# Conservation of Energy find the speed of the blocks

• uchicago2012
In summary, the problem involves finding the speed of two blocks, one falling and one sliding horizontally, after they have moved 2 meters. The conservation of energy is used to solve for the speed of the falling block, assuming no work is done by the pulley. The speed of the sliding block is found to be the same as the falling block, due to the conservation of energy principle. However, the direction of change in potential energy is unclear.
uchicago2012

## Homework Statement

In the figure the second block slides horizontally without friction while the first block falls. Use the Conservation of Energy to find the speed of the blocks after they have moved 2 meters, starting from rest. The falling block has mass 3 kg, the sliding block has mass 5 kg, and the pulley is ideal.
See Figure 1.

## Homework Equations

Uf + Kf = Ui + Ki

## The Attempt at a Solution

So for the 3 kg block:
mghf = 1/2mvf2 = mghi + 1/2mvi2
(3 kg)(9.8 m/s2)(2 m) + 1/2(3 kg)(vf)2 = 0
1/2(3 kg)(vf)2 = 58.8 J
(vf)2 = 39.2 m2/s2
vf = 6.26 m/s

I'm not sure if I quite got the point of the conservation of energy bit. Does it mean the work done by the pulley is zero? That's what I had to assume to get vf for the 3 kg block. I'm not sure what to do about the 5 kg block, though, because if I just use 2 m for the h for it, then I get the same vf as the 3 kg block, which seems odd to me. But maybe I'm missing the point.

#### Attachments

• Figure 1.jpg
5 KB · Views: 377
The pulley exerts a force on the rope and it is perpendicular to the rope. No work is involved by the pulley.

The change of the potential energy is equal to that of the falling block, but does it increase or decrease?

The blocks move together with the same speed. The total KE of the system is the sum of the KE-s of both blocks.

ehild

## 1. How is energy conserved in the speed of blocks?

The law of conservation of energy states that energy cannot be created or destroyed, only converted from one form to another. In the case of the speed of blocks, the kinetic energy of the moving blocks is conserved as long as there are no external forces acting on them.

## 2. What factors affect the speed of blocks?

The speed of blocks is affected by the mass and velocity of the blocks. A heavier block will require more energy to move at a certain speed compared to a lighter block. Similarly, a block with a higher initial velocity will require more energy to maintain that speed compared to a block with a lower initial velocity.

## 3. Can the speed of blocks be calculated using the conservation of energy principle?

Yes, the conservation of energy principle can be used to calculate the speed of blocks. By equating the initial kinetic energy of the blocks (if any) to the final kinetic energy, the final speed can be determined.

## 4. Does friction affect the conservation of energy in the speed of blocks?

Yes, friction can affect the conservation of energy in the speed of blocks. Friction is a dissipative force that converts the kinetic energy of the blocks into heat energy. This means that the speed of the blocks will decrease over time due to friction.

## 5. How does the height of the blocks affect their speed?

The height of the blocks can affect their speed through potential energy. If the blocks are placed at a higher height, they will have more potential energy. As they move down, this potential energy is converted into kinetic energy, which affects the speed of the blocks. However, the conservation of energy principle still applies, meaning that the total energy (potential + kinetic) will remain constant.

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