Solid sphere vs. disk ramp test and time difference.

In summary, you need to solve for the time difference between a solid sphere and a solid disk moving down a ramp at an inclination angle of theta, with a vertical height of h, released from rest at the top. This involves calculating the kinetic and potential energy, solving for the velocity, and using kinematic equations to determine the time. The final answer should be calculated symbolically, in terms of the given variables. It is not valid to set the distance (D) from the kinematic formula to equal D sin(theta).
  • #1
Epictetus
5
0
A solid sphere and a solid disk are released from rest at the top of the ramp. The inclination angle is theta to the horizontal and the vertical height of the ramp is h. Determine the time difference between the objects for them to read the bottom of the ramp.

This is what I've solved:

I(disk)= 1/2mr^2 = I + md(parallel)^2 = 1/2 mr^2 + mr^2 = I = 3/2 mr^2

Energy
Kinetic energy ---> Potential energy

mgh = 1/2 I(omega)^2
mgh = 1/2 (3/2 mr^2) (omega)^2
Omega = square root [4mgh/3mr^2]

Solving for the velocity by mulitplying by radius r:
V= 2/r times sq. root [gh/3] times r = 2 sq.root [gh/3]

Since it's a ramp, I used dsin theta for the hypotenuse and used a kinematic equation

dsin theta = (v initial + v /2) t

Solving for t (time)

t= dsin theta / (2 sq. ro. [gh/3] ) / 2

t = d sin theta / sq. r. [gh/3]


The time for the sphere was also calculated the same way so no need for me to put it up here. My questios are: How am I supposed to find the time difference if there are no definate values for theta, and h. I would have to set up the final answers and subtract them from each other but that wouldn't get me any where. Also, is it valid to set d from the kinematic formula to equal d sin theta?


Please help! Thanks.
 
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  • #2
Epictetus said:
My questios are: How am I supposed to find the time difference if there are no definate values for theta, and h. I would have to set up the final answers and subtract them from each other but that wouldn't get me any where.
Just do it symbolically, in terms of the given variables. Nothing wrong with that.

Also, is it valid to set d from the kinematic formula to equal d sin theta?
No. If D is the distance along the ramp, and h is the height, then h = D sin(theta).
 
  • #3


As a scientist, it is important to always consider the variables and assumptions in any experiment or calculation. In this case, it seems that the values for theta and h are not given, so it is not possible to accurately determine the time difference between the two objects. In order to find the time difference, we would need to know the specific values for these variables.

Additionally, it is not valid to equate d from the kinematic formula to d sin theta. This is because the distance traveled by the objects will be different due to the different paths they take (a disk rolling and a sphere sliding). The distance traveled by the objects will also depend on the value of theta and the height of the ramp, which are unknown in this scenario.

In order to accurately determine the time difference, it would be necessary to have more information about the experiment, such as the specific values for theta and h. Without this information, it is not possible to accurately calculate the time difference between the two objects. It is important to always consider the limitations and uncertainties in any scientific study or experiment.
 

1. What is the purpose of a solid sphere vs. disk ramp test?

The purpose of a solid sphere vs. disk ramp test is to compare the rolling motion of a solid sphere and a disk on an inclined ramp to study the effects of shape on motion and the resulting time differences.

2. How is the solid sphere vs. disk ramp test set up?

The test is set up by placing a solid sphere and a disk side by side on an inclined ramp and releasing them at the same time. The ramp angle and starting position of the objects are controlled variables, while the time taken for each object to reach the bottom of the ramp is the measured variable.

3. What is the expected outcome of the solid sphere vs. disk ramp test?

The expected outcome is that the solid sphere will reach the bottom of the ramp faster than the disk due to its shape and distribution of mass. This is because the disk has a larger mass concentrated at the edges, resulting in a higher moment of inertia and slower rotational motion.

4. How does the result of the solid sphere vs. disk ramp test relate to real-world scenarios?

The result of the test can be applied to real-world scenarios, such as the rolling motion of objects like balls or wheels. It can also be used to understand the principles of rotational motion and how different shapes affect the speed and motion of objects.

5. Are there any limitations to the solid sphere vs. disk ramp test?

Yes, there are limitations to the test. It assumes a frictionless surface and neglects other factors such as air resistance and imperfections in the shape and weight distribution of the objects. It is also important to conduct multiple trials and average the results to account for any errors or variations in the setup.

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