# A problem from conservation of energy

• dotrantrung
In summary: This is the similar problem, could you tell me why in that problem, 2 mass have equal velocity when the angle is 45 degree?In that problem, the position of the masses were P1(0,y1) of the mass moving on the vertical wall, and P2(x2,0) of the mass moving on the horizontal floor. The distance between them was equal to the length L of the stick: y12 + x22=L2. Taking the time-derivative, 2 y_1 \dot y_1 + 2x_2 \
dotrantrung

## Homework Statement

Hi everyone, my teacher gave this problem as an extra credit for last exam, which I just did very bad.

The figure is attached to the post.
There are 2 objects, which have the same mass (m). 2 objects are connected to each other by a string length (L), which is massless.
At initial, the they are sitting on a vertical wall, no velocity, and there is NO friction.
It start sliding down to another wall which is 30 degrees to the horizontal.

So, we just have (m): mass of object 1 and 2, (L): length of string, and 30 degrees is the angle between horizontal plan to the wall it start sliding down.

## Homework Equations

Determine the velocity of 2 objects at some time after the motion (there is no exact point of time, it could be "t")
The hint is: object #v1 object #2 have the same velocity. (because they have a string between)

## The Attempt at a Solution

I tried to do it by using conservation of energy, but I cannot go all the way because I can just figure out one equation but there is 2-3 unknowns.
However, by doing other homework, I pretty sure that there is no normal force of the wall acting on 2 objects. (because if you do some home work, the result are usually v=sqrt(2gh). And my teacher also confirmed so.

#### Attachments

• 1940217_283948788429548_1550090374_n.jpg
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dotrantrung said:
The figure is attached to the post.
There are 2 objects, which have the same mass (m). 2 objects are connected to each other by a string length (L), which is massless.
At initial, the they are sitting on a vertical wall, no velocity, and there is NO friction.
It start sliding down to another wall which is 30 degrees to the horizontal.

So, we just have (m): mass of object 1 and 2, (L): length of string, and 30 degrees is the angle between horizontal plan to the wall it start sliding down.

## Homework Equations

Determine the velocity of 2 objects at some time after the motion (there is no exact point of time, it could be "t")
The hint is: object #v1 object #2 have the same velocity. (because they have a string between)

Are you sure? That string can be slack. Which mass travels with bigger speed initially?

ehild

it is initially at rest. I don't really know why v1 and v2 is equal, but my prof said that v1 and v2 are equal. so it just 1 velocity for both of them.

You can check with an experiment. You certainly have some toy cars. Connect two of them with a string and make the arrangement as in the figure - with a big book, for example, and see if the string stays slack or not, and the cars move with the same speed, when one moves still vertically downward and the other moves on the slope.

ehild

Last edited:
Oh, I forgot, that is a rigid string. moreover, my teacher just post the answer today, and he just ask how to derive to this equation: v1=v2= sqrt[gL (1-1/(2sqrt{3}))]

So the two masses are connected with a stick instead of a string.

Even then, neither the velocity, nor the speed of the two masses are equal in general. Think what are the velocities/speeds when the stick is rotated about one end.

You gave the speed as a number, but the original problem asked the speed as function of the time.

Have you copied the problem correctly? ehild

In that problem, the position of the masses were P1(0,y1) of the mass moving on the vertical wall, and P2(x2,0) of the mass moving on the horizontal floor.

The distance between them was equal to the length L of the stick: y12 + x22=L2.
Taking the time-derivative,

$2 y_1 \dot y_1 + 2x_2 \dot x_2 =0$ *The time derivative of a coordinate is equal to the velocity component. Mass 1 moved vertically downward with velocity v1, $\dot y_1 = v_1$, and mass 2 moved horizontally with velocity v2 to the right, , $\dot x_2 = v_2$.

The speeds were equal, so v1= - v and v2=v. Subbing into eq. *

$-y_1 v + x_2 v =0$ , that is, x2=y1. The rod made 45°angle with both the wall and the floor when the speeds of the masses were equal.

According to the formula your professor gave, it is the speed when both masses move with the same speeds. That happens at a certain position of the rod.

ehild

Last edited:

## 1. What is the principle of conservation of energy?

The principle of conservation of energy states that energy cannot be created or destroyed, but can only be transformed from one form to another. This means that the total energy of a closed system remains constant over time.

## 2. How does conservation of energy apply to real-life situations?

Conservation of energy applies to almost every aspect of our daily lives. For example, when we turn on a light, the electrical energy is converted to light energy. When we drive a car, the chemical energy in the fuel is transformed into kinetic energy to move the car.

## 3. What happens if energy is not conserved?

If energy is not conserved, it means that the total energy of a system changes over time. This could result in unexpected or even dangerous consequences, such as an explosion or a malfunctioning machine. Therefore, it is crucial for energy to be conserved in all situations.

## 4. Can energy be converted from one form to another without any loss?

No, energy conversions always involve some loss of energy in the form of heat, sound, or other forms of energy. This is known as energy dissipation. However, the total amount of energy in the system will remain the same before and after the conversion.

## 5. How is the conservation of energy related to the first law of thermodynamics?

The first law of thermodynamics is based on the principle of conservation of energy. It states that energy cannot be created or destroyed, but can only be transferred or converted. This law is essential in understanding energy transformations and the behavior of systems in thermodynamic processes.

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