Momentum and Collisions Review
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Part A: Multiple-Multiple Choice
- Momentum is a vector quantity.
- The standard unit on momentum is the Joule.
- An object with mass will have momentum.
- An object which is moving at a constant speed has momentum.
- An object can be traveling eastward and slowing down; its momentum is westward.
- Momentum is a conserved quantity; the momentum of an object is never changed.
- The momentum of an object varies directly with the speed of the object.
- Two objects of different mass are moving at the same speed; the more massive object will have the greatest momentum.
- A less massive object can never have more momentum than a more massive object.
- Two identical objects are moving in opposite directions at the same speed. The forward moving object will have the greatest momentum.
- An object with a changing speed will have a changing momentum.
a. TRUE - Momentum is a vector quantity. Like all vector quantities, the momentum of an object is not fully described until the direction of the momentum is identified. Momentum, like other vector quantities, is subject to the rules of vector operations.
b. FALSE - The Joule is the unit of work and energy. The kg m/s is the standard unit of momentum.
c. FALSE - An object has momentum if it is moving. Having mass gives an object inertia. When that inertia is in motion, the object has momentum.
d. TRUE - This is true. However, one should be quick to note that the object does not have to have a constant speed in order to have momentum.
e. FALSE - The direction of an object's momentum vector is in the direction that the object is moving. If an object is traveling eastward, then it has an eastward momentum. If the object is slowing down, its momentum is still eastward. Only its acceleration would be westward.
f. FALSE - To say that momentum is a conserved quantity is to say that if a system of objects can be considered to be isolated from the impact of net external forces, then the total momentum of that system is conserved. In the absence of external forces, the total momentum of a system is not altered by a collision. However, the momentum of an individual object is altered as momentum is transferred between colliding objects.
g. TRUE - Momentum is calculated as the product of mass and velocity. As the speed of an object increases, so does its velocity. As a result, an increasing speed leads to an increasing momentum - a direct relationship.
h. TRUE - For the same speed (and thus velocity), a more massive object has a greater product of mass and velocity; it therefore has more momentum.
i. FALSE - A less massive object would have a greater momentum owing to a velocity which is greater than that of the more massive object. Momentum depends upon two quantities * mass and velocity. Both are equally important.
j. FALSE - When comparing the size of two momentum vectors, the direction is insignificant. The direction of any vector would never enter into a size comparison.
k. TRUE - Objects with a changing speed also have a changing velocity. As such, an object with a changing speed also has a changing momentum.
- Momentum is a form of energy.
- If an object has momentum, then it must also have mechanical energy.
- If an object does not have momentum, then it definitely does not have mechanical energy either.
- Object A has more momentum than object B. Therefore, object A will also have more kinetic energy.
- Two objects of varying mass have the same momentum. The least massive of the two objects will have the greatest kinetic energy.
a. FALSE - No. Momentum is momentum and energy is energy. Momentum is NOT a form of energy; it is simply a quantity which proves to be useful in the analysis of situations involving forces and impulses.
b. TRUE - If an object has momentum, then it is moving. If it is moving, then it has kinetic energy. And if an object has kinetic energy, then it definitely has mechanical energy.
c. FALSE - If an object does NOT have momentum, then it definitely does NOT have kinetic energy. However, it could have some potential energy and thus have mechanical energy.
d. FALSE - Consider Object A with a mass of 10 kg and a velocity of 3 m/s. And consider Object B with a mass of 2 kg and a velocity of 10 m/s. Object A clearly has more momentum. However, Object B has the greatest kinetic energy. The kinetic energy of A is 45 J and the kinetic energy of B is 100 J.
e. TRUE - When comparing the momentum of two objects to each other, one must consider both mass and velocity; both are of equal importance when determining the momentum value of an object. When comparing the kinetic energy of two objects, the velocity of an object is of double importance. So if two objects of different mass have the same momentum, then the object with the least mass has a greater velocity. This greater velocity will tip the scales in favor of the least massive object when a kinetic energy comparison is made.
