A uniform solid sphere is placed on a smooth horizontal surface and a horizontal force F is applied on it at a distance h above the surface. The acceleration of the center?
depends how smooth and how high you push
If it is perfectly smooth so the sphere spins freely without any friction force causing it to roll along the table, then that force F is the only net horizontal force on the sphere and a = F/m
To find the acceleration of the center of a uniform solid sphere when a horizontal force F is applied at a distance h above the surface, we can use Newton's second law of motion. The equation for the acceleration (a) of an object is:
a = F / m
where F is the applied force and m is the mass of the object.
In this case, we need to find the mass of the solid sphere. The mass (m) of a uniform solid sphere can be calculated using the formula:
m = (4/3) * π * r^3 * ρ
where r is the radius of the sphere and ρ is the density.
Since the sphere is placed on a smooth horizontal surface, no external torque is acting on it. Therefore, the force (F) applied at a distance (h) above the surface does not result in any rotational motion. Instead, it causes translation of the sphere.
To calculate the acceleration of the center, we need to first calculate the mass of the solid sphere:
m = (4/3) * π * r^3 * ρ
Once we have the mass, we can substitute it into the equation for acceleration:
a = F / m
After calculating the value of a, we will obtain the acceleration of the center of the uniform solid sphere.