Hit the ball with a greater force. C Decrease the time of contact between the club and the ball. D Decrease the initial momentum of the golf club. E I need help
A,B
A 1200 kg car slows from 40.0 m/s to 5.0 m/s in 2.0 s. What force was applied by the brakes to slow the car? A -13,000 N B -21,000 N C -48,000 N D -55,000 N E I need help
B
A 40 kg girl skates at 5.5 m/s on ice toward her 70 kg friend who is standing still, with open arms. As they collide and hold each other, what is their speed after the collision? Answer A 1.0 m/s B 2.0 m/s C 4.0 m/s D 5.0 m/s E I need help
B
A 5.0 kg bowling ball strikes a stationary bowling pin. After the collision, the ball and the pin move in directions as shown and the magnitude of the pin's momentum is 18 kg-m/s. What was the velocity of the ball before the collision? A 3.0 m/s B 4.5 m/s C 5.0 m/s D 6.0 m/s E I need help
B
A baseball bat has a velocity of +v when it elastically collides with a baseball that has a velocity of -2v. The bat barely changes velocity during the collision. How fast is the baseball going after it's hit? A 3 v B 4 v C 7 v D 8 v E I need help
B
A cannon ball with a mass of 100.0 kg flies in horizontal direction with a speed of 250 m/s and strikes a ship initially at rest. The mass of the ship is 15,000 kg. Find the speed of the ship after the ball becomes embedded in it. A 1.3 m/s B 1.7 m/s C 2.0 m/s D 2.4 m/s E I need help
B
A golf ball is hit against a solid cement wall, and experiences an elastic collision. The golf ball strikes the wall with a velocity of +35 m/s. What velocity does it rebound with? A -70 m/s B -35 m/s C 35 m/s D 70 m/s E I need help
B
Air bags are used in cars because they: A increase the force with which a passenger hits the dashboard. B increase the duration (time) of the passenger's impact. C decrease the change in momentum of a collision. D decrease the impulse in a collision. E I need help
B
The momentum change of an object is equal to the ______. A force acting on the object. B impulse acting on the object. C velocity change of the object. D object's mass times the force acting it. E I need help
B
Two objects with identical masses have an elastic collision: the initial velocity of m1 is +6 m/s and m2 is -3 m/s. What is the velocity of m1 after the collision? A -6 m/s B -3 m/s C 3 m/s D 6 m/s E I need help
B
Two railcars, one with a mass of 4000 kg and the other with a mass of 6000 kg, are at rest and stuck together. To separate them a small explosive is set off between them. The 4000 kg car is measured travelling at 6 m/s. How fast is the 6000 kg car going? A -10 m/s B -4 m/s C +4 m/s D +10 m/s E I need help
B
Using the F-t graph shown, what is the change in momentum during the time interval from 0 to 6.0 s? A 100 Ns B 135 Ns C 150 Ns D 165 Ns E I need help page 66 has graph on powerpoint
B
Using the F-t graph shown, what is the change in momentum during the time interval from 6.0 to 10 s? A 30 Ns B 50 Ns C 60 Ns D 75 Ns E I need help page 70 has graph on powerpoint
B
Determine the momentum of a system of two objects: the first has a mass of 8.0 kg and a velocity of 8.0 m/s to the east while the second has a mass of 5.0 kg and a velocity of 15 m/s to the west. A -22 kg m/s B -11 kg m/s C +11 kg m/s D +22 kg m/s
B west
An external, positive force acts on a system of objects. Which of the following are true? Select two answers. AThe velocity of the system remains the same. BThe velocity of the system increases. C The momentum of the system decreases. D The momentum of the system increases. E I need help
B, D
If a car is in a front end collision, which of the below factors will help reduce the injury to the driver and passengers? Select two answers. A An absolutely rigid car body that doesn't deform. B Deployment of an air bag for each adult in the car. C Deployment of an air bag only for the driver. D The proper wearing of a seatbelt or child seat for each person in the car. E I need help
B, D
One car crashes into a concrete barrier. Another car crashes into a collapsible barrier at the same speed. What is the difference between the two crashes? Select two answers. A change in momentum B force on the passengers C impact time on the passengers D final momentum E I need help
B,C
What is the momentum of a 20 kg object moving to the left with a velocity of 5 m/s? A -4 kgm/s B -5 kgm/s C -20 kgm/s D -100 kgm/s E I need help
D
