![]() This is a restoring force, because when the spring is stretched, the force exerted by by the spring is opposite to the direction it is stretched. Where x is the amount the spring is stretched. If an object applies a force to a spring, the spring applies an equal and opposite force to the object. The larger k is, the stiffer the spring is and the harder the spring is to stretch. K is a measure of how difficult it is to stretch a spring. For a spring this can be written:į = kx, where k is known as the spring constant. This linear relationship between the force and the displacement is known as Hooke's law. An ideal spring is one in which the amount the spring stretches or compresses is proportional to the applied force. In the case of gravitational potential energy, the object has the potential to do work because of where it is, at a certain height above the ground, or at least above something.Įnergy can also be stored in a stretched or compressed spring. An object with potential energy has the potential to do work. Work done by gravity = W = mgh (h = height lost by the object)Īn alternate way of looking at this is to call this the gravitational potential energy. The work done by the force of gravity is the force multiplied by the distance, so if the object drops a distance h, gravity does work on the object equal to the force multiplied by the height lost, which is: This force is the force of gravity, with a magnitude equal to mg, the weight of the object. This means there must be a net force on the object, doing work. If you drop an object it falls down, picking up speed along the way. You could apply the projectile motion equations, or you could think of the situation in terms of energy (actually, one of the projectile motion equations is really an energy equation in disguise). Let's say you're dropping a ball from a certain height, and you'd like to know how fast it's traveling the instant it hits the ground. Note that the work in this equation is the work done by the net force, rather than the work done by an individual force. There is a strong connection between work and energy, in a sense that when there is a net force doing work on an object, the object's kinetic energy will change by an amount equal to the work done: For an object traveling at a speed v and with a mass m, the kinetic energy is given by: It is energy associated with a moving object, in other words. If you move the book at constant speed horizontally, you don't do any work on it, despite the fact that you have to exert an upward force to counter-act gravity.Īn object has kinetic energy if it has mass and if it is moving. If you pick the book up and place it gently back on the floor again, though, you're doing negative work, because the book is going down but you're exerting an upward force, acting against gravity. If you pick a book off the floor and put it on a table, for example, you're doing positive work on the book, because you supplied an upward force and the book went up. If the force has a component in the direction opposite to the displacement, the force does negative work. Work can be either positive or negative: if the force has a component in the same direction as the displacement of the object, the force is doing positive work. The unit of work is the unit of energy, the joule (J). If a force is applied but the object doesn't move, no work is done if a force is applied and the object moves a distance d in a direction other than the direction of the force, less work is done than if the object moves a distance d in the direction of the applied force. Whenever a force is applied to an object, causing the object to move, work is done by the force. The initial and final information can often tell you all you need to know. Often you can look at the starting conditions (initial speed and height, for instance) and the final conditions (final speed and height), and not have to worry about what happens in between. With energy the approach is usually a little different. When forces and accelerations are used, you usually freeze the action at a particular instant in time, draw a free-body diagram, set up force equations, figure out accelerations, etc. Energy gives us one more tool to use to analyze physical situations. ![]()
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