## Work Of Forces Acting On A Rigid Body

The work of forces acting at various points on a single rigid body can be calculated from the work of a resultant force and torque. To see this, let the forces **F**1, **F**2 … **F**n act on the points **X**1, **X**2 … **X***n* in a rigid body.

The trajectories of **X***i*, *i* = 1, …, *n* are defined by the movement of the rigid body. This movement is given by the set of rotations and the trajectory **d** of a reference point in the body. Let the coordinates **x***i**i* = 1, …, *n* define these points in the moving rigid body’s reference frame*M*, so that the trajectories traced in the fixed frame *F* are given by

- X

## How Do I Find Work Done By A Non

How would I find the percent of mechanical energy lost to thermal energy due to friction if a 3.250g bullet enters a wooden block with a velocity of 80.00 m/s, and if it exits the block with a velocity of 20.00 m/s?

Thank-you!

You can do this using the conservation of energy. “Non-Conservative Force” only means that use won’t get the kinetic energy back by moving the bullet backwards.

Your system consists of the wooden block and the bullet. There is nothing else that can exchange energy so the whole energy is always the sum of

- the kinetic energy of the bullet
- the thermal energy of the bullet
- the kinetic energy of the block
- the thermal energy of the block

At first everything but the kinetic energy of the bullet is zero.

If your block is very heavy and is not accelerated by the bullet, its kinetic energy will stay =0. So all the lost kinetic energy must have been converted to thermal energy.

## When A Force Does No Work

A force with no motion or a force perpendicular to the motion does no work

These two examples of forces which do no work are paradoxical. You can certainly feel fatigued when doing either of these, so how can you say that no work is done?

In the case at left, no matter how hard or how long you have pushed, if the crate does not move, then you have done no work on the crate. It is sitting still in the same place! Why then do you feel fatigued . The resolution to this dilemma comes in considering that when your muscles are used to exert a force on something, the individual muscle fibers are in a continual process of contracting and releasing to maintain the net collective result of a steady force on an external object. That contracting and releasing involves force and motion, and constitutes internal work in your body. The energy shows up as warming in your muscle tissue, but if the crate doesn’t move, there is still no net work on the crate.

There are many important examples of forces which do no work because they act perpendicular to the motion. For circular motion, the centripetal force always acts at right angles to the motion. It changes the direction of the motion, but it does no work on the object. This can be applied to any circular orbit.

**Also Check: How Did Geography And Religion Influence Ethiopia’s Development **

## The Formula For Work: Physics Equation With Examples

In physics, we say that a force does;**work ;**if the application of the force displaces an object in the direction of the force. In other words, work is equivalent to the application of a force over a distance. The amount of work a force does is directly proportional to how far that force moves an object. The general formula for work and for determining the amount of work that is done on an object is:

*W*=;*F;× D;*× cos

where;*W;*is the amount of work,;*F* is the vector of force,;;*D* is the magnitude of displacement, and is the angle between the vector of force and the vector of displacement. The SI unit for work is the;**joule;**, and its dimensions are *kgm2/s2*. Another way to understand it is that one joule is equivalent to the amount of energy transferred when one newton of force moves an object a distance of one meter.

## Force And Displacement Meaning According To Physics

According to Physics definition of work = F S; or FScos, taking dot product of force and displacement. Where is angle between force and displacement vector. This is simple way to define work in Physics.

**Some important points for work **

Hence from the above figure. you have notice that, when force and displacement are parallel, then work is positive. And If force and displacement are anti-parallel, then work is negative. Another important point work is scalar quantity. Some people confused due to, sometime work is positive or sometime negative.

Because they thought that if work is positive, So its direction is toward right. And if it is negative then direction is towards left. **But this is not correct at all**. Because work is a scalar quantity, you cant associate any direction with it. Work is calculate with the help of force and displacement.

Therefore force is a vector quantity, and displacement is also a vector quantity. But work is dot product of force and displacement, So it is a scalar quantity. Hence sign of work indicate, the direction of force and displacement. If work sign is positive then force and displacement direction are same.

And if it is negative, then force and displacement direction are opposite. This is true meaning of work sign.

#### ;If force and displacement are perpendicular;

Therefore; work done by lady is zero. Hence lady is carrying sack from one place to other place, but she is not doing any work according to Physics definition.

