What specifically is constant LINEAR momentum?
-the object of mass m that is MOVING IN A STRAIGHT LINE with a velocity v
In order to increase the momentum from a negative value to zero, what is it necessary to add?
-a positive momentum
Is the force required to hold an umbrella during hail the same as, more than, or less than the force required in the rain?
-the force required is greater in the hail
-when hailstones hit an umbrella, they bounce back upward
-as a result, change in momentum is greater hail
-therefor, the impulse and the force are greater with hail
If the net force acting on an object is zero, is its momentum conserved or not conserved?
Therefore, what is the sum of the net force acting on a system?
-the sum of the external forces acting on it
If the net external force acting on a system is zero, what about the momentum?
-the net momentum is conserved
What is a collision?
-a situation in which two objects strike one another in which the net external force is zero or negligibly small
What about kinetic energy?
-most or even all of a system's kinetic energy may be converted to other forms during a collision
Provide an example of when KE may increase as a result of a collision?
-if the collision sets off an explosion
To summarize, describe conditions of inelastic conditions in terms of momentum and kinetic energy
-momentum of a system is conserved
-kinetic energy of a system is not conserved
In a completely inelastic collision, what occurs to the KE?
-the maximum amount of kinetic energy is lost
What is the relationship between initial velocity and final velocity in a system that has just experienced an inelastic collision?
final velocity = 1/2 initial velocity
Using momentum to evaluate a collision between two objects allows us to bypass what?
-the details of the collision itself
-->doesn't matter how long the objects spent in contact
-->doesn't matter how much force objects exerted on each other
If you want to change the momentum of two objects involved in a collision, how must you do so?
-using external forces
For what type of conditions is momentum most useful for?
-for multi-object system with unknown internal forces
If the two people standing on ice push off of each other, what is the relationship between their momenta?
-are equal in magnitude and opposite in direction
When is the momentum of a system conserved?
-when the net external force on a system is equal to zero
-->the only forces that are present are internal forces
When is mechanical energy conserved?
-when work non-conservative is equal to zero
-->only work is conservative
If forces are conservative, what is the relationship between KE initial and KE final?
KE initial = KE final
What is the potential energy of gravity equal to during elastic collisions? Why?
-the potential energy of gravity is equal to zero because collisions typically occur on a flat surface
What is the difference between partially inelastic conditions and completely inelastic collisions?
-the degree to which KE is lost
-->in both instances, KE system final < KE system initial
What event of importance occurs during completely inelastic conditions?
-so much energy is lost that objects will not separate after the collision
Therefore, how would you describe the forces that act during an elastic collision?
-internal and conservative
Therefore, how would you describe the forces that act during an inelastic collision?
-internal and non-conservative
Describe the two 2 subclasses of inelastic collisions
1. partially inelastic collisions (objects bounce off of each other, minimal KE loss)
2. completely inelastic collisions (objects stick together, maximal KE loss)
If two people are at rest on ice (horizontal frictionless surface), then push off of each other...is momentum conserved?
Therefore, how would you describe the forces that act during this collision?
-internal and non-conservative
-the potential energy of gravity is converted to KE as the ball drops
-->both are mechanical forces so E is conserved
What will be the effect of momentum conservation if Earth is added to the system?
-momentum will be conserved
What is the center of mass of an object?
-the only part of an extended object that obeys point particle physics
What are the four ways to determine the COM?
1. Symmetry Method
2. Balance Method
3. Hanging Method
4. Calculation Method (1D and 2D)
Is the geometric center the COM for asymmetrical objects?
-no, the COM is not likely to be the midpoint/geometric center of an object that is asymmetric
When objects sit in a 2D plane, what is the first step to calculating the COM?
-figure out how much mass is at each coordinate
-pick one object to set as the origin
-->it is easier to plug in zero to an equation than non-zero values
-determine the x and y coordinates of other masses and any connecting rods (or similar objects)
What type of collisions are those in which both momentum and kinetic energy are conserved?
