Name: Conservation of Mechanical Energy
Uploaded: 2019-07-19
Duration: 5 min 12 s
Description: When a body falls from a height towards the ground, its potential energy decreases but not the total mechanical energy. Let us understand this using data.

Question

The two blocks in an Atwood machine have masses

2 kg

and

3 kg

. Find the work done by gravity during the fourth second after the system is released from rest.

Accepted Answer

Given,
Bigger block of mass, $m_{1} = 3 kg$

Smaller block of mass, $m_{2} = 2 kg$

At time, $t = 4 second$

Let acceleration of the blocks be $a$ , as shown in the figure.
Applying Newton's second law for the blocks,
$3 g - T = 3 a$

$T - 2 g = 2 a$

Adding both the equations,

$g = 5 a$
$\Rightarrow a = \frac{g}{5}$

The acceleration of the bodies is constant. We can use the equations of motion in uniform acceleration. Let the velocity of the blocks be $u$ and $v$ after the end of third second and fourth second, respectively. We can calculate the velocities using the first equation,

$v_{f} = v_{o} + a t$ where $v_{f}$ is final velocity and $v_{o}$ is initial velocity.

Substituting values,
$u = 0 + a \times 3 = \frac{3 g}{5}$

$v = 0 + a \times 4 = \frac{4 g}{5}$

Applying conservation of mechanical energy from the end of third second to the end of fourth second,

The kinetic energy at $t = 3 and 4 \sec$

$K E_{i} = \frac{1}{2} \times 5 \times {(\frac{3 g}{5})}^{2}$

$K E_{f} = \frac{1}{2} \times 5 \times {(\frac{4 g}{5})}^{2}$

There is no external force doing work, applying conservation of mechanical energy.
$ΔU + ΔK \cdot E = 0$

$ΔU = - ΔK \cdot E$

$ΔU = \frac{1}{2} (5) u^{2} - \frac{1}{2} (5) v^{2}$

Applying values,

$∆ U = - (\frac{5}{2}) (\frac{7}{25}) {(9 \cdot 8)}^{2} = - 67 J$

Work done by gravity is negative of the change in potential energy.

$W_{g} = 67 J$

The two blocks in an Atwood machine have masses $2 kg$ and $3 kg$ . Find the work done by gravity during the fourth second after the system is released from rest.

Important Questions on Work and Energy

Learn and Prepare for any exam you want !

The two blocks in an Atwood machine have masses 2 kg and 3 kg. Find the work done by gravity during the fourth second after the system is released from rest.

Important Questions on Work and Energy

Learn and Prepare for any exam you want !

The two blocks in an Atwood machine have masses $2 kg$ and $3 kg$ . Find the work done by gravity during the fourth second after the system is released from rest.