Video: Finding the Acceleration of an Object That Is Subjected to Multiple Constant Forces

Find the acceleration of the object of mass 5.0 kg shown in the accompanying diagram.

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Video Transcript

Find the acceleration of the object of mass 5.0 kilograms shown in the accompanying diagram.

In this diagram, we see the mass π being acted on by three separate forces. To find the acceleration of π, weβll want to use Newtonβs second law. This law connects the net force acting on an object with its mass and its acceleration. If we know the net force acting on π and weβre given its mass, we can solve for the acceleration of that mass.

Our first task is to solve for the net force acting on π. Based on our diagram, that net force will have two components: one in the π direction and one in the π direction.

In the π direction, the net force equals the sum of the π direction forces on π. That is equal to 10.0 minus 2.0π, which equals 8.0π newtons. In the π direction, the component of the net force is negative 4.0 in units of newtons. So the net force acting on π is 8.0π minus 4.0π newtons.

By Newtonβs second law, if we divide the net force by the objectβs mass, then thatβs equal to the objectβs acceleration π. When we insert our value of 5.0 kilograms for π, we divide that mass into the net force to find an acceleration of 1.6π minus 0.8π, with units of meters per second squared.