A car triples its velocity while maintaining constant mass; by what factor does its linear momentum change?

Three times greater than its original value.

Three times less than its original value.

It remains unchanged since mass is constant.

It becomes nine times greater due to tripling both parameters.

If two billiard balls collide head-on with equal but opposite velocities, what law best describes the effects after collisions?

The Law of Conservation of Momentum

The Law of Conservation of Mass

The Law of Universal Gravitation

Which quantity remains conserved when no external forces act on a closed system?

Total linear momentum of that system

Kinetic energy of each individual particle within that system only

Total mechanical energy when there are internal non-conservative forces acting within that system only

Total angular momentum regardless of external torques acting on that system only

A particle moves under constant net force and experiences an impulse J, how does quadrupling the particle's duration of impact affect its change in momentum?

The change in momentum remains constant at J since impulse is defined as the product of force and time, which are independent choices here.

The change in momentum doubles to 2J because longer interaction time means larger impact on particle.

The change in momentum is four times greater or 4J as extending time multiplies the overall effect by same factor.

Change in momentum reduces to (J/4) because longer duration leads to spreading out force application, reducing efficiency.

What is the SI unit for momentum?

Kilogram meter per second (kg*m/s)

Meter per second squared (m/s^2)

During an inelastic collision between two gliding hockey pucks of equal mass, if one is stationary and the other moving at speed V, what will be their common speed post collision?

The common speed post-collision will be (V/2), half the initial speed of the moving puck.

The common speed post-collision will be V; they stick together and move with original speed due to conservation of momentum.

The common speed post-collision will be (3V/4); three-quarters of the initial speed since some energy transfers as heat.

The common speed post-collision will be (V/4), quarter of the initial speed - reasoning that half momentum equates to half velocity.

When comparing two scenarios where different constant forces are applied for different durations but produce equal impulses on objects, which quantity among those given below would also be necessarily equal for both cases?

Displacement during application of force

A cart undergoing a head-on elastic collision with an identical stationary cart on a frictionless track results in what final velocity compared to its initial velocity?

The moving cart comes to rest while transferring all its velocity to the other cart.

Both carts move forward at half of the original cart's initial velocity due to conservation of momentum.

The moving cart continues forward at its initial velocity because kinetic energy is conserved in elastic collisions.

The moving cart reverses direction post-collision due to an elastic collision causing inversion of velocities.

A bowling ball rolls without slipping on a flat surface; if friction suddenly doubled while all other forces remained constant, would the ball's impulse momentum increase, decrease, or remain the same?

Not enough information to determine

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4.2 Impulse and Momentum

5 min read•january 29, 2023

Daniella Garcia-Loos

Linear Momentum

In this unit, we'll only be talking about , but look forward to angular momentum in the next unit! Conceptually, its quite hard to describe without using quantities, but essentially, it is a measurement of mass in motion. The most basic equation for is:

p = mv

Momentum Fast (haha) Facts:

It's a vector
Units are
It is NOT the same as kinetic energy
- Kinetic energy is a scalar and describes a different relationship

Let's try to derive using momentum!

Now that looks pretty familiar, doesn't it?

Let's take a closer look at one part of this derivation.

This change in momentum actually has a special name, ! (Or as some like to call, )

Or the calculus version:

We tend to use calculus when the force or the mass is variable, like with a rocket!

Impulse

is a vector because force has a direction, and the units are the same as momentum(N*s).

Here are some key things to know about :

is the product of force and time, represented mathematically as J = F*Δt.

has the same effect on an object as a constant force applied over a certain period of time.

can be used to analyze the effect of forces on moving objects, such as during collisions.

can be used to find the final velocity of an object after a force has been applied for a given period of time.

can also be used to find the force required to stop an object or change its velocity by a certain amount in a specific period of time.

can be used in the context of both elastic and inelastic collisions, where inelastic collisions are defined as collisions where kinetic energy is not conserved and are defined as collisions where kinetic energy is conserved.

can be used to analyze the motion of an object in a resistive medium, such as air resistance or friction.

The -momentum theorem states that the applied to an object is equal to the change in momentum of the object, mathematically represented as J = Δp.

The conservation of momentum states that the total momentum of a remains constant, unless acted upon by an external force.

In a collision, the total experienced by the two colliding objects must be equal and opposite, this is also known as .

Additionally, AP loves to ask questions about in relation to graphs!

is the area under the curve (check out the integral!) of a .

Taken from Physics Forums

The curves won't always look as pretty as they did in AP Physics 1 because we have the power of calculus now!

