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.

01:53

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‘š being acted on by three separate forces. To find the acceleration of π‘š, we’ll want to use Newton’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‘š and we’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‘š. Based on our diagram, that net force will have two components: one in the 𝑖 direction and one in the 𝑗 direction.

In the 𝑖 direction, the net force equals the sum of the 𝑖 direction forces on π‘š. That is equal to 10.0 minus 2.0𝑖, which equals 8.0𝑖 newtons. In the 𝑗 direction, the component of the net force is negative 4.0 in units of newtons. So the net force acting on π‘š is 8.0𝑖 minus 4.0𝑗 newtons.

By Newton’s second law, if we divide the net force by the object’s mass, then that’s equal to the object’s acceleration π‘Ž. When we insert our value of 5.0 kilograms for π‘š, we divide that mass into the net force to find an acceleration of 1.6𝑖 minus 0.8𝑗, with units of meters per second squared.

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