Sphere rolling down a ramp problem

In summary, the conversation is about finding the speed of a solid sphere with uniform density as it rolls down a ramp. The equation for conservation of energy is discussed and the correct setup is given. The conversation ends with the question being answered and gratitude expressed for the help provided.
  • #1
iamtrojan3
56
0

Homework Statement


A solid sphere of uniform density (weight = 3.2 lbs starts from rest and rolls down a ramp (H = 1.57 m, q = 18.3°.)

Find the speed of the sphere's CM when it reaches the bottom of the ramp.

haha sorry bout that...

Homework Equations



see below

The Attempt at a Solution


i dont' know what's wrong with my set up here,
m*g*d*sin(theta) = .5mv^2 + (2/5)(.5)mv^2

any help?

thanks!
 
Last edited:
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  • #2
It might help if we knew what the question was!
 
  • #3
Ops... forgot to add the question. silly me >.<
 
  • #4
Your conservation of energy equation looks wonky. If I'm doing this right, you should have that m*g*h = (0.5)mv2 + (2/5)*(0.5)mv2. You're already given the height of the ramp!
 
  • #5
i hate when they put extra information in it, you just feel obligated to use it.

yes your right, thanks a lot for the help!
 
  • #6
You're welcome! :)
 

FAQ: Sphere rolling down a ramp problem

What is the sphere rolling down a ramp problem?

The sphere rolling down a ramp problem is a classic physics problem involving the motion of a spherical object rolling down an inclined plane or ramp. It is used to demonstrate the principles of kinetic energy, potential energy, and conservation of energy.

How is the acceleration of the sphere calculated?

The acceleration of the sphere can be calculated using the formula a = gsinθ, where a is the acceleration, g is the acceleration due to gravity (usually taken as 9.8 m/s^2), and θ is the angle of the ramp. This assumes that there is no friction present.

What factors affect the speed of the sphere?

The speed of the sphere rolling down a ramp is affected by several factors, including the angle of the ramp, the mass and radius of the sphere, and the presence of friction. A steeper ramp, a larger and/or heavier sphere, and less friction will result in a faster speed.

How does the height of the ramp affect the potential energy of the sphere?

The potential energy of the sphere is directly proportional to the height of the ramp. As the height increases, so does the potential energy. This potential energy is then converted into kinetic energy as the sphere rolls down the ramp.

What happens to the kinetic and potential energy of the sphere at the bottom of the ramp?

At the bottom of the ramp, the potential energy of the sphere is at its minimum, while the kinetic energy is at its maximum. This results in the sphere having the highest speed at this point. Additionally, the total energy (kinetic + potential) remains constant throughout the motion, in accordance with the law of conservation of energy.

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