Tag: work, energy and power

Questions Related to work, energy and power

A particle of mass $1\ kg$ moving with a velocity of $(4\hat {i}-3\hat {j})m/s$ collides with a fixed surface. After the collision velocity of the particle is $(4\hat {i}-3\hat {j})m/s$. Collision is

collisions in one dimension collisions work, energy and power mechanics physics

  1. Elastic

  2. Ineleastic

  3. Perfectly inelastic

  4. Data

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Correct Option: A

Two masses $m _{1}$ and $m _{2}$, approaches each other with equal speeds and collide elastically. After collision $m _{2}$ comes to rest. Then $m _{1}$/$m _{2}$ is

collisions in one dimension collisions work, energy and power mechanics physics

  1. $1$

  2. $\dfrac{1}{2}$

  3. $\dfrac{1}{3}$

  4. $\dfrac{1}{4}$

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Correct Option: B

Two identical balls each of mass in are moving in opposite direction with a speed v. if they collide elastically maximum potentail energy stored in the ball is :

collisions in one dimension collisions work, energy and power mechanics physics

  1. 0

  2. $\dfrac { 1 }{ 2 } { mv }^{ 2 }$

  3. ${ mv }^{ 2 }$

  4. $2{ mv }^{ 2 }$

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Correct Option: A
Explanation:

Net momentum before collision will be $mv+(-mv)=0$, $negative$ because from $opposite $ direction.

so after the collision they will get stopped to make the net momentum again $zero$ and whole energy will be get stored
 as $PE$. ($inelastic $ $ collision$)

There is one other possibility too that is they $exchange$ their velocities so that again the net momentum will become
 $zero.$ $elastic$ $ collision$ .
In elastic collision there is no loss in $KE$  so $no$ storage of $PE.$


Two particles moving initially in the same direction undergo a one dimensional,elastic collision. Their relative velocities before and after the collision are $\overrightarrow { { v } _{ 1 } } $ and $\overrightarrow { { v } _{ 2 } } $. Then:

collisions in one dimension collisions work, energy and power mechanics physics

  1. $\left| \overrightarrow { { v } _{ 1 } } \right| = \left| \overrightarrow { { v } _{ 2 } } \right| $

  2. $\overrightarrow { { v } _{ 1 } } = - \overrightarrow { { v } _{ 2 } }$ only if the two are of equal mass.

  3. $\overrightarrow { { v } _{ 1 } } = -\overrightarrow { { v } _{ 2 } } = {\left| \overrightarrow { { v } _{ 1 } } \right|}^{2}$

  4. $\left| \overrightarrow { { v } _{ 1 }} . \overrightarrow { { v } _{ 2 }} \right| = -  {\left| \overrightarrow { { v } _{ 1 } } \right|}^{2}$

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Correct Option: D

The coefficient of restitution of a perfectly elastic collision is :

collisions in one dimension collisions work, energy and power mechanics physics

  1. $1$

  2. $0$

  3. $\infty$

  4. $-1$

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Correct Option: A
Explanation:

The Coefficent of Restitution is a measure of the "bounciness" of a collision between two objects: how much of the kinetic energy remains for the objects to rebound from one another vs. how much is lost as heat, or work done deforming the objects.

The coefficient, e is defined as the ratio of relative speeds after and before an impact, taken along the line of the impact:
$e=\dfrac { Speed\quad of\quad separation }{ Speed\quad of\quad approach } $

(i)   For perfectly elastic collision $e = 1$
(ii)  For perfectly inelastic collision $e = 0$
(iii) For other collision $0 \lt e \lt 1$

A ball moving with a velocity v strikes a wall moving toward the ball with a velocity u. An elastic impact lasts for t sec. Then the mean elastic force acting on the ball is 

collisions in one dimension collisions work, energy and power mechanics physics

  1. $\displaystyle \frac { 2mv }{ t } $

  2. $\displaystyle \frac { 2m\left( \upsilon +u \right) }{ t } $

  3. $\displaystyle \frac { 2m\left( \upsilon +2u \right) }{ t } $

  4. $\displaystyle \frac { m\left( 2\upsilon +u \right) }{ t } $

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Correct Option: B
Explanation:

Relative speed of the ball $\displaystyle =\left( \upsilon +u \right) $
Speed after rebouncing $\displaystyle =-\left( \upsilon +u \right) $
Now, $\displaystyle F=m\frac { \Delta \upsilon  }{ \Delta t } =\frac { m }{ t } \left[ \left( \upsilon +u \right)  \right] -[-\left[ \left( \upsilon +u \right)  \right]] $
$\displaystyle =\frac { 2m }{ t } \left( \upsilon +u \right) $

A ball with mass m and speed $V _0$ hit a wall and rebounds back with same speed.
Calculate the change in the object's kinetic energy.

collisions in one dimension collisions work, energy and power mechanics physics

  1. $-mv _0 ^2$

  2. $- \frac{1}{2}mv _0 ^2$

  3. Zero

  4. $ \frac{1}{2}mv _0 ^2$

  5. $mv _0 ^2$

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Correct Option: C
Explanation:

The speed of the ball remains the same $v _0$ before and after the collision with wall.

Thus the kinetic energy remains $\dfrac{1}{2}mv _0^2$.
Since kinetic energy is a scalar quantity, the change in it is zero.

The coefficient of restitution (e) for a perfectly elastic collision is

collisions in one dimension collisions work, energy and power mechanics physics

  1. $-$1

  2. 0

  3. $\infty$

  4. 1

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Correct Option: D
Explanation:

$(O.R/e)=\dfrac{Relative:speed:after:collision}{Relative:speed:before:collision}$

For an elastic collision coefficient of restitution is 1.

 A body of mass $m$ moving at a constant velocity $v$ hits another body of the same mass moving at the same velocity but in the opposite direction and sticks to it. The common velocity after collision is

collisions in one dimension collisions work, energy and power mechanics physics

  1. $v$

  2. $0$

  3. $2v$

  4. $\dfrac{v}{2}$

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Correct Option: B
Explanation:

Since the collision is inelastic, applying momentum conservation for inelastic collisions,
$ mv + m(-v) = (m+m)V $
$ V = 0 $.

The co-efficient of restitution for a perfectly elastic collision is:

collisions in one dimension collisions work, energy and power mechanics physics

  1. $1$

  2. $0$

  3. lies in between $0$ and $1$

  4. infinity

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Correct Option: A
Explanation:

The coefficient of restitution is defined as the ratio of the relative velocity of separation to that of approach, in a situation of two objects colliding with each other. 

The relative velocity of approach is the difference between the individual velocities of the two bodies before the collision.
The relative velocity of separation is that after the collision.
In a perfectly elastic collision, the two relative velocities are exactly equal. Hence the coefficient becomes $= 1$