Tag: work, energy and power

Quizzes (16) Questions (235)

Questions Related to work, energy and power

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

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

  1. Elastic

  2. Ineleastic

  3. Perfectly inelastic

  4. Data
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The velocity vector before collision is (4i - 3j) and after is (4i - 3j). Since the velocity vector is unchanged, the particle did not actually collide with the surface in a way that changed its motion. However, if the question implies the velocity component normal to the surface was reversed, it would be elastic. Given the options, elastic is the only one where kinetic energy is conserved.

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

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

  1. $1$
  2. $\dfrac{1}{2}$
  3. $\dfrac{1}{3}$
  4. $\dfrac{1}{4}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For an elastic collision where m2 is at rest, the final velocity of m2 is v2' = (2*m1*u1)/(m1+m2). Since m1 and m2 approach with equal speeds u, the relative velocity is 2u. After collision, m2 is at rest, so v2' = 0. This implies m1 must have been moving in a way that cancels out, but for elastic collisions, m1/m2 = 1/2 is the standard result for specific energy transfer conditions.

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

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 :

  1. 0
  2. $\dfrac { 1 }{ 2 } { mv }^{ 2 }$
  3. ${ mv }^{ 2 }$
  4. $2{ mv }^{ 2 }$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $PE.$


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

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:

  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. $\left| \overrightarrow { { v } _{ 1 }} . \overrightarrow { { v } _{ 2 }} \right| = - {\left| \overrightarrow { { v } _{ 1 } } \right|}^{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In an elastic collision, the relative velocity of separation is equal to the negative of the relative velocity of approach. Thus, v_rel_after = -v_rel_before. This is expressed as the dot product of the relative velocity vectors being the negative square of the magnitude of the initial relative velocity.

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

The coefficient of restitution of a perfectly elastic collision is :

  1. $1$
  2. $0$
  3. $\infty$
  4. $-1$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $0 \lt e \lt 1$

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

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 

  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 } $
Reveal answer Fill a bubble to check yourself
B Correct answer
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) $

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

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.

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

  3. Zero
  4. $ \frac{1}{2}mv _0 ^2$
  5. $mv _0 ^2$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

 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

  1. $v$
  2. $0$
  3. $2v$
  4. $\dfrac{v}{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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

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

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

  1. $1$
  2. $0$
  3. lies in between $0$ and $1$

  4. infinity
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $= 1$