Question

A cylindrical object can roll down an incline, as shown in Figure 1. The incline is slightly less

Answer 1

Answer:

a = 2d / t²

or

a = 2gh / (3d)

Explanation:

One method is to use the equation:

Δx = v₀ t + ½ at²

d = (0) t + ½ at²

d = ½ at²

a = 2d / t²

By measuring the length of the incline d, and the time it takes to reach the bottom t, the students can calculate the acceleration, using only the meter stick and the stopwatch.

Another method is to use conservation of energy to find the final velocity.

Initial potential energy = final rotational energy + kinetic energy

PE = RE + KE

mgh = ½ Iω² + ½ mv²

For a solid cylinder, I = ½ mr².  For rolling without slipping, ω = v/r.

mgh = ½ (½ mr²) (v/r)² + ½ mv²

mgh = ¼ mv² + ½ mv²

mgh = ¾ mv²

4gh/3 = v²

Using constant acceleration equation:

v² = v₀² + 2aΔx

4gh/3 = 0² + 2ad

a = 2gh / (3d)

Using this equation, the students can measure the height of the incline h, and the length of the incline d, to calculate the acceleration.  The only equipment needed is the meter stick.