Two objects (A & B), initially sliding to the right and left respectively on a horizontal frictionless table, both stop after a head on collision. During this collision, the momentum of the A + B system is...?
If object is is more massive than object B, this means the initial momentum of the system is....?
Bob the snowboarder speeds up while descending a hill with friction. He then flies off a cliff (we neglect air resistance). While BOB is descending the initial hill, what happens to his KE?
What will happen to the size of his momentum?
-increases (since it is dependent on mv and Bob is speeding up)
If we were to compare an equal height drop while Bob was on the hill vs. through the air, in which case would the increase in speed be greater?
-while Bob was in the air
-while the PE loss would be the same in both cases, it would ALL go into KE while in the air (since ME is conserved) while only SOME of it would go into KE while on the hill (some PE went to heat due to the friction force, not to KE)
If you drop your keys, their momentum increases as they fall. Why is the momentum of the keys not conserved? Does this mean that the momentum of the universe increases as the keys fall? Explain
-the momentum of the keys increases as they fall because a net force acts on them
-the momentum of the universe is unchanged because an equal and opposite force acts on the Earth
A system of particles is known to have zero momentum. Does it follow that the KE of the system is also zero? Explain.
-if the kinetic energy is zero the speeds must be zero as well (due to the fact that mass itself cannot be zero). This means that the momentum is also zero.
Crash statistics show that is safer to be riding in a heavy car in an accident than in a light car. Explain in terms of physical properties?
-when a heavy object and a light object collide they exert equal and opposite forces on one another
-since the light object has more mass, its acceleration is greater. this can result in more severe injuries for the light vehicle
An object at rest on a frictionless surface is struck by a second object. Is it possible for both objects to be at rest after the collision? Explain.
-the fact that the initial momentum of the system is nonzero means that the final momentum also must be nonzero
-thus, it is not possible for both objects to be at rest after the collision
In what scenario can two objects on a horizontal frictionless surface have a collision in which all the initial KE of the system is lost?
-when the objects have momenta of equal magnitude prior to the collision
-->if these objects collide in a head-on, completely inelastic collision, they will be at rest after the collision
-->in this case, all of the initial kinetic energy is converted into other forms of energy
Can two such objects have a collision in which all the initial momentum of the system is lost?
-in order for its momentum to change, an external force must act on teh system
At the instant a bullet is fired from a gun, the bullet and the gun have equal and opposite momenta. Which object--the bullet or the gun--has the greater KE? Explain.
-the KE of the bullet is much greater than the gun
-if the momenta of the gun and the bullet are equal immediately after firing, we know that the bullet must have a greater v since its mass is much smaller than that of the gun
-accordingly, if we calculate KE from the velocities of the objects, the KE for the bullet will be greater (since the v term is squared)
A block of wood is struck by a bullet. Is the block more likely to be knocked over if the bullet is metal and embeds itself in the wood, or if the bullet is rubber and bounces off the wood?
-the rubber bullet is more likely to knock the block over
-the reason is that the change in momentum is twice as great when an object rebounds was it is when the object is simply brought to rest
A net force of 200 N acts on a 100 kg boulder, and a force of the same magnitude acts on a 100 g pebble. Is the change of the boulder's momentum in one second greater than, less than, or equal to the change of the pebble's momentum in the same time period?
-the boulder and the pebble have the same rate of momentum change, since the same force acts on both objects
-(force is the rate of change of momentum)
A friend tosses a ball fo mass m to you with a speed v. When you catch the ball, you feel a noticeable sting in your hand. If you now catch a ball of mass 2m and speed v/2, is the sting you feel greater than, less than, or the same as that felt when you caught the first ball.
-the two balls have the same momentum. however, the first ball has a KE equal to 1/2mv^2 and the second ball has half that much KE
-->thus, less energy is dissipated in stopping the second ball, so it has less "sting"