Question

Now Chandra and Darcel decide to try a problem. Suppose that the heiaht of the incline is h=15.8 m. Find the speed at the bottom for each of the following objects. In a race, which object would win?

solid sphere
spherical shell
hoop cylinder
tie

Answer 1

The speed at the bottom of the incline can be calculated using the principle of conservation of energy. Solid spheres, spherical shells, and hoops will have the same speed. Solid cylinders and hollow spheres will have a higher speed at the bottom than the other objects.

Step-by-step explanation:

To find the speed at the bottom of the incline for each object, we can use the principle of conservation of energy. The potential energy at the top of the incline will be converted into kinetic energy at the bottom, assuming no energy is lost due to friction. The formula to calculate the speed is given by v = sqrt(2gh), where v is the speed, g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the incline.

For a solid sphere, spherical shell, and hoop, since they are all solids and start from rest, they will have the same speed at the bottom of the incline. To calculate the speed, plug in the given height:

v = sqrt(2 * 9.8 * 15.8) ≈ 17.9 m/s

For a cylinder, the speed is dependent on whether it is solid or hollow. If it is solid, it will have the same speed as the other solid objects. However, if it is hollow, it will roll without slipping and reach a higher speed at the bottom compared to the other objects. Therefore, the solid cylinder and hollow sphere will have a higher speed at the bottom than the solid sphere, spherical shell, and hoop.