Calculating Acceleration of a Spherical Shell

In summary, a hollow spherical shell with a mass of 2.10 rolls down a slope at an angle of 34.0 degrees with the horizontal. The friction force is perpendicular to the slope and there is a component of gravity in the x direction. To find the acceleration of the center of mass, Newton's 2nd law must be applied to both the translational and rotational motion of the shell. A freebody diagram can also be used to clarify the situation.
  • #1
nurjamali
1
0
A hollow spherical shell with mass 2.10 rolls without slipping down a slope that makes an angle of 34.0 with the horizontal.
Find the magnitude of the acceleration of the center of mass of the spherical shell.

I understood that the friction force is normal to the slope and there is a component of gravity in x direction(taking x-y plane at an angle of 34.0)
But I don't know the relation for calculating acceleration of the center of mass.
 
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  • #2
The friction force is parallel to the slope.

To find the acceleration, apply Newton's 2nd law to both the translational and rotational motion of the shell.
 
  • #3
Also, draw a freebody diagram to make things clearer to yourself..
 

1. How do you calculate the acceleration of a spherical shell?

The acceleration of a spherical shell can be calculated using the formula a = (4/3)πrρ, where a is the acceleration, r is the radius of the spherical shell, and ρ is the density of the shell.

2. What is the unit of measurement for acceleration of a spherical shell?

The unit of measurement for acceleration of a spherical shell is meters per second squared (m/s²).

3. Can the acceleration of a spherical shell be negative?

Yes, the acceleration of a spherical shell can be negative if the force acting on it is opposite to its direction of motion. This is known as deceleration or negative acceleration.

4. How does the mass of a spherical shell affect its acceleration?

The mass of a spherical shell has a direct effect on its acceleration. A larger mass will require a greater force to accelerate it at the same rate as a smaller mass.

5. Is there a difference in calculating acceleration for a hollow spherical shell vs a solid one?

Yes, there is a difference in calculating acceleration for a hollow spherical shell and a solid one. For a hollow shell, the mass used in the formula is the mass of the shell itself, while for a solid shell, the mass used is the mass of the entire object enclosed by the shell.

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