Question

A uniform, solid sphere of radius 5.00 cm and mass 3.00 kg starts with a translational speed of 3.00 m/s at the top of an inclined plane that is 2.00 m long and tilted at an angle of 25.0degree with the horizontal. Assume the sphere rolls without slipping down the ramp. Calculate the final speed of a solid sphere.

Answer 1

The final speed of the solid sphere rolling down the inclined plane is approximately 4.16 m/s.

Step-by-step explanation:

To calculate the final speed of the solid sphere rolling down the inclined plane, we can use conservation of energy. The initial kinetic energy is equal to the final potential energy and final rotational kinetic energy. The formula to calculate the final speed is:

v = sqrt((2gh)/(1+(R^2)/(2h)))

Where v is the final speed, g is the acceleration due to gravity (9.8 m/s²), h is the height of the inclined plane (2.00 m), and R is the radius of the sphere (0.05 m).

Substituting the values into the formula, we get:

v = sqrt((2*9.8*2)/(1+(0.05^2)/(2*2)))

v ≈ 4.16 m/s