Physics chapter 9 (linear momentum)
Four floor tiles are laid out in an L-pattern as shown. The origin of the x-y axes is at the center of the lower left tile. What is the x-coordinate of the center of mass? What is the y-coordinate of the center of mass?
-Xcm = (1/4)a -Ycm = (3/4)a
Two toy cars of mass A 1110g and B 1550g are stationary, lined up at the start line of a race. Which car crosses the finish line 1.0 away first? Which car has the larger kinetic energy when it crosses the finish line 1.0 away? Which car has a larger momentum when it crosses the finish line 1.0 away? Which car has traveled farther after 10 ss? After 10 ss which car has larger kinetic energy? After 10 ss which car has a larger momentum?
-car A because since their force is the same car A will have larger acceleration and will therefore get their earlier -Both cars have the same kinetic energy -Car B because larger mass has greater momentum - car A will travel farther -car A will have greater kinetic energy - both cars have same momentum
Two guys who weight the same are holding onto a massless pole while standing on horizontal frictionless ice. 1) If the guy on the left starts to pull on the pole, where do they meet?
0 because because the Their masses mass times position cancel out as they are in opposite positions in the x coordinate.
perfectly inelastic collision
2 objects collide and stick together
Two masses, of size m and 3m, are at rest on a friction less surface. A compressed, mass-less spring between the masses is suddenly allowed to uncompress, pushing the masses apart. After the masses are apart, the speed of m is _______ the speed of 3m.
3 times
why is the barrel of a rifle so long?
Answer: v = a x t long barrel, more time to accelerate, bigger velocity
Two balls of equal mass are thrown horizontally with the same initial velocity. They hit identical stationary boxes resting on a frictionless horizontal surface. The ball hitting box 1 bounces back, while the ball hitting box 2 gets stuck.
Box 1, because the box1 will have same velocity has the the ball, while the box 1 will have half of the velocity
Object A is a square sheet of plywood centered on the origin. Object B is made by taking object A and slicing it in half along the x axis to make two rectangular sheets having the same mass. The bottom half is then moved to make a T shape as shown. Compare the location of the center of mass (CM) of the two objects:
Center of mass is higher for A. The center of mass of the two rectangular pieces is half-way between the center of each piece. This location is lower in Object B since the center of the bottom piece is further down.
A bullet of mass m and velocity v is fired into a wood block of mass M initially at rest on a frictionless surface. The bullet buries itself in the wood block and then the wood block is seen to have a final velocity vf .True (A) or False (B): mv =Mvf
False. Conservation of momentum implies mv =(M+m)vf
A bullet of mass m and velocity v is fired into a wood block of mass M initially at rest on a frictionless surface. The bullet buries itself in the wood block and then the wood block is seen to have a final velocity vf. True (A) or False (B): (1/2)mv2 = (1/2)(M+m) vf 2
False. Since this was an inelastic collision, some of the KE was converted into Ethermal. KE is not conserved in this collision.
1D collisions
In 1D, we represent direction of vectors p and v with a sign. (+) = right (-) = left usually Ptotalbefore=Ptotalafter
What direction in momentum?
In direction of velocity
A big ball, mass M=10m, speed v, strikes a small ball, mass m, at rest. Could the following occur?: The big ball comes to a complete stop and the small ball takes off with speed 10v. (Assume that both balls remain at the same temperature.)
It cannot occur because it would violate energy conservation. The total KE of the system after the collision is 10 times the KE before the collision. Since the temperatures don't change, we need not worry about thermal energy. Although you can convert KE into E_thermal with 100% efficiency, you can't go the other way. You cannot convert E_thermal into KE with 100% efficiency.
If the collision is elastic then __________ is always conserved.
KE, so we can write 1/2mava + 1/2mbvb= 1/2mava prime +1/2mbvb prime
A block having mass m slides on a frictionless surface and runs into a block of mass M which is initially at rest. The blocks stick together and their speed after the collision is half the speed the moving block had before the collision. How do the masses of the blocks compare?
M=m Since there are no external forces acting on the system, the total momentum will be the same before and after the collision. The momentum before the collision is mV, and the momentum after is (m+M)V/2. These are the same only if M = m.
conservation of momentum
Momentum of a system remains constant when there are no net external forces acting on it.
A moving mass m1 is approaching a stationary mass m2 on friction less table. Is it possible that, as a result of the collision, all of the kinetic energy of both masses is converted to heat?
No, because the total momentum before is not 0, then total momentum after the collision cannot be 0 so there has to be kinetic energy left
p total =
P1 + P2 in other words sum of m1v1 + m2v2
Two objects, one having twice the mass of the other, are initially at rest. Two forces of equal magnitude act on the objects in opposite directions as shown. Which of the following statements about the acceleration of the center of mass of the system is true?
The center of mass does not move. The acceleration of the center of mass is equal to the total external force divided by the total mass. In this case the total external force is zero since the two applied forces are equal and opposite.
What is the term impulse usually reserved for ?
The term "impulse" is usually reserved for situations in which a BIG force acts for a short time to cause a rapid change in momentum. Like a bat hitting a baseball:
A bomb which is initially at rest in outer space explodes into 3 identical pieces. In which way will the velocity be distributed.
The velocity will make a equilateral triangle where the magnitude of velocity is the same for all. The initial momentum of the system is zero since the bomb starts out at rest. Since there are no external forces acting, the total momentum must always be zero. The selected configuration is the only one where the three momenta could add to zero.