- Impulse is a force.
- Impulse is a vector quantity.
- An object which is traveling east would experience a westward directed impulse in a collision.
- Objects involved in collisions encounter impulses.
- The Newton is the unit for impulse.
- The kg•m/s is equivalent to the units on impulse.
- An object which experiences a net impulse will definitely experience a momentum change.
- In a collision, the net impulse experienced by an object is equal to its momentum change.
- A force of 100 N acting for 0.1 seconds would provide an equivalent impulse as a force of 5 N acting for 2.0 seconds.
a. FALSE - Impulse is NOT a force. Impulse is a quantity which depends upon both force and time to change the momentum of an object. Impulse is a force acting over time.
b. TRUE - Impulse is a vector quantity Like momentum, impulse is not fully described unless a direction is associated with it.
c. FALSE - An object which is traveling east could encounter a collision from the side, from behind (by a faster-moving object) or from the front. The direction of the impulse is dependent upon the direction of the force exerted upon the object. In each of these scenarios, the direction of the force would be different.
d. TRUE - In a collision, there is a collision force which endures for some amount of time. The combination of force and time is what is referred to as an impulse.
e. FALSE - The Newton is the unit of force. The standard metric unit of impulse is the N•s.
f. TRUE - The N•s is the unit of momentum. The Newton can be written as a kg•m/s^2. When substituted into the N•s expression, the result is the kg m/s.
g. TRUE - In a collision, there is a collision force which endures for some amount of time to cause an impulse. This impulse acts upon the object to change its velocity and thus its momentum.
h. TRUE - Yes!!! This is the impulse-momentum change theorem. The impulse encountered by an object in a collision causes and is equal to the momentum change experienced by that object.
i. TRUE - A force of 100 N for 0.10 s results in an impulse of 10 N•s. This 10 N•s impulse is equivalent to the impulse created by a force of 5 N for 2.0 seconds.
Momentum and Impulse Connection
- Two colliding objects will exert equal forces upon each other even if their mass is significantly different.
- During a collision, an object always encounters an impulse and a change in momentum.
- During a collision, the impulse which an object experiences is equal to its velocity change.
- The velocity change of two respective objects involved in a collision will always be equal.
- While individual objects may change their velocity during a collision, the overall or total velocity of the colliding objects is conserved.
- In a collision, the two colliding objects could have different acceleration values.
- In a collision between two objects of identical mass, the acceleration values could be different.
- Total momentum is always conserved between any two objects involved in a collision.
- When a moving object collides with a stationary object of identical mass, the stationary object encounters the greater collision force.
- When a moving object collides with a stationary object of identical mass, the stationary object encounters the greater momentum change.
- A moving object collides with a stationary object; the stationary object has significantly less mass. The stationary object encounters the greater collision force.
- A moving object collides with a stationary object; the stationary object has significantly less mass. The stationary object encounters the greater momentum change.
a. TRUE - In any collision between two objects, the colliding objects exert equal and opposite force upon each other. This is simply Newton's law of action-reaction.
b. TRUE - In a collision, there is a collision force which endures for some amount of time to cause an impulse. This impulse acts upon the object to change its momentum.
c. FALSE - The impulse encountered by an object is equal to mass multiplied by velocity change - that is, momentum change.
d. FALSE - Two colliding objects will only experience the same velocity change if they have the same mass and the collision occurs in an isolated system. However, their momentum changes will be equal if the system is isolated from external forces.
e. FALSE - This statement is mistaking the term velocity for momentum. It is momentum which is conserved by an isolated system of two or more objects.
f. TRUE - Two colliding objects will exert equal forces upon each other. If the objects have different masses, then these equal forces will produce different accelerations.
g. FALSE - It the colliding objects have different masses, the equal force which they exert upon each other will lead to different acceleration values for the two objects.
