Distance of Solid Sphere Down Ramp | Physics Problem

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In summary, the conversation involves finding the distance a solid sphere will move in the horizontal direction after rolling down a ramp and dropping through a vertical height. The speaker used the conservation of energy equation to find the ball's velocity and time, but was unsure of the distance until the other person pointed out that it is simply the horizontal velocity multiplied by the time. The conversation ends with a realization that a previous error was made in the calculation.
  • #1
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K got to do test corrections, and i just need help on this one.

A solid sphere released from rest rolls down a ramp, dropping through a vertical height of 0.61m. The ball leaves the bottom of the ramp, which is 1.22m above the floor (moving horizontally). What distance does the ball move in the horizontal direction before landing?

I used the conservation of energy equation (Ek + Ep = Ek + Ep) to find the velocity of the ball. V = 3.45 m/s

I also got the time it took t = 0.49 s

Cant figure out the distance for some reason. lol
 
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  • #2
You say V = 3.45 m/s. I assume this is the ball's horizontal velocity as it enters free fall. In that case, then the ball's horizontal range is simply V*t. (3.45 m/s)*(0.49 s) = 1.69 m.

Your fall time looks correct (I get about 0.50 s).

Edit:

I can't check your velocity value because you didn't provide the ball's mass.

Of course I don't need to know the mass, what was I thinking. :) mgh=1/2mv^2. Your value for V is absolutely correct. What an elementary error on my part.
 
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  • #3
lol thanks for the help.
 

1. What is the formula for calculating the distance traveled by a solid sphere down a ramp?

The formula for calculating the distance traveled by a solid sphere down a ramp is: d = (1/2) * g * t^2 * sin(theta), where d is the distance traveled, g is the acceleration due to gravity, t is the time, and theta is the angle of the ramp.

2. How does the mass of the solid sphere affect the distance traveled down the ramp?

The mass of the solid sphere does not affect the distance traveled down the ramp. The distance traveled depends on the angle of the ramp, acceleration due to gravity, and time taken to roll down the ramp.

3. What role does friction play in the distance traveled by a solid sphere down a ramp?

Friction can affect the distance traveled by a solid sphere down a ramp by slowing down the sphere's motion. This can decrease the time taken for the sphere to reach the bottom of the ramp, resulting in a shorter distance traveled.

4. How does increasing the angle of the ramp affect the distance traveled by a solid sphere?

Increasing the angle of the ramp will result in a longer distance traveled by the solid sphere. This is because the steeper angle will increase the acceleration due to gravity, resulting in a faster and longer roll down the ramp.

5. Is the distance traveled by a solid sphere down a ramp affected by the shape or size of the sphere?

No, the distance traveled is not affected by the shape or size of the sphere. As long as the sphere is a solid object and is rolling down the ramp without slipping, the distance traveled will be the same regardless of its shape or size.

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