![]() One Newton is the force required to impart an acceleration of 1m/s2 to a mass of 1 kg. Remember that in SI units the unit of force is called the Newton (N). This experiment requires you to record measurements in Newtons. It is interesting to note that W cancelled out in the derivation of Equation 3 so that the weight of the block doesn’t matter. ![]() Thus, if the plane is gradually tipped up until the block just breaks away and the plane angle is then measured, the coefficient of static friction is equal to the tangent of this angle, which is called the limiting angle of repose. If the plane is tipped up until at some value θmax the block just starts to slide, we have: It is opposed by the frictional force Ffr, As long as the block remains at rest, Ffr must be equal to W sin θ. The component Wsin θis parallel to the plane and constitutes the force urging the block to slide down the plane. The block has weight W whose component Wcosθ (where θ is the plane angle) is perpendicular to the plane and is thus equal to the normal force, FN. The arrangement is illustrated in Figure 1 above. One way of investigating the case of static friction is to observe the so-called “limiting angle of repose.” This is defined as the maximum angle to which an inclined plane may be tipped before a block placed on the plane just starts to slide. This is why a slight push is necessary to get the block started for the measurement of µk. This means that a somewhat larger force is needed to break a body away and start it sliding than is needed to keep it sliding at constant speed once it is in motion. We find that µsis slightly larger than µk. Where Ffris the frictional force in the static case, Ffr max is the maximum value this force can assume and µsis the coefficient of static friction. This situation may be expressed in equation form as: But if static equilibrium demands a frictional force larger than this maximum, static equilibrium conditions will cease to exist because this force is not available and the body will start to move. We conclude that in the static case where a body is at rest the frictional force automatically adjusts itself to keep the body at rest up to a certain maximum. However, there is a threshold value of the pushing force beyond which larger values will cause the body to break away and slide. This means that the frictional force automatically adjusts itself to be equal to the pushing force and thus to just be enough to balance it. As long as the pushing force is not strong enough to start the body moving, the body remains in equilibrium. When a body lies at rest on a surface and an attempt is made to push it, the pushing force is opposed by a frictional force. Thus, corresponding values of Ffr,and FN can be found, and plotting them will show whether Ffrand FN are indeed proportional. The normal force between the two surfaces is equal to the weight of the block and can be increased by placing weights on top of the block. This tension, in turn, is equal to the total weight attached to the cord’s end. Since there is no acceleration, the net force on the block is zero, which means that the frictional force is equal to the tension in the cord. ![]() The weights are varied until the block moves at constant speed after having been started with a slight push. The other surface is the bottom face of a block that rests on the plane and to which is attached a weighted cord that passes over the pulley. As you will see in your later study of physics the distinction between conservative and non-conservative forces is a very important one that is fundamental to our concepts of heat and energy. A method of checking the proportionality of Ffr, and FNand of determining the proportionality constant µk is to have one of the surfaces in the form of a plane placed horizontally with a pulley fastened at one end. Yet, the energy used to overcome friction is dissipated, which means it is lost or made unavailable as heat. Thus, the energy expended in lifting an object may be regained when the object descends. This is in contrast to what is called a “conservative” force such as gravity, which is against you on the way up but with you on the way down. Friction is called a “non-conservative” force because energy must be used to overcome it no matter which way you go. In short, friction is always against you. This means that if you reverse the direction of sliding, the frictional force reverses too. Note carefully that Ffris always directed opposite to the direction of motion. µk is therefore more precisely called the coefficient of kinetic or sliding friction. The subscript k stands for kinetic, meaning that µk is the coefficient that applies when the surfaces are moving one with respect to the other. FN is the normal force and µk is the coefficient of kinetic friction. ![]()
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