Question

A constant force is applied to an object, causing the object to accelerate at 6.0 m/s^2?

A. What will the acceleration be if the force is halved?

B.What will the acceleration be if the object's mass is halved?

C. What will the acceleration be if the force and the object's mass are both halved?

D. What will the acceleration be if the force is halved and the object's mass is doubled?

Answer 1

Using Newton's 2nd Law of Motion, F = ma

where

F = force
m = mass
a = acceleration

F = m(6) -- call this Equation 1

From Equation 1, m = F/6

and if force is halved, m = (F/2)/a

therefore

F/6 = (F/2)/a

a/6 = 1/2

a = 3 which means that if the force is halved, the acceleration is also halved.

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From Equation 1, if the mass is halved

F = (m/2)(a) = m(6)

a = 12 m/sec^2 which means that if the mass is halved, the acceleration is doubled.

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If force and mass are both halved, then the equation becomes

(F/2) = (m/2)a

and simplifying the above,

F = ma --- which means that if both force and mass are both halved, the acceleration is the same as the original one.

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Force is halved and mass is doubled.

(F/2) = (2m)(a)

F = (4m)a = m(8)

a = 2 which means that if force is halved and mass is doubled, the acceleration is reduced to 1/4 or 25% of its original acceleration.