Physics By KruNit: July 2013

The second note is built into this equation; momentum is a vector, and the momentum has the same direction as the velocity.

Impulse-Momentum Change Equation
In a collision, a force acts upon an object for a given amount of time to change the object's velocity. The product of force and time is known as impulse. The product of mass and velocity change is known as momentum change. In a collision the impulse encountered by an object is equal to the momentum change it experiences.

Impulse = Momentum Change

F • t = mass • Delta v

Again, this is a vector equation, so the change in momentum is in the same direction as the force.

CONSERVATION MOMENTUM

Types of collisions: (momentum is conserved in each case)

elastic - kinetic energy is conserved
inelastic - kinetic energy is not conserved
completely inelastic - kinetic energy is not conserved, and the colliding objects stick together after the collision.

The total energy is always conserved, but the kinetic energy does not have to be; kinetic energy is often transformed to heat or sound during a collision.

Impulse Momentum Exam and Problem Solutions

1. Objects shown in the figure collide and stick and move together. Find final velocity objects.

Using conservation of momentum law;

m₁.V₁+m₂.V₂=(m₁+m₂).V_final

3.8+4.10=7.V_final

64=7.V_final

V_final=9,14m/s

2. 2kg and 3kg objects slide together, and then they break apart. If the final velocity of m₂ is 10 m/s,

a) Find the velocity of object m₁.

b) Find the total change in the kinetic energies of the objects.

a) Using conservation of momentum law;
(m₁+m₂).V=m₁.V₁+m₂.V₂

5.4=30+2.V₁

V₁=-5m/s

b) E_Kinitial=1/2/m₁+m₂).V²

E_Kinitial=1/2.5.16=40joule

E_Kfinal=1/2.2.5²+1/2.3.10²

E_Kfinal=175 joule

Change in the kinetic energy is =175-40=135 joule

3. As shown in the figure below, object m₁ collides stationary object m₂. Find the magnitudes of velocities of the objects after collision. (elastic collision)

In elastic collisions we find velocities of objects after collision with following formulas;

V₁'=(m₁-m₂)/(m₁+m₂).V₁

V₂'=(2m₁/m₁+m₂).V₁

m₁=6kg, m₂=4kg, V₁=10m/s

V₁'=(6-4/6+4).10=2m/s

V₂'=(2.6/6+4).10=12m/s

4. Momentum vs. time graph of object is given below. Find forces applied on object for each interval.

F.Δt=ΔP

F=ΔP/Δt

Slope of the graph gives us applied force.

I. Interval:

F₁=P₂-P₁/10-0=-50/10=-5N

II. Interval:

F₂=50-50/10=0

III. Interval:

F₃=100-50/10=5N

5. A box having mass 0,5kg is placed in front of a 20 cm compressed spring. When the spring released, box having mass m₁, collide box having mass m₂ and they move together. Find the velocity of boxes.

Energy stored in the spring is transferred to the object m₁.

1/2.k.X²=1/2.mV²

50N/m.(0,2)²=0,5.V²

V=2m/s

Two object do inelastic collision.

m₁.V₁=(m₁+m₂).V_final

0,5.2=2.V_final

V_final=0,5m/s

Thank : http://www.physicstutorials.org/home/exams/impulse-momentum-exams-and-solutions/impulse-momentum-exam2-and-solutions

Simple machines

Simple machines make work easier for us by allowing us to push or pull over increased distances.

