This manufacturing cell uses air pressure to move parts thro

This manufacturing cell uses air pressure to move parts through the process. The pressure creates the force vs time plot shown above. What is the part velocity at t = 1.2 sec, assuming it starts from rest?

Solution

In a force time graph, the area below the graph is force multiplied by time. This Quantity is equal to Impulse and it denotes change in momentum of the object.

In the above case, the area below the graph is (0.5*3*0.5 + 2.1) Newton-Seconds, equal to 2.85 Newton-second.

Impulse = 0.5*3*0.5 + 2.1 = 2.85 Newton-Seconds

Since it is given that the object starts from rest, the initial velocity is zero. Hence,

Mass of the body * change in velocity = change in momentum

2.85 Newton-second = 0.2 kg * X meters/sec

final velocity = 14.25 meter per second.