How to Calculate Changes in Kinetic Energy Using Net Force
In physics, if you want to find the change in an object’s kinetic energy, you have to consider only the work done by the net force acting on the object. In other words, you convert only the work done by the net force into kinetic energy.
For example, when you play tug-of-war against your equally strong friends, you pull against each other but nothing moves. Because there’s no movement, no work is done and you have no net increase in kinetic energy from the two forces.
Take a look at the figure. You may want to determine the speed of the 100-kilogram refrigerator at the bottom of a 3.0-meter-long ramp, using the fact that the net work done on the refrigerator goes into its kinetic energy. How do you do that? You start by determining the net force on the refrigerator and then find out how much work that force does. Converting that net-force work into kinetic energy lets you calculate what the refrigerator’s speed will be at the bottom of the ramp.
What’s the net force acting on the refrigerator? The component of the refrigerator’s weight acting along the ramp is
where m is the mass of the refrigerator and g is the acceleration due to gravity. The normal force is
which means that the kinetic force of friction is
where μk is the kinetic coefficient of friction. The net force accelerating the refrigerator down the ramp, Fnet, therefore, is
You’re most of the way there! If the 3.0-meter-long ramp is at a 30-degree angle to the ground and there’s a kinetic coefficient of friction of 0.57, plugging the numbers into this equation results in the following:
The net force acting on the refrigerator is about 6.2 newtons. This net force acts over the entire 3.0-meter ramp, so the work done by this force is
You find that 19 joules of work goes into the refrigerator’s kinetic energy. That means you can find the refrigerator’s kinetic energy like this:
You want the speed here, so solving for v and plugging in the numbers gives you
The refrigerator will be going 0.61 meters/second at the bottom of the ramp.