Impulse
Impulse
The above version of Newton’s Second Law can be rearranged to define the impulse, J, delivered by a constant force, F. Impulse is a vector quantity defined as the product of the force acting on a body and the time interval during which the force is exerted. If the force changes during the time interval, F is the average net force over that time interval. The impulse caused by a force during a specific time interval is equal to the body’s change of momentum during that time interval: impulse, effectively, is a measure of change in momentum.
The unit of impulse is the same as the unit of momentum, kg · m/s.
Example
A soccer player kicks a 0.1 kg ball that is initially at rest so that it moves with a velocity of 20 m/s. What is the impulse the player imparts to the ball? If the player’s foot was in contact with the ball for 0.01 s, what was the force exerted by the player’s foot on the ball?
What is the impulse the player imparts to the ball?
Since impulse is simply the change in momentum, we need to calculate the difference between the ball’s initial momentum and its final momentum. Since the ball begins at rest, its initial velocity, and hence its initial momentum, is zero. Its final momentum is:
Because the initial momentum is zero, the ball’s change in momentum, and hence its impulse, is 2 kg · m/s.
What was the force exerted by the player’s foot on the ball?
Impulse is the product of the force exerted and the time interval over which it was exerted. It follows, then, that . Since we have already calculated the impulse and have been given the time interval, this is an easy calculation:
Impulse and Graphs
SAT II Physics may also present you with a force vs. time graph, and ask you to calculate the impulse. There is a single, simple rule to bear in mind for calculating the impulse in force vs. time graphs:
The impulse caused by a force during a specific time interval is equal to the area underneath the force vs. time graph during the same interval.
If you recall, whenever you are asked to calculate the quantity that comes from multiplying the units measured by the y-axis with the units measured by the x-axis, you do so by calculating the area under the graph for the relevant interval.
Example
What is the impulse delivered by the force graphed in the figure above between t = 0 and t = 5?
The impulse over this time period equals the area of a triangle of height 4 and base 4 plus the area of a rectangle of height 4 and width 1. A quick calculation shows us that the impulse is:
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