A 13,500 kg railroad freight car travels on a level track at a speed of 4.5 m/s. It collides and couples with a 25,000 kg second car, initially at rest and with brakes released. No external force acts on the system. What is the speed of the two cars after the collision? A 0.40 m/s B 0.80 m/s C 1.6 m/s D 3.2 m/s E I need help
C
A 5.0 kg object with an initial velocity of 3.0 m/s experiences the force shown in the graph. What is its velocity at 6.0 s? A 15 m/s B 18 m/s C 30 m/s D 32 m/s E I need help page 67 has graph on powerpoint
C
A stationary 10.0 kg bomb explodes into three pieces. A 2.00 kg piece moves west at 200.0 m/s. Another piece with a mass of 3.00 kg moves north with a velocity of 100.0 m/s. What is the velocity (speed and direction) of the third piece? A 50 m/s -22.6o North of South B 500 m/s -29.7o South of East C 100 m/s -36.9o South of East D 350 m/s -44.3o South of East E I need help
C
Two objects have an elastic collision. Object m1 is to the left of m2 with an initial velocity of +6 m/s and m2 has a velocity of +2 m/s. After the collision, m1 has a velocity of +1 m/s. What is the velocity of m2? A 2 m/s B 3 m/s C 5 m/s D 6 m/s E I need help
C
Which of the following variables are fixed, using the Impulse - Momentum equation, when analyzing a moving car that strikes a barrier and comes to rest? A Force delivered to the passengers. B Interval of time before the passengers come to rest. C Momentum change of the car. D Acceleration of the passengers within the car. E I need help
C
In an inelastic collision, kinetic energy can be transformed into what after the collision? Select two answers. A Nothing, kinetic energy is conserved. B More kinetic energy. C Thermal energy. D Light energy. E I need help
C, D
A 5 kg cannon ball is loaded into a 300 kg cannon. When the cannon is fired, it recoils at -5 m/s. What is the cannon ball's velocity after the explosion? A 60 m/s B 90 m/s C 180 m/s D 300 m/s E I need help
D
A bowling ball, with a velocity of +v, collides with a ping pong ball at rest. The velocity of the bowling ball is virtually unaffected by the collision. What will be the velocity of the ping pong ball? A -2v B -v C +v D +2v E I need help
D
A tennis ball of mass m strikes a wall at an angle θ relative to normal then bounces off with the same speed as it had initially. What is the change in momentum of the ball in the x direction? A 0 B -2mv C -mv cosθ D -2mv cosθ E I need help page 189
D
An external force acts on an object for 0.0020 s. During that time the object's momentum increases by 400 kg-m/s. What was the magnitude of the force? A 8,000 N B 25,000 N C 40,000 N D 200,000 N E I need help
D
An external force of 25 N acts on a system for 10.0 s. The impulse delivered was 250 N-s. What is the magnitude of the change in momentum of the system? A 10 Ns B 25 Ns C 50 Ns D 250 Ns E I need help
D
An external force of 25 N acts on a system for 10.0 s. What is the magnitude of the impulse delivered to the system? A 10 Ns B 25 Ns C 50 Ns D 250 Ns E I need help
D
In the absence of external forces, momentum is conserved in which of the following situations? A Elastic collisions only. B Inelastic collisions only. C Explosions only. D Elastic and Inelastic collisions and explosions. E I need help
D
Two objects have an elastic collision. Before they collide, they are approaching with a velocity of 4 m/s relative to each other. With what velocity do they move apart from one another after the collision? A 0 m/s B 1 m/s C 2 m/s D 4 m/s E I need help
D
Two objects have an elastic collision. Object m1, has an initial velocity of +4 m/s and m2 has a velocity of -3 m/s. After the collision, m1 has a velocity of 1 m/s. What is the velocity of m2? A -6 m/s B -1 m/s C 4 m/s D 8 m/s E I need help
D
Two objects with identical masses have an elastic collision: the initial velocity of m1 is +6 m/s and m2 is -3 m/s. What is the velocity of m2 after the collision? A -6 m/s B -3 m/s C 3 m/s D 6 m/s E I need help
D
Determine the momentum of a system of three objects: The first has a mass of 7.0 kg and a velocity of 23 m/s north; the second has a mass of 9.0 kg and a velocity of 7.0 m/s north; and the third has a mass of 5.0 kg and a velocity of 42 m/s south. A -14 kg m/s B -7.0 kg m/s C +7.0 kg m/s D +14 kg m/s E I need help
D north
Determine the momentum of a system of two objects: m1, has a mass of 6.0 kg and a velocity of 20 m/s north, and m2, has a mass of 3 kg and a velocity 20 m/s south. A -60 kg m/s B -30 kg m/s C +30 kg m/s D +60 kg m/s E I need help
D north
For the bat hitting a ball, we'll fix ___, vary ___and see the impact on ____.