There are SIX simple machines:

Type	Example	Activity
1. Pulley - How Stuff Works A pulley is a simple machine that uses grooved wheels and a rope to raise, lower or move a load.		Pulleys
2. Lever - Enchanted Learning animations A lever is a stiff bar that rests on a support called a fulcrum which lifts or moves loads.		Levers
3. Wedge - pictures using LEGO bricks A wedge is an object with at least one slanting side ending in a sharp edge, which cuts material apart.		Wedges
4. Wheel & Axle - Activity using pencils and thread spools A wheel with a rod, called an axle, through its center lifts or moves loads.		Wheels
5. Inclined Plane - pictures using LEGO bricks An inclined plane is a slanting surface connecting a lower level to a higher level.		Inclined Planes
6. Screw - Activity using pencil and paper in a new way A screw is an inclined plane wrapped around a pole which holds things together or lifts materials.		Screws

Simple Machine Quiz

1. A fork is an example of a:

2. A bicycle is an example of a:

3. A bathtub is an example of a/an:
4. A swivel chair is an example of a:

5. A teeter totter on the playground is a:

6. You would use a pulley to:

Credit : http://www.mikids.com/SimpleMachines/smquiz.htm

Work energy and Power # 2

Power

The word “power” is most often associated with electricity in everyday use, but this is not the case in physics.

Power is the rate at which work is done.
This means that power measures how quickly energy is being used.
Since it is the rate at which something is happening, time must be involved somehow.
If you look at the basic formula for power, you’ll see that it is the same as many formulas that involve time.

P = power (Watts)
W = Δ E = work (Joules)
t = time (seconds)

Sometimes you will see Δ E instead of W in the above formula.

Δ E just means change in energy, which is what work is all about.

Power is really how fast you are using up energy, so it could be measured in Joules per second.

In honour of his search for a more efficient engine (which was better at converting energy!), the unit for power is called the Watt after James Watt.
Think of a light bulb… you always talk about how many Watts the bulb is, like a 60 W bulb.
That just means that the light bulb is using 60 Joules of energy every second.

Switch to Index

Energy Skate Park: Basics	Generator	Faraday's Electromagnetic Lab
Masses & Springs	My Solar System	Energy Skate Park
Gas Properties	Balloons & Buoyancy	States of Matter
Nuclear Fission	The Ramp

Work energy and power

Kinetic Energy and the Work-Energy Theorem

We'll start with some definitions.

What this second definition means is that work equals the product of the distance an object travels and the component of the force acting on that object directed parallel to the object's direction of motion. That sounds more complicated than it really is: an example will help.
A box is pulled along the floor, as shown in Figure 14.1. It is pulled a distance of 10 m, and the force pulling it has a magnitude of 5 N and is directed 30° above the horizontal. So, the force component that is PARALLEL to the 10 m displacement is (5 N)(cos 30°).

Kinetic Energy and the Work Energy Theorem

One newton. meter is called a joule, abbreviated as 1 J.

Work is a scalar. So is energy.
The units of work and of energy are joules.
Work can be negative … this just means that the force is applied in the direction opposite displacement.

This means that the kinetic energy of an object equals one half the object's mass times its speed squared.

The net work done on an object is equal to that object's change in kinetic energy. Here's an application:

Here, because the only horizontal force is the force of the brakes, the work done by this force is W_net.

Let's pause for a minute to think about what this value means. We've just calculated the change in kinetic energy of the train car, which is equal to the net work done on the train car. The negative sign simply means that the net force was opposite the train's displacement. To find the force:

Potential Energy

Potential energy comes in many forms: there's gravitational potential energy, spring potential energy, electrical potential energy, and so on. For starters, we'll concern ourselves with gravitational potential energy.
Gravitational PE is described by the following equation:

mgh

In this equation, m is the mass of an object, g is the gravitational field of 10 N/kg on Earth, and h is the height of an object above a certain point (called "the zero of potential").³ That point can be wherever you want it to be, depending on the problem. For example, let's say a pencil is sitting on a table. If you define the zero of potential to be the table, then the pencil has no gravitational PE. If you define the floor to be the zero of potential, then the pencil has PE equal to mgh, where h is the height of the pencil above the floor. Your choice of the zero of potential in a problem should be made by determining how the problem can most easily be solved.
REMINDER: h in the potential energy equation stands for vertical height above the zero of potential.
Practice problems for these concepts can be found at: Energy Conservation Practice Problems for AP Physics B & C

kinetic-energy-and-potential-energy

Work and energy Test

Momentum, Work, Energy, And Power Practice Test

1. Consider a minor parking-lot accident. Car A backs out at 30 cm/s toward the west, and car B looks for a place to park, driving north at 40 cm/s. Both cars mass 1,000 kg. What is the total system momentum before the collision? Remember that momentum is a vector quantity. Also, be careful with your units.