⚠️ So..what does really mean?

Have you ever tried an egg drop experiment? One where you tried to shield a poor egg from cracking as soon as it hit the ground?

Think back to which experiments worked best...theoretically the ones that work best should be the ones that increase the amount of time of impact!

Center of Mass Velocity

The center of mass of a system of objects is a point that represents the average position of all the objects in the system. The velocity of the center of mass of a system of objects is the rate of change of the position of the center of mass with respect to time.

Here are some key things to remember when solving a problem asking for the velocity of the center of mass:

The momentum of an object is equal to its mass multiplied by its velocity, represented mathematically as p = m*v.

The total momentum of a system of objects is equal to the sum of the momenta of all the individual objects in the system.

The center of mass of a system of objects will have a velocity that is directly proportional to the total momentum of the system and inversely proportional to the total mass of the system.

In other words, if the total momentum of a system of objects increases, the velocity of the center of mass will also increase, and if the total mass of a system of objects increases, the velocity of the center of mass will decrease.

For a , if no external forces are acting on it, the total momentum of the system will remain constant, which means that the velocity of the center of mass will also remain constant.

In the context of collisions, the total momentum before and after the collision must be the same, assuming no external forces are acting on the system. This means that the velocity of the center of mass will change accordingly.

Practice Questions

During the 2007 French Open, Venus Williams hit the fastest recorded serve in a premier women’s match, reaching a speed of 58 m/s (209 km/h). What is the average force exerted on the 0.057-kg tennis ball by Venus Williams’ racquet, assuming that the ball’s speed just after impact is 58 m/s, that the initial horizontal component of the velocity before impact is negligible, and that the ball remained in contact with the racquet for 5.0 ms (milliseconds)?(Taken from Lumen Learning)

Answer: To determine the change in momentum, substitute the values for the initial and final velocities into the equation above.

Now the magnitude of the net external force can determined by using

Answer:

Use the formula on your formula chart, and don't forget to include your bounds/limits of integration!

Taken from College Board

Answer:

Again, use the formula on your chart and integrate with bounds. Take note that there is an alternate form of resolving this with another formula

Key Terms to Review (11)

Center of Mass Velocity

: The center of mass velocity refers to the average velocity of an object's center of mass. It represents the overall motion of an object by taking into account both its translational and rotational motion.

Closed System

: A closed system refers to a physical system that does not exchange matter with its surroundings but can exchange energy with them. In other words, no mass enters or leaves the system, but energy can be transferred in or out.

Elastic Collisions

: Elastic collisions are collisions between objects where both kinetic energy and momentum are conserved. In an elastic collision, the total kinetic energy before the collision is equal to the total kinetic energy after the collision.

Force vs. Time Graph

: A Force vs. Time graph represents how the applied force on an object changes over time during an interaction or event. It shows how much force is being exerted at different moments during that event.

Impulse

: Impulse refers to the change in momentum of an object when a force is applied to it for a certain amount of time.

Integral of Force vs. Time Graph

: The integral of a Force vs. Time graph represents the area under that graph, which corresponds to impulse or change in momentum. It gives us information about how much force was applied to an object over a specific period of time.

Jimpulse

: Jimpulse is a term used to describe the product of impulse and time. It represents the change in momentum experienced by an object over a specific time interval.

kg*m/s

: The unit of momentum, which is the product of an object's mass and velocity.

Linear Momentum

: Linear momentum refers to the quantity of motion possessed by an object. It is defined as the product of an object's mass and its velocity.

Newton's Second Law

: Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. It can be mathematically expressed as F = ma.

Newton's Third Law

: Newton's Third Law states that for every action, there is an equal and opposite reaction. In other words, when one object exerts a force on another object, the second object exerts a force of equal magnitude but in the opposite direction on the first object.

4.2 Impulse and Momentum

5 min read•january 29, 2023

Daniella Garcia-Loos

Linear Momentum

p = mv

Momentum Fast (haha) Facts:

It's a vector
Units are
It is NOT the same as kinetic energy
- Kinetic energy is a scalar and describes a different relationship

Let's try to derive using momentum!

Now that looks pretty familiar, doesn't it?

Let's take a closer look at one part of this derivation.

This change in momentum actually has a special name, ! (Or as some like to call, )

Or the calculus version:

We tend to use calculus when the force or the mass is variable, like with a rocket!

Impulse

is a vector because force has a direction, and the units are the same as momentum(N*s).

Here are some key things to know about :

is the product of force and time, represented mathematically as J = F*Δt.