A ball of mass m moving with speed u collides | vedclass

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

Question

(D) The velocity of the ball before collision can be resolved into two components: horizontal component $u_x = u \cos 	heta$ and vertical component $

Vedclass · Accepted Answer

$m u(1+e) \sin 	heta$

Vedclass · Answer

(D) The velocity of the ball before collision can be resolved into two components: horizontal component $u_x = u \cos 	heta$ and vertical component $u_y = -u \sin 	heta$ (taking downward as negative).Since the surface is smooth,there is no impulse in the horizontal direction,so the horizontal velocity remains unchanged: $v_x = u \cos 	heta$.In the vertical direction,the coefficient of restitution $e$ is defined as the ratio of the velocity of separation to the velocity of approach along the normal: $e = \frac{v_y}{u_y}$.Thus,the vertical velocity after collision is $v_y = e u \sin 	heta$ (upward).The impulse $I$ imparted to the ball by the surface is equal to the change in momentum of the ball: $\vec{I} = m(\vec{v} - \vec{u})$.Since there is no change in horizontal momentum,the impulse is only in the vertical direction: $I = m(v_y - u_y) = m(e u \sin 	heta - (-u \sin 	heta)) = m u(1+e) \sin 	heta$.The magnitude of the impulse imparted to the surface by the ball is equal to the magnitude of the impulse imparted to the ball by the surface,which is $m u(1+e) \sin 	heta$.

$A$ ball of mass $m$ moving with speed $u$ collides with a smooth horizontal surface at an angle $\theta$ with it as shown in the figure. The magnitude of the impulse imparted to the surface by the ball is [Coefficient of restitution of collision is $e$].

Similar Questions

The bob of a simple pendulum (mass $m$ and length $l$) is dropped from a horizontal position. It strikes a block of the same mass $m$ placed on a horizontal frictionless table. The collision is elastic. The kinetic energy of the block after the collision will be

Two equal masses $m_1$ and $m_2$ moving along the same straight line with velocities $+3 \, m/s$ and $-5 \, m/s$ respectively collide elastically. Their velocities after the collision will be respectively

When two bodies collide elastically,then

$A$ body of mass $1\,kg$ collides head-on elastically with a stationary body of mass $3\,kg$. After the collision,the smaller body reverses its direction of motion and moves with a speed of $2\,m/s$. The initial speed of the smaller body before the collision is $..........\,m/s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module