A force-time graph for a linear motion is sho | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The change in linear momentum $\Delta p$ is equal to the impulse,which is the area under the force-time $(F-t)$ graph.$\Delta p = \int F \, dt = \

Vedclass · Accepted Answer

$0 \, N \cdot s$

Vedclass · Answer

(B) The change in linear momentum $\Delta p$ is equal to the impulse,which is the area under the force-time $(F-t)$ graph.$\Delta p = \int F \, dt = 	ext{Area under } F-t 	ext{ graph}$.The graph consists of circular segments. From $t = 0$ to $t = 2$,the area is a quarter-circle below the time axis with radius $r = 2$. Area $= -\frac{1}{4} \pi r^2 = -\frac{1}{4} \pi (2)^2 = -\pi$.From $t = 2$ to $t = 6$,the area is a semi-circle above the time axis with radius $r = 2$. Area $= +\frac{1}{2} \pi r^2 = +\frac{1}{2} \pi (2)^2 = +2\pi$.From $t = 6$ to $t = 8$,the area is a quarter-circle below the time axis with radius $r = 2$. Area $= -\frac{1}{4} \pi r^2 = -\frac{1}{4} \pi (2)^2 = -\pi$.The total area (net impulse) $= -\pi + 2\pi - \pi = 0$.Therefore,the linear momentum gained between $0$ and $8$ seconds is $0 \, N \cdot s$.

$A$ force-time graph for a linear motion is shown in the figure,where the segments are circular. The linear momentum gained between $0$ and $8$ seconds is

Similar Questions

$N$ bullets,each of mass $m \, kg$,are fired with a velocity $v \, m/s$ at the rate of $n$ bullets per second upon a wall. The reaction force offered by the wall to the bullets is given by:

$A$ body of mass $5 \,kg$ is moving with a velocity of $\vec{v}=(2 \hat{i}+6 \hat{j}) \,m/s$ at $t=0 \,s$. After time $t=2 \,s$,the velocity of the body is $(10 \hat{i}+6 \hat{j}) \,m/s$. The change in momentum of the body is ......... $kg \cdot m/s$.

$A$ $4 \ kg$ disk slides over level ice toward the east at a velocity of $1 \ m/s$,as shown. The disk strikes a post and rebounds toward the north at the same speed. The change in the magnitude of the eastward component of the momentum of the disk is ............. $kg \cdot m/s$.

Why does a child feel more pain when she falls down on a hard cement floor,than when she falls on the soft muddy ground in the garden?

Force is the mutual interaction between the bodies according to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module