**Work and Energy; **

**Also Check: Why Are There Different Branches Of Chemistry **

## Work Done By Constant Forces And Contact Forces

The simplest work to evaluate is that done by a force that is constant in magnitude and direction. In this case, we can factor out the force; the remaining integral is just the total displacement, which only depends on the end points *A* and *B*, but not on the path between them:

We can also see this by writing out in Cartesian coordinates and using the fact that the components of the force are constant:

shows a person exerting a constant force \overset along the handle of a lawn mower, which makes an angle \theta with the horizontal. The horizontal displacement of the lawn mower, over which the force acts, is \overset. The work done on the lawn mower is W=\overset·\overset=Fd\,\text\,\theta , which the figure also illustrates as the horizontal component of the force times the magnitude of the displacement.

**Figure 7.3** Work done by a constant force. A person pushes a lawn mower with a constant force. The component of the force parallel to the displacement is the work done, as shown in the equation in the figure. A person holds a briefcase. No work is done because the displacement is zero. The person in walks horizontally while holding the briefcase. No work is done because \text\,\theta is zero.

In , where the person in is walking horizontally with constant speed, the work done by the person on the briefcase is still zero, but now because the angle between the force exerted and the displacement is 90\text and \text\,90\text=0 .

## Work Done By A Constant Force

When a force acts on an object over a distance, it is said to have done work on the object. Physically, the work done on an object is the change in kinetic energy that that object experiences. We will rigorously prove both of these claims.

The term work was introduced in 1826 by the French mathematician Gaspard-Gustave Coriolis as weight lifted through a height, which is based on the use of early steam engines to lift buckets of water out of flooded ore mines. The SI unit of work is the newton-meter or joule .

**Don’t Miss: Algebra Road Trip Project Answer Key **

## What Is The Formula For Work

**Definition:** In our daily life work implies an activity resulting in muscular or mental exertion. However, in physics the term work is used in a specific sense involves the displacement of a particle or body under the action of a force. work is said to be done when the point of application of a force moves.Work done in moving a body is equal to the product of force exerted on the body and the distance moved by the body in the direction of force.**Work = Force × Distance moved in the direction of force**.

**The work done by a force on a body depends on two factors** Magnitude of the force, and Distance through which the body moves

**Unit of Work**When a force of 1 newton moves a body through a distance of 1 metre in its own direction, then the work done is known as 1 joule.Work = Force × Displacement1 joule = 1 N × 1 mor 1 J = 1 Nm

## No Related Questions Found

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

**You May Like: How To Convert In Chemistry **

## Difference Between Work And Power

The differences between work and power are mentioned in the following table:

Work | Power |

Work is referred to as the process of energy that is transferred to an objects motion by applying force. It is generally represented as the product of displacement and force. | Power is the amount of energy that is transferred in a unit of time.; |

The SI unit of work is Joule | The SI unit of power is Watt |

The formula for calculating the force is Work = Force * Displacement. | The formula of calculating power is Power = Work/Time |

Work can be done in various other measures like kWh, MWh, GWh and volt | Energy can be measured in units like GW, MW and kW. |

Work does not depend on time. | Power depends on time.; |

## Work Power And Efficiency

When a force causes a body to move, work is being done on the object by the force. Work is the measure of energy transfer when a force moves an object through a distance .

So when work is done, energy has been transferred from one energy store to another, and so:

energy transferred = work done

Energy transferred and work done are both measured in joules .

**Read Also: When Was Geometry Dash Made **

## Example 1 Calculating The Kinetic Energy Of A Package

Suppose a 30.0-kg package on the roller belt conveyor system in Figure 3;is moving at 0.500 m/s. What is its kinetic energy?

#### Strategy

Because the mass *m* and speed *v* are given, the kinetic energy can be calculated from its definition as given in the equation \text=\fracmv^2\\.

#### Solution

The kinetic energy is given by;\text=\fracmv^2\\.

Entering known values gives KE = 0.5 2,;which yields

KE = 3.75 kg; m2/s2 = 3.75 J.

#### Discussion

Note that the unit of kinetic energy is the joule, the same as the unit of work, as mentioned when work was first defined. It is also interesting that, although this is a fairly massive package, its kinetic energy is not large at this relatively low speed. This fact is consistent with the observation that people can move packages like this without exhausting themselves.

## Example 2 Determining The Work To Accelerate A Package

Suppose that you push on the 30.0-kg package in Figure 3;with a constant force of 120 N through a distance of 0.800 m, and that the opposing friction force averages 5.00 N.