F, Δt, Δp.
Collision with a Wall equations
Fxdelta t = px (prime) - px = -pcosx - (pcosx) = -2pcosx Fydelta t = py(prime) - py = psinx - psinx = 0
Momentum Change =
Impulse
The force acting over a period of time on an object is now defined as
Impulse
Explosion Description Momentum Conserved? Kinetic Energy Conserved?
Object or objects break apart yes No. Release of potential energy increases kinetic energy
General Inelastic Collision Description Momentum Conserved? Kinetic Energy Conserved?
Objects bounce off each other yes No. Kinetic energy is converted to other forms of energy
Elastic Collision Description Momentum Conserved? Kinetic Energy Conserved?
Objects bounce off each other yes yes
Perfect Inelastic Collision Description Momentum Conserved? Kinetic Energy Conserved?
Objects stick together yes No. Kinetic energy is converted to other forms of energy
Can the impulse applied to an object be negative? Why or why not? Give an example to explain your answer.
Yes, since Impulse is a vector quantity, it has magnitude and direction. Direction can be described as negative or positive. Imagine a baseball is thrown in the positive direction and you catch it with a baseball glove. The glove changes the baseball's momentum from positive to zero - hence applying a negative impulse to the ball.
By taking the _________under a Force-time graph, we have found both Impulse and Δp. If the force is not constant, the ____________can be found by breaking it into solvable shapes (rectangles, triangles) and summing them up.
area, area
Δp is fixed, for car air bags because Since Δp is fixed, by extending the time interval (Δt increases) that it takes a passenger to come to rest (seat belt and air bag), the force, F delivered to the passenger is ___________-. __________force on the passenger means ___________physical harm. By increasing the area of the body that feels the force (the air bag is big), ____________pressure is delivered to parts of the body - reducing the chance of puncturing the body.
as long as the passenger remains in the car, the car (and the passengers) started with a certain velocity and finished with a final velocity of zero, independent of seat belts or air bags. smaller less less
force is _________________ proportional to Δt changing Δt of a given impulse by a small amount can ............................
inversely greatly change the force exerted on an object
In both an inelastic collision and an explosion, energy _______________ between kinetic and potential energy. But they are ________________________! An inelastic collision transforms ____________ into other forms of energy, such as _______________________ An explosion changes ______________ into _________________ Thus, the equations to predict their motion will be ______________.
changes, time reversed KE into PE PE into KE inverted
In an isolated system both momentum and total energy are ____________. But the _____________can change from one form to another. ______________________ and ___________________ predict what will happen in these events.
conserved , energy Conservation of momentum and change in kinetic energy
Momentum is not ......................................... · The total momentum in a closed system is always the ________. · The only way the momentum of a system can change is if momentum is _______________________________________________-
created or destroyed. same added or taken away by an outside force
Since momentum is a vector, you need to specify a _____________-
direction such as to the right, up, down, to the east, or use positive (to the right) or negative (to the left), or any direction that is relevant to the problem.
A cart with a compressed spring is a good example. When the spring is against a wall, and it is released, the cart starts moving - converting elastic potential energy into kinetic energy and sound. an example of .................
explosion
A firecracker is an example of an ____________________. The chemical potential energy inside the firecracker is transformed into ................................
explosion KE, light and sound
deltap is related to the
external force.
