What is the Total Energy of a Rolling Sphere on a Sloped Floor?

In summary, a solid metal ball with a radius of 0.500m and a mass of 1.50 kg is rolling down a sloped floor at an angle of 30.0° to the horizontal with a final angular velocity of 2.00 rad/s. The total energy of the ball when it is 2.00m from the bottom of the slope is 30.225 Joules, assuming there is no friction. This is calculated using the equations for final energy, velocity, moment of inertia, and potential energy. The final answer is confirmed by considering the distance along the slope to the bottom instead of the vertical height.
  • #1
Extremist223
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0

Homework Statement


A solid metal ball of radius 0.500m, and a mass of 1.50 kg, is found to be rolling down a sloped floor whose angle is 30.0° to the horizontal (assume no slipping). The ball has a final angular velocity of 2.00 rad/s. What is the total energy of the ball when it it is 2.00m from the bottom of the slope? (Assume there is no friction)


Homework Equations


Energy final = 1/2mv^2 + 1/2Iw^2 + mghf
v= rw
v= .5 (2) = 1m/s
I = moment of inertia = 2/5(mr^2)

The Attempt at a Solution


Ef= 1/2(1.5kg)(1m/s^2)+ 1/2(2/5(1.5kg(.5m^2) + 1.5kg(9.8m/s^2)(2m)
Ef= 0.75 + 0.075 + 29.4
Ef= 30.225 Joules

Does this seem right?
 
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  • #2
I suspect they mean a distance of 2m along the slope to the bottom
what is the 'h' in the potential energy formula
 
  • #3
thank you, that makes the answer right it ends up being sin30 (2m)= 1 which makes my answer right thanks a lot.
 

What is the concept of energy of a sphere rolling?

The energy of a sphere rolling is the total energy possessed by a spherical object as it moves along a surface. It takes into account both its translational kinetic energy (due to its linear motion) and its rotational kinetic energy (due to its spinning motion).

How is the energy of a sphere rolling calculated?

The energy of a sphere rolling can be calculated using the equation E = 1/2mv2 + 1/2Iω2, where m is the mass of the sphere, v is its linear velocity, I is its moment of inertia, and ω is its angular velocity.

What factors affect the energy of a sphere rolling?

The energy of a sphere rolling is affected by its mass, linear velocity, and moment of inertia. Additionally, the surface it is rolling on, the presence of external forces, and the shape and surface texture of the sphere can also impact its energy.

How does the energy of a sphere rolling change over time?

As a spherical object rolls, its energy will change in relation to the changes in its velocity and angular velocity. If there are no external forces acting on the sphere, the total energy will remain constant due to the principle of conservation of energy.

Why is understanding the energy of a sphere rolling important?

Understanding the energy of a sphere rolling is important in various fields such as physics, engineering, and sports. It allows for the prediction and analysis of the motion of spherical objects, and can also help in optimizing the design and performance of rolling objects.

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