#### Strategy and Concept for Part 1

This is a motion in one dimension problem, because the downward force and the normal force have equal magnitude and opposite direction, so that they cancel in calculating the net force, while the applied force, friction, and the displacement are all horizontal. As expected, the net work is the net force times distance.

#### Solution for Part 1

The net force is the push force minus friction, or *F*net = 120 N 5.00 N = 115 N. Thus the net work is

\beginW_}&=&F_}d=\\\text&=&9.20\text\cdot}=92.0\text\end\\

#### Discussion for Part 1

This value is the net work done on the package. The person actually does more work than this, because friction opposes the motion. Friction does negative work and removes some of the energy the person expends and converts it to thermal energy. The net work equals the sum of the work done by each individual force.

#### Strategy and Concept for;Part 2

The forces acting on the package are gravity, the normal force, the force of friction, and the applied force. The normal force and force of gravity are each perpendicular to the displacement, and therefore do no work.

#### Solution for;Part 2

**Recommended Reading: What Is Meant By The Process Of Differentiation In Geography **

## Work Has Units Of Energy

The total energy of a system is its internal or thermal energy plus its mechanical energy. Mechanical energy can be divided into energy of motion and “stored” energy . The total mechanical energy in any system is the sum of its potential and kinetic energies, each of which can take various forms.

Kinetic energy is energy of motion through space, both linear and rotational. If a mass *m* is held a distance *h* above the ground, its potential energy is *m gh*. Where the acceleration due to gravity,

**g**, has the value of 9.80 m/s2 near Earth’s surface.

If the object is released from rest at height h and allowed to fall downward to Earth , its kinetic energy at impact is m**v2** = mgh, as all of the energy has been converted from potential to kinetic during the fall . At all times, the sum of the potential energy of the particle and its kinetic energy remains constant.

- Because force has units of;
*newtons*; in the SI system and distance is in meters, work and energy in general have units of kgm2/s2. This SI unit of work is known as the;*Joule*.

## Physics Work And Energy

When an object moves towards the direction of the force applied, then work is said to be done. But for work to be done energy is the most important thing as it is the ability to work. When work is done by animals or humans, they get the energy from food and when work is done by machines, they get energy from electricity or fuel.;

Work;

Work is done when a force produces some kind of motion. For example, when a man climbs a mountain, work is done because while climbing a mountain he is moving against the force of gravity. Hence, work depends upon two factors. They are:;

Magnitude of force

The direction in which the body moves due to the force applied.

Hence, work is measured by the product of displacement and force of a body along with its direction of the force. It is referred to as scalar quantity and the SI unit of work is Joule. The equation thus stands as:

Work = F * S

If a body is displaced by S while a Force F acts on it, in such a case

Work W = FS Cos

One thing to note here is that force is said to work when it produces a motion in an object. For example, a man tries to move a wall but the wall does not move, hence the work done by the man is zero as there is no displacement produced. But he does lose energy because in his attempt to push the wall he stretches his muscles and thus feels tired.;

Energy

Hence from the formula given above, we can state:

1. The kinetic energy of a body gets doubled whenever its mass gets doubled.

**Also Check: What Kind Of Math Is On The Ged Test **

## Understand Work Meaning In Physics

**Work meaning- **To do anything which involves mental or physical effort **.;** But in Physics work is different, With normal definition of work. Because in Physics mental work is not considered work .Here i want to clear you, in day to day life, which you understand meaning of work is different in Physics.

Hence suppose if you are reading hard for your examination. So you are doing mental work, but in Physics meaning you are not doing any work. To understand Physics work, force and displacement are consider. See the above picture, how man is doing work ?whereas lady is not doing any work.

## The Angle Between The Force Vector And The Displacement Vector

The work done by a force on an object can be positive, negative, or zero, depending upon the direction of displacement of the object with respect to the force. For an object moving in the opposite direction to the direction of force, such as friction acting on an object moving in the forward direction, the work is done due to the force of friction is negative.

Similarly, an object experiences a zero force when the angle of displacement is perpendicular to the direction of the force. Consider an example of a coolie lifting a mass on his head moving at an angle of 90 with respect to the force of gravity. Here, the work done by gravity on the object is zero.

Stay tuned to BYJUS and Keep Falling in Love with Learning!

**You May Like: Where’s My Water Cool Math Games **