Impulse SI unit
force x time (Ns) end up equaling kg⋅m/s
SI unit for momentum
kg⋅m/s
momentum =
mass × velocity p =mv
When objects of different mass travel with the same velocity, the one with __________ _______ is harder to stop. When objects of equal mass travel with different velocities, the ___________ one is harder to stop.
more mass faster one
Conservation of Momentum is used to explain and predict the _____________of a system of objects. As with energy, it will only be necessary to compare the system at two times: ..................................
motion just before and just after an event
Perfect Inelastic Collisions in Two Dimensions p-conservation in x and y: final momentum final velocity final direction
p1x = px (prime) p2y = py (prime) p (prime) = square root of px (prime) squared + py(prime) squared v (prime) = p (prime)/ m1 +m2 theta = tan -1 (py (prime)/ px (prime))
There is really no such thing as a ....................................During all collisions, some ___________ is always transformed into other forms of energy.But some collisions transform so little energy away from kinetic energy that they can be dealt with as ....................................
perfect elastic collision KE perfect elastic collisions.
In chemistry, the collisions between molecules and atoms are modeled as............................................. to derive the Ideal Gas Law.
perfect elastic collisions
There are two types of Inelastic Collisions.
perfect inelastic general inelastic
A common perfect inelastic collision is where two cars collide and stick at an intersection. The cars are traveling along paths that are ________________ just prior to the collision.
perpendicular
Conservation of Momentum in Two Dimensions means the conservation equation can be solved independently for each component
px = px (prime) py = py(prime)
explosion in two dimensions before and after equations
px = py = 0 p'1x + p'2x + p'3x = 0 p'1y + p'2y + p'3y = 0
two spheres colliding with each other and rebounding. If there are no external forces (this is a closed system), then the momentum before and after the collision is the _____________.
same
elastic collisions:
two objects collide and bounce off each other while conserving kinetic energy - energy is not transformed into any other type.
inelastic collisions:
two objects collide, converting some kinetic energy into other forms of energy such as potential energy, heat or sound.
Explosions in two dimensions During an explosion, the total momentum is ________________, since no external force acts on the system · By Newton's Third Law, the forces that occur between the particles within the object will add up to __________, so they don't affect the _____________. · If the initial momentum is _________, the final momentum is __________. · The third piece must have ____and ________momentum to the sum of the other two pieces.
unchanged zero, momentum zero equal and opposite
Using these equations, we will predict the motion of three specific cases, and relate them to observation: · Two equal mass particles collide. · A heavy particle collides with a light particle at rest. · A light particle collides with a heavy particle at rest.
v1 (prime) = (m1-m2/m1 +m2)v1 + (2m2/m1+m2)v2 v2 (prime) = (2m1/m1+m2)v1 + (m2-m1/m1+m2)v2
Collision of same mass particles
v1 (prime) = v2 v2(prime) = v1
Elastic Collision Simultaneous Equations
v1 + v1 (prime) = v2 (prime) + v2
Small mass striking heavier mass at rest
v1(prime) = - v1 v2(prime) = 0 Picture a moving golf ball hitting a stationary bowling ball.
Large mass striking lighter mass at rest
v1(prime) = v1 v2(prime) = 2v1 Picture a bowled bowling ball striking a beach ball at rest.
Momentum is a __________quantity
vector (magnitude and direction)
If a system contains more than one object, its total momentum is the ______________ of the momenta of those objects.
vector sum
momenta add as _________, not as ____________.
vectors, scalars
The "prime" sign will denote the .........................
velocity after the collision or explosion.
Newton's First Law tells us that the __________ and ____________ of an object won't change unless the object is affected by an external force.
velocity and momentum
In order to determine the total momentum of a system:
· Determine a direction to be considered positive. · Assign positive values to momenta in that direction. · Assign negative values to momenta in the opposite direction. The Momentum of a System of Objects Add the momenta to get the total momentum of the system.
Objects in an isolated system can interact with each other in two basic ways:
· They can collide. · If they are stuck together, they can explode (push apart).
Assume a baseball batter swings with a given force that is applied over the interval of the ball in contact with the bat. The ball is approaching the batter with a positive momentum. What is the goal of the batter? The batter wants to hit the ball and get the largest ________ possible for his force which depends on his ____________and ________________. The greater the _________, the ____________the ball will fly off his bat, which will result in it going _______________, hopefully to the seats. the batter wants to maximize the __________that his bat (which is providing the force) is in contact with the ball. This means he should follow through with his swing. The batter needs to apply a large ___________to reverse the ball's large _____________from the _______________direction (towards the batter) to the ______________direction (heading towards the center field bleachers).
Δp, strength and timing, Δp, faster, further time impulse, momentum, negative, positive
For the car air bags, we'll fix _______, vary ___and see its impact on ____
Δp, Δt, F.
