exmaples of claulculating the workdone on a particel

The bottom line is that you need to analyze each particular case to determine the work done by the forces, whether positive, negative or zero. In this case, kinetic friction exerted by the rug on the object could be in the same direction as the displacement of the object, relative to the floor, and do positive work.

You can pull the rug out from under an object in such a way that it slides backward relative to the rug, but forward relative to the floor. If you’re driving your car at the speed limit on a straight, level stretch of highway, the negative work done by air resistance is balanced by the positive work done by the static friction of the road on the drive wheels. Static friction can keep someone from sliding off a sled when the sled is moving and perform positive work on the person. As an external force, static friction can do work. The force of static friction does no work in the reference frame between two surfaces because there is never displacement between the surfaces. Where | l A B | | l A B | is the path length on the surface. 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: The simplest work to evaluate is that done by a force that is constant in magnitude and direction. Work Done by Constant Forces and Contact Forces In the English system, still used in the United States, the unit of force is the pound (lb) and the unit of distance is the foot (ft), so the unit of work is the foot-pound ( ft This combination is called a joule, for historical reasons that we will mention later, and is abbreviated as J. The units of work are units of force multiplied by units of length, which in the SI system is newtons times meters, N The maximum work is done by a given force when it is along the direction of the displacement ( cos θ = ± 1 cos θ = ± 1), and zero work is done when the force is perpendicular to the displacement ( cos θ = 0 cos θ = 0).

As a result, the work done by a force can be positive, negative, or zero, depending on whether the force is generally in the direction of the displacement, generally opposite to the displacement, or perpendicular to the displacement. The components of a vector can be positive, negative, or zero, depending on whether the angle between the vector and the component-direction is between 0 ° 0 ° and 90 ° 90 ° or 90 ° 90 ° and 180 ° 180 °, or is equal to 90 ° 90 °. Recall that the magnitude of a force times the cosine of the angle the force makes with a given direction is the component of the force in the given direction. From the properties of vectors, it doesn’t matter if you take the component of the force parallel to the displacement or the component of the displacement parallel to the force-you get the same result either way. In words, you can express Equation 7.1 for the work done by a force acting over a displacement as a product of one component acting parallel to the other component. Which choice is more convenient depends on the situation. In two dimensions, these were the x- and y-components in Cartesian coordinates, or the r- and φ φ-components in polar coordinates in three dimensions, it was just x-, y-, and z-components. We could equally well have expressed the dot product in terms of the various components introduced in Vectors. We choose to express the dot product in terms of the magnitudes of the vectors and the cosine of the angle between them, because the meaning of the dot product for work can be put into words more directly in terms of magnitudes and angles. The infinitesimal work is the dot product of these two vectors the total work is the integral of the dot product along the path. The force acting on a particle and its infinitesimal displacement are shown at one point along the path between A and B. If the line joining A and B is horizontal, what is the work done on the object by the gravitational force? Explain your answer.Figure 7.2 Vectors used to define work. What is the work done by the force of gravity on the object?Ī mass of 10 kg is at a point A on a table.

The initial and the final points of the path of the object lie on the same horizontal line. Is force of friciton positive, negative or zero work?Īn object thrown at a certain angle to the ground moves in a curved path and falls back to the ground.

When force acts opposite to direction of motionĪngle made between direction of force and direction of motion is 180 degree Work Done when Force Acts opposite to Direction of Motion Since angle between force and distance is 90 degree Here, Force is appled in vertical directionīut luggage is carried in horizontal direction

Exmaples of claulculating the workdone on a particel