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Name: Maggie
Status: educator
Grade: 6-8
Location: Outside U.S.
Country: USA
Date: April 28, 2011


Question:
I teach 8th grade Physical Science. We are studying gravity, kinetic and potential energy. A student asked me the question that if you drop two different sized objects they should hit the ground at the same time. But why when you release these objects on a ramp the one that is heavier will reach the bottom first? I have no idea how to explain that.


Replies:
Hi Maggie, You may be interested to know that when Galileo investigated gravity, he also used ramps instead of dropping them vertically. The reason he did this is because the ramp let the balls go slower so that his timing was more accurate. The dropped balls simply dropped too fast. Using this set-up Galileo did show that balls of different mass accelerated towards earth at the same rate. This is despite a couple problems with this set-up that may be related to yours: 1) There is rolling friction, which would retard a small ball more than a large ball (for a larger ball the deformation of the ball or surface causing the rolling friction is smaller relative to the diameter of the ball) 2) There is the energy needed to not only cause the balls to move or translate down the ramp, but also to rotate as well. The rotational energy means that less energy is available for translation of the ball. In contrast to (1), this would tend to retard the larger ball more. There may also be other experimental set up issues. Is your ramp flexible? If the larger ball is causing the ramp to flex, it will experience a steeper decline and accelerate faster. My advice would be to use a rigid ramp and a small 4-wheeled cart and load it with different weights. You still might have some measurable frictional effect but if the cart has freely rotating stiff wheels and axles it should make for a better demonstration. John C Strong


Maggie,

What matters more than mass is mass distribution. Consider two disks or cylinders of different distribution. Have one be heavy and hollow, but have the other be light and solid. The light, solid cylinder will reach the bottom of the ramp first.

This is because of the term often called rotational inertia or moment of inertia. There are two kinds of kinetic energy. Translational KE is the kinetic energy of moving. Rotational KE is the energy of spinning. Just like when dropping, translational kinetic energy depends on mass and speed. Rotational kinetic energy depends on rotational inertia and angular speed (how fast the object spins). Rotational inertia depends on mass, size, and mass distribution. For a cylinder spinning around its center, rotational inertia is the product of mass, the square of the radius, and a constant between zero and one: I=kMR^2. Mass in rotational KE works like in translational KE. The R^2 part when multiplied by the square of the angular speed, results in v^2, just like in translational KE. Mass distribution has a different effect.

For a cylinder with all its mass on the outside edge, a hollow cylinder, k=1 and rotational kinetic energy equals translational kinetic energy. Half of the potential energy goes to moving and half goes to spinning. For a solid cylinder, k=1/2. Two thirds of the energy goes to moving while only one-third goes to spinning. If two cylinders are made of the same material, the heavier object is usually solid. This is why we often see the heavier object roll faster.

Dr. Ken Mellendorf Physics Instructor Illinois Central College


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