SNHS Physics Blog 5: Work and its Relationship to Energy

Yunhui Shim

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When we pull a heavy suitcase through the airport or push a heavy shopping cart in a store, we are doing work. These are some simple cases of work being done, in which force is applied to an object and the object moves in the direction of the applied force. W, or work is defined as the force times the distance moved and can be derive by the multiplication of force times the distance, with units of the newton meter (N*m), or joule (J). 1 Joule of work can be conceptualized as the amount of work that could be done, as you lift a gallon of milk an inch high.

Although, the definition seems easy, this concept is not very intuitive. Suppose on pushes on a crate, but the crate refuses the budge, even for a bit. The work done on the crate, no matter how hard one pushes, is zero. This is because, the distance in this case is zero. The angle of the force also comes into play, when considering the work done. When a person is pulling on a suitcase on a level surface, with a strap, this makes an angle with the horizontal. In this case work is calculated by the following rule that the only component of force in direction of the displacement can do work, or W=Fdcosθ. The work done is zero, in cases when the force become perpendicular to the displacement, because the cosine of a right angle is zero. In other instances, work done can be negative, if the force acts opposite to the displacement, or when the angle is 180 degrees. Work done by separate forces can be summed, and the total of the work can be derived by the individual amounts of work added together.

When work is done on an object, the energy of the object also changes. When one stops pushing a cart, the work goes into increasing kinetic energy, and when one climbs a mountain, the work goes into increasing the potential energy. Energy is defined as the capacity to do work, and we will learn about how work and energy are inseparable concepts in physics.

Kinetic energy is defined as the energy of motion. When a box of mass m is pushed across an ice-skating rink of force F, the acceleration of box is given by Newton’s second law of a=F/m. The speed and displacement of the accelerating object can be derived by the following kinematics equation of 〖ν_f〗^2-〖ν_i〗^2=2ad. When the a is replaced with F/m, and Fd is replaced by W, can learn that W=0.5m(〖ν_f〗^2-〖ν_i〗^2). The quantity of 0.5mv^2 has special significance in that, it defines what kinetic energy is. In general, the kinetic energy of an object is the energy due to the motion. Kinetic energy increases linearly with the mass, and the squared value of velocity.

Now, to find out how work and energy are related, we can match the two pieces of information we learned together. Specifically, the total work done on an object is equal to the change in kinetic energy.

However, we can’t stop here because there is another type of energy that we must go over. It is potential energy. Work must be done if we want to lift the bowling ball from the floor to the shelf, and when we lift the ball, we have just stored potential energy to the ball. If the ball later falls down from the shelf, gravity is able to do the same amount of work on the way down, and the work becomes “recovered”. Potential energy is stored energy. When the separation between the ball and the floor is increased, work that is done is stored in the form of increased potential energy. Potential energy has many forms. Out of all, the most common is the gravitational potential energy. To calculate for the potential energy for gravity, one must multiply the mass, acceleration due to gravity, and the distance together. Elastic materials also have potential energy. Springs and rubber bands are referred to as elastic because after distortion, they can return to their original size and shape. Potential energy that is stored in a distorted elastic material is called the elastic potential energy, and when a strong is stretched or compressed by x, the force exerted on the spring increases uniformly from 0 to kx(k is the spring constant). The average force is derived by halving the kx, or 0.5kx, and 0.5kx^2 is thus the spring potential energy.