(a) 700 kg · m/s, generally northwest

(b) 100 kg · m/s, generally northwest

(d) There is not enough information to answer this.

2. Impulse is the product of

(a) time and distance.

(b) time, mass, and acceleration.

(d) time and velocity.

3. Consider a hockey player skating down the ice at 10.0 m/s. His mass is 82.0 kg. What is his kinetic energy?

(a) 820 J

(b) 410 J

(d) 4.10 × 10 ³ J

4. An object whose mass is 10.0 kg is lifted through a distance of 4.000 m on a planet where the gravitational acceleration is 6.000 m/s ² . How much work is required to do this?

(a) 60.0 J

(b) 24.0 J

(d) 240 J

5. Suppose that an object is pushed with steady force along a frictionless surface. When you multiply the object’s mass by the length of time for which it is pushed and then multiply the result by the object’s acceleration over that period of time, you get

(a) momentum.

(b) velocity.

(d) a meaningless quantity.

6. According to the law of conservation of momentum, in an ideal closed system,

(a) when two objects collide, the system neither loses nor gains any total momentum.

(b) when two objects collide, neither object loses or gains any momentum.

(d) when two objects collide, the magnitudes of their momentum vectors multiply.

7. When making calculations in which all the quantities have their units indicated throughout the entire process,

(a) the units multiply and divide just like the numbers.

(b) the units cannot cancel out.

(d) the units can be added and subtracted, but not multiplied or divided.

8. One joule, reduced to base units, is equivalent to

(a) one kilogram-meter per second squared.

(b) one kilogram-meter.

(d) one meter per second squared.

9. A 5,000-kg motorboat sits still on a frictionless lake. There is no wind to push against the boat. The captain starts the motor and runs it steadily for 10.00 seconds in a direction straight forward and then shuts the motor down. The boat has attained a speed of 5.000 meters per second straight forward. What is the impulse supplied by the motor?

(a) 2.500 × 10 ⁵ kg · m/s

(b) 2.500 × 10 ⁴ kg · m/s

(d) 6.250 × 10 ⁴ kg · m/s

10. Which of the following does not have an effect on the momentum of a moving spherical particle?

(a) The speed of the particle

(b) The diameter of the particle

(d) The mass of the particle

Answers

1. c

2. b

3. d

4. d

5. c

6. a

7. a

8. c

9. b

10. b

Work and energy

Work and Energy

Energy is an important concept in every day life. It appears as gravitational potential energy of objects raised to a certain height, as elastic potential energy in a stretched rubber band, as kinetic energy of moving objects, or as chemical energy in the food that we eat. Closely associated with energy is the concept of work. Energy is transferred to another system when you do work. Power provides a measure of the energy expended per unit time. Efficiency of machines provides a measure of the energy converted into useful work.

Familiarity with the following terms will help you get the most from this module:

Terms	Definition
Work	The product of a constant force magnitude and the magnitude of the displacement

Joule	The unit of work which is the special name for Newton meter

Energy	The capacity to do work

Potential energy	The energy due to position

Kinetic energy	The energy due to motion

Power	The rate of doing work

Watt	The unit of power which is the special name for Joule per second

Machines	Devices that help us do work

Actual Mechanical Advantage	It determines the number of times a machine multiplies force

Ideal Mechanical Advantage	The ratio of the effort distance to the resistance distance

Efficiency	The ratio of the actual mechanical advantage to the ideal mechanical advantage, or the ratio of the work output to the work input

Physics By KruNit

Friday, July 19, 2013

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test conservation of Momentum

Momentum