Question

What is the impulse of force shown in the following figure?

A. 205 Ns
B. 450 Ns
C. 800 Ns
D. 1000 Ns

Answer 1

In the figure, we are given a F-t graph, and it depicts the variation of force with respect to time. Impulse is measured with respect to force and time and we can easily find its value by calculating the area under the graph, with the help of the given values.

Formula Used:
Formula for Impulse:
$I=\int{F(t).dt}$, where F is the force of the body and t is the time in which the force acts on the body.

Complete step by step answer:
Impulse, which is symbolised as I or Imp, is defined in classical mechanics as the integral of the force over a given time interval in which the force acts. We know that force is a vector quantity. Hence we can say that impulse is also a vector value.
When impulse is applied to an object, it can produce an equivalent change in vector for its linear momentum and it takes place in the same direction.
Impulsive forces act for a very short period of time. Hence we can say that it is a momentary force.

Impulse can be calculated by,
$I=\int{F(t).dt}$
This is the area under the f-t graph.
Hence, impulse equals to the area of the triangle
$I=\dfrac{1}{2}F\times t=\dfrac{1}{2}\times 100\times (10-1)=450Ns$
Hence the value of the impulse is $450Ns$
Therefore we can conclude that option B is the correct answer among the given options.

Note: The topic of jerks is often confused with impulse. Students must remember that impulse is the change in momentum which considers the mass of the object whereas jerk is only the rate of change of acceleration of the body. The mass is irrelevant in that case.