Energy Conservation of an object on an incline

[inner08]

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?

 

[neutrino]

Your idea is right, you may want to re-check you calculations. Also, h is not the required answer - it's h/sin(37).

 

[kyle8921]

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.