Sphere rolling up a ramp No mass given

In summary, the conversation discusses calculating the distance a solid sphere with a given radius, velocity, and friction moves up an incline before coming to rest. The equation for potential and kinetic energy is used to determine the distance, taking into account the sphere's rotation. However, the given answer does not match the calculated value, indicating a possible error in the solution.
  • #1
mightymango
2
0
Sphere rolling up a ramp.. No mass given!

Homework Statement



A solid sphere of radius 20cm, has a velocity of 5.0m/s and is moving on a surface with just enough friction to allow it to spin. It rolls up an incline of 30 degrees. Calculate the distance rolled before it comes to rest on the incline.

Homework Equations



PE + KE = PE
mgh + .5mv^2 = mgh

The Attempt at a Solution



I cancel out m, and plug in: (9.81)(0) + (1/2)(5.0)^2 = (9.81)(h). h is 1.27, so I use trig to find the length of ramp, which is 2.54 m.
However, I feel like I'm missing something crucial in this answer, and none of the choices match.
 
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  • #2


mightymango said:

Homework Statement



A solid sphere of radius 20cm, has a velocity of 5.0m/s and is moving on a surface with just enough friction to allow it to spin. It rolls up an incline of 30 degrees. Calculate the distance rolled before it comes to rest on the incline.

Homework Equations



PE + KE = PE
mgh + .5mv^2 = mgh

The Attempt at a Solution



I cancel out m, and plug in: (9.81)(0) + (1/2)(5.0)^2 = (9.81)(h). h is 1.27, so I use trig to find the length of ramp, which is 2.54 m.
However, I feel like I'm missing something crucial in this answer, and none of the choices match.

Are you accounting for the the fact this rather large sphere is spinning?
 
  • #3


Your KE would be split into rotational KE + translational KE such that:

KE = ½Iω2+ ½mv2 and you know that v=rω
 
  • #4


Ok. So I accounted for the spin of the sphere.

New equation is (1/2)(2/5)mr^2w^2 + (1/2)mv^2 = mgh

m's cancel. I plugged in .2m for r, 5 for v, and 25 for w using v=rw. After isolating h, I multiplied by 2 to find the distance on the ramp. However, I'm still not getting the right answer... Not sure what I'm doing wrong.
 
  • #5


What value did you get for h and what is the given answer?
 

Related to Sphere rolling up a ramp No mass given

1. How does the mass of the sphere affect its movement up the ramp?

The mass of the sphere does not have a direct effect on its movement up the ramp. The force of gravity, which is dependent on the mass of the sphere, will play a role in the acceleration of the sphere down the ramp, but the mass itself will not determine how the sphere rolls up the ramp.

2. What factors influence the speed of the sphere as it rolls up the ramp?

The speed of the sphere as it rolls up the ramp is influenced by several factors, including the angle of the ramp, the force of gravity, the shape and size of the sphere, and any friction between the ramp and the sphere. Additionally, the initial velocity of the sphere and the amount of energy transferred to it from other sources can also affect its speed.

3. What kind of energy does the sphere have while rolling up the ramp?

The sphere has both kinetic and potential energy while rolling up the ramp. Kinetic energy is the energy of motion, and the sphere gains kinetic energy as it speeds up while rolling up the ramp. Potential energy is the energy an object has due to its position or elevation, and the sphere gains potential energy as it moves higher up the ramp.

4. Is it possible for the sphere to roll up the ramp without any external force?

No, it is not possible for the sphere to roll up the ramp without any external force. The force of gravity and the friction between the ramp and the sphere are both external forces that are necessary for the sphere to roll up the ramp. Without these forces, the sphere would remain stationary or roll back down the ramp.

5. How does the angle of the ramp affect the motion of the sphere?

The angle of the ramp plays a significant role in the motion of the sphere. A steeper angle will result in a faster acceleration of the sphere down the ramp, while a shallower angle will result in a slower acceleration. Additionally, the angle of the ramp can also affect the amount of friction between the ramp and the sphere, which can impact the speed and movement of the sphere up the ramp.

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