Energy Conservation of an object on an incline

In summary, an object with a mass of 1kg and an initial speed of 2m/s is sliding down a 4m high incline that is inclined at 53 degrees. It then slides on a horizontal surface for 3m before sliding up an incline plane inclined at 37 degrees. The surfaces have a kinetic coefficient of 0.4. To find the distance the object will travel up the 37 degree incline before stopping, the laws of conservation of energy are used to calculate the object's final speed on the 53 degree incline, the horizontal surface, and then as it moves up the 37 degree incline. The required answer is h/sin(37), where h is the height of
  • #1
inner08
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An 1kg object is sliding down a 4m high incline which is inclined at 53 degrees. The initial speed is 2m/s. It then slides on a horizontal section 3m long which is at ground level and then slides up an incline plane that is inclined at 37 degrees. All surfaces have a kinetic coefficient of uc = 0.4. What distance will the object travel up the 37 degree incline before stopping?

Work Done:

Starting off Values:
Vi = 2m/s
Vf = ?
d = 3.19 (using trig)
m = 1kg
uc = 0.4

I drew a diagram and then I figured I would use the laws of conservation formula. I know their is kinetic and potential energy when the object is at a certain height. When the object is on the horizontal surface, their will only be kinetic and friction forces acting on it. So I thought i'd find the object's final speed on the 53degree incline (1/2mVf^2 = 1/2mVi^2 + mgh -fx). After I found Vf, I used that as the new initial speed for the horizontal surface. I then thought i'd find the final speed on the horizontal speed using the laws of conservation of energy (1/2mVf^2 = 1/2mVi^2 -fx). Finally, I took this value and used it as the new initial speed as the object is about to move up the 37 degree incline. I substituted it in the formula: mgh = 1/2mVi^2 - fx.

I keep getting an answer like 2.41m but the answer in the book is 1.95m. I'm not quite sure where I went wrong?
 
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  • #2
Your idea is right, you may want to re-check you calculations. Also, h is not the required answer - it's h/sin(37).
 
  • #3


I would approach this problem by first identifying the key principles and equations related to energy conservation. In this case, we can use the conservation of mechanical energy, which states that the total mechanical energy (potential energy + kinetic energy) of a system remains constant as long as there are no external forces acting on it.

In this scenario, the object starts with a certain amount of potential energy due to its initial height and a certain amount of kinetic energy due to its initial speed. As it slides down the incline, its potential energy decreases while its kinetic energy increases. At the bottom of the incline, the object has converted all of its potential energy into kinetic energy.

As it moves onto the horizontal surface, the object will continue to have the same amount of kinetic energy, as there are no external forces acting on it. However, the kinetic coefficient of friction will cause a decrease in its kinetic energy as it moves along the surface. This decrease in kinetic energy will result in a decrease in speed.

On the 37 degree incline, the object will start with a certain amount of kinetic energy and will gain potential energy as it moves up the incline. When it reaches the top, all of its kinetic energy will have been converted into potential energy.

Using the conservation of mechanical energy, we can set the initial mechanical energy (due to its initial speed) equal to the final mechanical energy (due to its final height on the 37 degree incline). This will allow us to solve for the distance traveled on the incline.

It is important to note that the kinetic energy lost due to friction on the horizontal surface will also need to be taken into account. This can be calculated using the kinetic coefficient of friction and the distance traveled on the horizontal surface.

It is possible that the discrepancy between your calculated answer and the answer in the book is due to rounding errors or a slight difference in the values used for the kinetic coefficient of friction. I would recommend checking your calculations and making sure that all necessary factors are included in your equation. It may also be helpful to double check the values given in the problem to ensure they are accurate.
 

1. What is energy conservation?

Energy conservation is the principle that states that energy cannot be created or destroyed, but can only be converted from one form to another. This means that the total amount of energy in a closed system remains constant.

2. How does energy conservation apply to an object on an incline?

When an object is on an incline, there are two main forms of energy at play: potential energy and kinetic energy. As the object moves down the incline, potential energy is converted into kinetic energy. At the same time, some of the kinetic energy is converted into other forms of energy, such as heat or sound, due to friction. However, the total amount of energy in the system remains constant, in accordance with the principle of energy conservation.

3. How can we calculate the potential and kinetic energy of an object on an incline?

The potential energy of an object on an incline can be calculated using the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the incline. The kinetic energy can be calculated using the formula KE = 1/2mv^2, where m is the mass of the object and v is the velocity of the object.

4. How does the angle of the incline affect the energy conservation of an object?

The angle of the incline affects the amount of potential and kinetic energy an object has. A steeper incline will result in a greater amount of potential energy, while a gentler incline will result in a greater amount of kinetic energy. However, as long as there is no external force acting on the object, the total amount of energy in the system will remain constant.

5. What factors can affect the energy conservation of an object on an incline?

Some factors that can affect the energy conservation of an object on an incline include the mass of the object, the angle of the incline, and the presence of external forces such as friction. Additionally, any changes in the height or velocity of the object will also affect the amount of potential and kinetic energy in the system.

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