![]() ![]() Because there is no motion along the vertical axis, ΣF y = 0, implies N = mg. The forces on the block along the vertical direction are the normal, N, and gravity, mg. The origin of the x-axis is where the rough region starts, therefore the work done by the force of friction on the box after it has moved a distance d is given by: What is the work done by the force of friction on the block after it has moved a distance d along the rough surface?Ĭonsider the coordinate system as shown in the figure. When either the force is not constant along the path or the displacement vector changes with position then the work is calculated as the dot product between the force and the displacement vector:Įxample 1: Moving along a straight line with a force of changing magnitudeĪ block is moving along a horizontal surface when it encounters a rough region where the coefficient of kinetic friction between the block and the surface depends on position and is given by μ(x)=μ ox, where μ o is a positive constant. Work done by a changing force or changing displacement Calculate the change of kinetic energy of an object in terms of the work done by the external forces on the object. ![]() Calculate the work done by a force along a path that changes with position.Calculate the work done by a force that changes along the path followed by the object.As noted in Chapter 7.After completing this module you should be able to: We will see that the work done by nonconservative forces equals the change in the mechanical energy of a system. Now let us consider what form the work-energy theorem takes when both conservative and nonconservative forces act. When the same rock is dropped onto the ground, it is stopped by nonconservative forces that dissipate its mechanical energy as thermal energy, sound, and surface distortion. (b) A system with nonconservative forces. The spring can propel the rock back to its original height, where it once again has only potential energy due to gravity. When a rock is dropped onto a spring, its mechanical energy remains constant (neglecting air resistance) because the force in the spring is conservative. (a) A system with only conservative forces. Comparison of the effects of conservative and nonconservative forces on the mechanical energy of a system. We often choose to understand simpler systems such as that described in Figure 2(a) first before studying more complicated systems as in Figure 2(b). Figure 2 compares the effects of conservative and nonconservative forces. For example, when a car is brought to a stop by friction on level ground, it loses kinetic energy, which is dissipated as thermal energy, reducing its mechanical energy. Mechanical energy may not be conserved when nonconservative forces act. How Nonconservative Forces Affect Mechanical Energy ![]() The energy expended cannot be fully recovered. EXMAPLES OF CLAULCULATING THE WORKDONE ON A PARTICEL PLUSThe force here is friction, and most of the work goes into thermal energy that subsequently leaves the system (the happy face plus the eraser). Less work is done and less of the face is erased for the path in (a) than for the path in (b). The amount of the happy face erased depends on the path taken by the eraser between points A and B, as does the work done against friction. Furthermore, even if the thermal energy is retained or captured, it cannot be fully converted back to work, so it is lost or not recoverable in that sense as well. Friction, for example, creates thermal energy that dissipates, removing energy from the system. An important characteristic is that the work done by a nonconservative force adds or removes mechanical energy from a system. Because of this dependence on path, there is no potential energy associated with nonconservative forces. As illustrated in Figure 1, work done against friction depends on the length of the path between the starting and ending points. ![]() Friction is a good example of a nonconservative force. A nonconservative force is one for which work depends on the path taken. Conservative forces were discussed in Chapter 7.4 Conservative Forces and Potential Energy. Show how the principle of conservation of energy can be applied by treating the conservative forces in terms of their potential energies and any nonconservative forces in terms of the work they do.įorces are either conservative or nonconservative.Define nonconservative forces and explain how they affect mechanical energy. ![]()
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