RNT1 Lecture Notes - Lecture 3: Kilowatt Hour, Conservative Force, Angular Acceleration

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26 Sep 2019
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We will always use N3.
Chapter 6 — Momentum
Momentum is a measure of how hard it is to bring a moving body to rest.
Clearly, momentum must depend on mass since mass is a measure of how hard it is to change
the motion of a body.
It must also depend on the velocity of a body since faster bodies will be harder to stop.
Simplest mathematical description: momentum (p) of a body is the product of the mass m of the
body and its velocity v:
Unit of momentum = kgAm/s = NAs
Examples of Momentum:
1. Car on the Freeway
weight about 2600 lb, which is a mass of about 1200 kg
speed about 70 mph, which is about 40 m/s.
Momentum of the car: p = (1200 kg)(40 m/s) = 48,000 N@s
2. Student Walking Across Campus
weight about 150 lb, which is a mass of about 70 kg
speed about 2 mph, which is about 1 m/s
Momentum of the student: p = (70 kg)(1 m/s) = 70 N@s
3. Bullet
weight of a bullet about 0.25 oz which is a mass of about 0.0075 kg
speed = 300 m/s (a bit less than the speed of sound)
Momentum of the bullet: p = (0.0075 kg)(300 m/s) = 2.25 N@s
Impulse — related to momentum and related to force.
Impulse changes momentum.
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Force must be involved with impulse because force changes velocity, which changes momentum.
The way the force changes velocity is governed by N2.
Impulse is a force acting over a time.
Impulse is just the product of force and time:
A given impulse can be produced by either a small force acting over a long time or a large force
acting over a short time.
Most useful — large force over a short time.
We are usually interested in the motion of the body over that long time.
For the large force acting over a short time, we are usually only interested in the change in the
motion over that short time.
We define a large force acting over a short time as an impulsive force.
We want to relate impulse to change in momentum.
We know that forces applied to objects change the motion of the object by changing velocity —
N2
The impulse applied to a body changes its motion by changing its momentum.
Conservation of Momentum
In physics, a quantity is conserved if it remains constant.
Under appropriate conditions, momentum is conserved.
Consider the collision between two bodies.
Body 1 and body 2 collide.
When the two bodies collide, they apply forces to each other.
From N3, these forces are equal and opposite.
This means that the two bodies apply impulses to each other where the impulse is the product of
the force and the time over which the two bodies are in contact.
This means that each body changes the momentum of the other body.
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The forces of interaction obey N3.
The forces that the two bodies apply to each other are equal and opposite.
This means that the impulses are also equal and opposite—obey N3.
Multiply both forces by the same time of contact to get impulses.
Suppose in the collision, body 1 increases the momentum of body 2 by a certain amount due to
the impulse it applies on body 2.
Since the impulse that body 2 applies to body 1 is equal and opposite, it will decrease the
momentum of body 1 by the same amount.
This means that the sum of the momenta of the two bodies after the collision is the same as the
sum of the momenta before the collision.
Principle of Conservation of Momentum: If the net external force on a system of particles is zero,
the total momentum of the system remains constant.
Note that momentum and impulse must have the same units. Unit of impulse is unit of force —
N — times the unit of time — s. Unit of impulse is N@s — also unit of momentum.
Let’s do an example. Suppose two blocks are on a frictionless surface. The first block, the
projectile, is moving toward the second block, the target, which is at rest. Suppose that the two
blocks stick together after the collision. We want to find the final velocity of the two blocks. Let’s
choose some numbers. Let m1 = 0.1 kg, m2 = 0.05 kg, and the initial speed of block 1 be v1 = 1m/s.
The figure above shows the system of blocks before and after the collision. The symbol V is the
final velocity of the two blocks, which is what we are trying to find.
The momentum before the collision is the sum of the momenta of the two blocks after the
collision:
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