a. Compare the time for different masses of the same radius and mass to roll dow
ID: 2111211 • Letter: A
Question
a. Compare the time for different masses of the same radius and mass to roll down an incline if height h and angle theta. Find the times for a loop, a disk, a solid sphere and a shell sphere. Place them in order of fastest to slowest.b. Using 4 uniform bricks of length â„“, what is the furthest you can get the top brick over the edge of a table without the stack toppling over? Measure from the edge of table horizontally to far edge of brick. a. Compare the time for different masses of the same radius and mass to roll down an incline if height h and angle theta. Find the times for a loop, a disk, a solid sphere and a shell sphere. Place them in order of fastest to slowest.
b. Using 4 uniform bricks of length â„“, what is the furthest you can get the top brick over the edge of a table without the stack toppling over? Measure from the edge of table horizontally to far edge of brick.
Explanation / Answer
7.
Friction force = F
Torque = F*r = I*alpha = I*a/r
F = Ia/r^2
mgSin theta - F = ma
mgSin theta = (I/r^2 + m)*a
a = mgSin theta / [I/r^2 + m]
Hence, highest acceleration (and time taken to reach bottom of slope) will be when I will be least.
I_loop = mr^2
I_disk = 1/2*mr^2
I_sphere = 2/5*mr^2
I_shell = 2/3*mr^2
Hence fastest to slowest order will be Sphere > Disk > Shell > Loop.
8.
L/2 + L/2 + L/2 + L = 5L/2
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