Find the acceleration of the object of mass 5.0 kilograms shown in the accompanying diagram.
In this diagram, we see the mass 𝑚 being acted on by three separate forces. To find the acceleration of 𝑚, 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 𝑚 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 𝑚. 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 𝑚. 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 𝑚 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 𝑎. When we insert our value of 5.0 kilograms for 𝑚, 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.