A body of mass 2 kg is acted on by a force F wlalieh varies with time t as shown in the figure. The momentum gained by the body at the end of 5 s/is F(N) 4 20 10 0 1 2 3 4 5 6 t(s)
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The momentum gained by the body at the end of 5s is 12 Ns.
A body of mass 2 kg is acted on by a force F which varies with time t as shown in figure.
The momentum gained by the body at the end of 5s, is..
Newton's 2nd law of motion, “It states that the rate of change of linear momentum of body is the resultant force acting on it.”
i.e., F = dP/dt
⇒∫F dt = ∫dP
from above equation,
- It is clear that if we have given F - t graph, then change in momentum is the area enclosed by the graph.
∴ The momentum gained by the body at the end of 5 s = area formed by graph in the range of 5s.
= area of trapezium [ see figure ]
= 1/2 × (sum of length of parallel sides) × separation between parallel sides
= 1/2 × (1s + 5s) × 4N
= 12 Ns
Therefore the momentum gained by the body at the end of 5s is 12 Ns.
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