What is the net force of a two-pound ball rolling down a ramp and accelerating at a rate of twelve meters per second squared?

Answer 1

a ball rolling without slippage down a ramp has two components, the mass accelerating in a straight line, and the mass also accelerating about an axis , like a flywheel (essentially adding more weight)

the force required to accelerate a mass of 2 lb ( 0.9072 kg ) @ 12 (m/s)/s is:

f = m * a

f = 0.9072 * 12

f = 10.89 newtons

since you have the rate of acceleration and the mass, if you had the balls diameter , you could then work out its rotational acceleration and radius of gyration, you could then work out the force required to rotate it

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actually you dont need the diameter

the radius of gyration k for a solid sphere is given by:

= (( sq. root 10 ) / 5) * r

= 0.632 * r

so the mass of the ball can said to be concentrated at this point for rotary acceleration purposes, but according to the maths, the rotary acceleration at the radius of gyration works out at 0.632 * linear acceleration (assuming no slippage)

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so force (f) to rotate ball = 0.9072 * (12 * 0.632) = 6.88 newtons

so total force required to accelerate and rotate ball = 10.89 + 6.88 = 17.77 newtons

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the gravity however, would have to be greater than that on earth