Calculating Revolutions of a Ball Dropped from a Ramp

In summary, the conversation discusses how to calculate the number of revolutions a ball/sphere makes when released from rest on a ramp and dropped from a table. The diameter of the ball, height of the ramp, and height of the table are known, and the horizontal distance the ball travels before landing has been correctly calculated. The rotational kinetic energy and angular velocity have also been calculated correctly. However, there is uncertainty about how to solve for the number of revolutions the ball makes before falling on the ground, and the speaker has been struggling with this problem. They also mention a separate problem involving calculating the rotational kinetic energy of a cylinder released from rest on a ramp. The speaker has checked their calculations and is unsure of how to proceed to solve for the
  • #1
smilingsteph
9
0
If I have a ball/sphere is released from rest, rolls (without slipping) down a ramp, then drops from the table the ramp is on, how many revolutions does the ball make during the fall?

The diameter of the ball, height of the ramp, and height of the table are known. And I calculated the horizontal distance the ball travels before landing correctly. I think I calculated the w, v, and centripetal acceleration correctly. But I am not sure how to solve for the number of revolutions the ball makes before falling on the ground. This problem is probably relatively simple, but I might be having issues with it from looking at it for so long and confusing myself. Any help would be appreciated, thanks!
 
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  • #2
smilingsteph said:
If I have a ball/sphere is released from rest, rolls (without slipping) down a ramp, then drops from the table the ramp is on, how many revolutions does the ball make during the fall?

The diameter of the ball, height of the ramp, and height of the table are known. And I calculated the horizontal distance the ball travels before landing correctly. I think I calculated the w, v, and centripetal acceleration correctly. But I am not sure how to solve for the number of revolutions the ball makes before falling on the ground. This problem is probably relatively simple, but I might be having issues with it from looking at it for so long and confusing myself. Any help would be appreciated, thanks!
Once the ball has left the ramp, are there any external torques acting on the ball?
 
  • #3
to my knowledge no.

cylinder:
m= 1.8kg
r= 0.12m
l= 0.50m

ramp:
h= 0.6m
l= 5.0m

"A cylinder is released from rest at the top of a ramp and allowed to roll without slipping. What is the rotational kinetic energy?"

I already correctly solved that the total kinetic energy at the bottom of the ramp is 10.59J.
 
  • #4
smilingsteph said:
to my knowledge no.

cylinder:
m= 1.8kg
r= 0.12m
l= 0.50m

ramp:
h= 0.6m
l= 5.0m

"A cylinder is released from rest at the top of a ramp and allowed to roll without slipping. What is the rotational kinetic energy?"

I already correctly solved that the total kinetic energy at the bottom of the ramp is 10.59J.
You are indeed correct, if we ignore drag then the only force acting on the sphere is it's weight, which acts through it's centre. So if the net torque is zero after the ball has left the ramp, what can you say about the angular velocity?
 
  • #5
w=18.08314 and I=0.03888 and v=2.1699768.

i keep getting that the rotational kinetic energy is ~4.23, but it keeps coming up as incorrect. are any of my preliminary calculations incorrect? but i'd have know correctly, w, v, and I to solve for the distance (which i know is correct). so I'm not sure what I am doing wrong after i solve for w, I, and v.
 
  • #6
smilingsteph said:
w=18.08314 and I=0.03888 and v=2.1699768.

i keep getting that the rotational kinetic energy is ~4.23, but it keeps coming up as incorrect. are any of my preliminary calculations incorrect? but i'd have know correctly, w, v, and I to solve for the distance (which i know is correct). so I'm not sure what I am doing wrong after i solve for w, I, and v.
You may want to recheck your moment of inertia calculation.
 
  • #7
so i rechecked my calculations and still get the moment of inertia. how do i go from there though to solve for the number of rotations in the fall?
 

1. How do I calculate the number of revolutions a ball will make when dropped from a ramp?

To calculate the number of revolutions, you will need to know the height of the ramp, the radius of the ball, and the final velocity of the ball when it reaches the bottom of the ramp. Using these values, you can use the formula: number of revolutions = (2π * height) / (circumference of the ball).

2. What is the circumference of the ball and how do I find it?

The circumference of a ball is the distance around its outer edge. To find it, you can use the formula: circumference = 2π * radius. The radius can be measured using a ruler or calculated by dividing the diameter by 2.

3. Is there a specific unit of measurement that should be used when calculating revolutions?

The units used for calculating revolutions will depend on the units used for the height and radius of the ball. For example, if the height is measured in meters and the radius in centimeters, the resulting number of revolutions will be in meters per centimeter. It is important to ensure that all measurements are in the same units before calculating.

4. Can I use the same formula for any ramp height and ball size?

Yes, the formula for calculating revolutions can be used for any ramp height and ball size as long as the units are consistent. However, it is important to note that this formula assumes a perfectly round and smooth ball and a frictionless surface. In real-life situations, there may be slight variations.

5. Are there any other factors that may affect the number of revolutions a ball makes when dropped from a ramp?

Yes, there are other factors that may affect the number of revolutions, including air resistance, imperfections in the ramp or ball, and the initial velocity of the ball. These factors may cause slight variations in the calculated number of revolutions, but the formula provides a good estimate for most situations.

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