h. FALSE - Total momentum is conserved only if the collision can be considered isolated from the influence of net external forces.
i. FALSE - In any collision, the colliding objects exert equal and opposite forces upon each other as the result of the collision interaction. There are no exceptions to this rule.
j. FALSE - In any collision, the colliding objects will experience equal (and opposite) momentum changes, provided that the collision occurs in an isolated system.
k. FALSE - In any collision, the colliding objects exert equal and opposite forces upon each other as the result of the collision interaction. There are no exceptions to this rule.
l. FALSE - In any collision, the colliding objects will experience equal (and opposite) momentum changes, provided that the collision occurs in an isolated system.
Momentum and Impulse Connection || The Law of Action-Reaction (Revisited)
- Perfectly elastic and perfectly inelastic collisions are the two opposite extremes along a continuum; where a particular collision lies along the continuum is dependent upon the amount kinetic energy which is conserved by the two objects.
- Most collisions tend to be partially to completely elastic.
- Momentum is conserved in an elastic collision but not in an inelastic collision.
- The kinetic energy of an object remains constant during an elastic collision.
- Elastic collisions occur when the collision force is a non-contact force.
- Most collisions are not inelastic because the collision forces cause energy of motion to be transformed into sound, light and thermal energy (to name a few).
- A ball is dropped from rest and collides with the ground. The higher that the ball rises upon collision with the ground, the more elastic that the collision is.
- A moving air track glider collides with a second stationary glider of identical mass. The first glider loses all of its kinetic energy during the collision as the second glider is set in motion with the same original speed as the first glider. Since the first glider lost all of its kinetic energy, this is a perfectly inelastic collision.
- The collision between a tennis ball and a tennis racket tends to be more elastic in nature than a collision between a halfback and linebacker in football.
a. TRUE - A perfectly elastic collision is a collision in which the total kinetic energy of the system of colliding objects is conserved. Such collisions are typically characterized by bouncing or repelling from a distance. In a perfectly inelastic collision (as it is sometimes called), the two colliding objects stick together and move as a single unit after the collision. Such collisions are characterized by large losses in the kinetic energy of the system.
b. FALSE - Few collisions are completely elastic. A completely elastic collision occurs only when the collision force is a non-contact force. Most collisions are either perfectly inelastic or partially inelastic.
c. FALSE - Momentum can be conserved in both elastic and inelastic collisions provided that the system of colliding objects is isolated from the influence of net external forces. It is kinetic energy that is conserved in a perfectly elastic collision.
d. FALSE - In a perfectly elastic collision, in an individual object may gain or lose kinetic energy. It is the system of colliding objects which conserves kinetic energy.
e. TRUE - Kinetic energy is lost from a system of colliding objects because the collision transforms kinetic energy into other forms of energy - sound, heat and light energy. When the colliding objects don't really collide in the usual sense (that is when the collision force is a non-contact force), the system of colliding objects does not lose its kinetic energy. Sound is only produced when atoms of one object make contact with atoms of another object. And objects only warm up (converting mechanical energy into thermal energy) when their surfaces meet and atoms at those surfaces are set into vibrational motion or some kind of motion.
f. TRUE - See above statement.
g. TRUE - If large amounts of kinetic energy are conserved when a ball collides with the ground, then the post-collision velocity is high compared to the pre-collision velocity. The ball will thus rise to a height which is nearer to its initial height.
h. FALSE - This is a perfectly elastic collision. Before the collision, all the kinetic energy is in the first glider. After the collision, the first glider has no kinetic energy; yet the second glider has the same mass and velocity as the first glider. As such, the second glider has the kinetic energy which the first glider once had.
i. TRUE - There is significant bounce in the collision between a tennis racket and tennis ball. There is typically little bounce in the collision between a halfback and a linebacker (though there are certainly exceptions to this one). Thus, the ball-racket collision tends to be more elastic.