A projectile is fired with initial speed vo at an angle of 45o above the horizontal. Assume no air resistance. True A or False B: During the flight, the x-component of the projectile's momentum remains constant
The x-component momentum remains constant because there no external force in the x-direction. For motion in the x-direction, the system is isolated.
A projectile is fired with initial speed vo at an angle of 45o above the horizontal. Assume no air resistance.True A or False B: During the flight, the y-component of the projectile's momentum remains constant.
The y-component of the momentum does not remain constant, because there is an external force (gravity) in the y-direction. For motion in the y-direction, the system is not isolated.
A yummy glazed doughnut is shown above. 1) Where is the center of mass of this fantastic culinary delight?
The yummy doughnut is round and has(equal weight distribution all over the doughnut, therefore, the center of mass must be in the middle
A bullet of mass m and velocity v is fired into a wood block of mass M initially at rest on a frictionless surface. The bullet buries itself in the wood block and then the wood block is seen to have a final velocity vf .Was this an elastic collision? A) Yes B) No
This is not an elastic collision. A lot of heat was generated as the bullet slid into the wood block.
impulse
To prove that momentum is conserved in collisions, we need the concept of impulse, which relates force to changes in momentum. (net force is the derivative of momentum, in other words rate of change of momentum)
Two masses m1 and m2 are approaching each other on a friction less table and collide. Is it possible that as a result of the collision, all of the kinetic energy of both masses is converted to heat?
Yes, all KE can dissapear, in that case the total momentum after and before is 0. So all kinetic energy can be converted to thermal energy
Suppose you are on a cart, initially at rest, which rides on a frictionless horizontal track. If you throw a ball off the cart towards the left, will the cart be put into motion?
Yes, it moves to the right
Two objects, one having twice the mass of the other, are initially at rest. Two forces, one twice as big as the other, act on the objects in opposite directions as shown above. 1) Which of the following statements about the acceleration of the center of mass of the system is true?
a = F/(3M) to the left because net force is F to the left and total mass is 3 M
inelastic collision
a type of collision in which the kinetic energy after the collision is less than the kinetic energy before the collision ( lost to thermal, sound etc)
For an extended object, a) Newton's Second Law does not apply; b) Newton's Second Law applies to the center of mass (CM) of the object.
b
Suppose a tennis ball and a bowling ball are rolling toward you. Both have the same momentum, and you exert the same force to stop each. How do the time intervals to stop them compare?
both take the same time
In a collision, momentum is ______.
conserved, it does not change but velocity changes
Consider two carts, of masses m and 2m, at rest on an air track. If you push first one cart for 3 s, and then the other for the same length of time, exerting equal force on each, the momentum of the light cart is _______ the momentum of the heavy cart.
equal to use change in P = fnet times delta t
Two masses, of size m and 3m, are at rest on a friction less surface. A compressed, mass-less spring between the masses is suddenly allowed to uncompress, pushing the masses apart. The kinetic energy of m is ________ the kinetic energy of 3m.
greater than
Two masses, of size m and 3m, are at rest on a frictionless surface. A compressed, mass-less spring between the masses is suddenly allowed to uncompress, pushing the masses apart. While the spring is in contact with both masses, the magnitude of the acceleration of 3m is __________ that of m.
less than
Elastic collision
one in which there is no net loss of total kinetic energy, no KE converted to PE, Etherm
Ball 1 strikes stationary Ball 2 in 1D elastic collision. The initial momentum of Ball 1, p1i , and the final momentum of Ball 2, p2f , are shown on the graph. In units shown on the graph, what is p1f ? (To the right is positive.)
p1f = -1 Since ptot = +3
Equation for momentum
p=mv
The center-of-mass moves like a point particle even if the particles are not glued together.
point particle Example: a projectile bomb is launched, and explodes in flight.
When the collison is elastic the relative velocity of the two objects are ________
reversed va - vb= -(va-vb)
The ball bounces off the floor elastically. The direction of change in momentum of the ball is ___________
straight up
center of mass
the point in an object that moves as if all the object's mass were concentrated at that point
A car is sitting on the surface of the earth and both the car and the earth are at rest. (pretend the earth is not rotating or revolving around the sun.) The car accelerated to a final velocity. After the car reaches its final velocity, the magnitude of the earth's momentum is _________ the magnitude of the car's momentum
the same as because before the car starts moving the total momentum is zero, and the total momentum after the car starts moving is also 0. As the car pushes forward the earth pushes it backwards so the momentum cancels out.
In which situation is the magnitude of the total momentum the largest? I: one mass is traveling with v and second mass is 2m and at rest. ii: one mass is traveling with v and second mass is traveling with v to the left
the same for both situations even though the p tot will be negative for second situation the magnitude is still the same
The total force or net force on an extended object is the _______________ of all the forces on all the particles.
vector sum of all the forces on all the particles. Some of the forces are external forces, from outside the object (for example, gravity) , and some of the forces are internal forces, acting between particles in the object. The internal forces all cancel in pairs, because of NIII.
Suppose you are on a cart, initially at rest, which rides on a frictionless horizontal track. You throw a ball at a vertical surface that is firmly attached to the cart. If the ball bounces straight back as shown in the picture, will the cart be put into motion after the ball bounces back from the surface?
yes, it moves to the left
All collisions between macroscopic (large) objects are inelastic - you always dissipate some KE in a collision. However, in elastic collison______
you can have an elastic collision between atoms: air molecules are always colliding with each other, but do not lose their KE.
