If an object’s mass is doubled while the applied force remains constant, what happens to its acceleration according to the formula for force?
The acceleration is halved
Newton's second law of motion is stated by the formula \(F = ma\), where F is the net applied force, m is the mass of the body, and a is the acceleration produced.
Rearranging this gives \(a = \frac{F}{m}\). With F held constant, acceleration a is inversely proportional to mass m.
Let the original mass be m and the acceleration be \(a_1 = \frac{F}{m}\). When the mass is doubled to 2m, the new acceleration is \(a_2 = \frac{F}{2m} = \frac{1}{2} \cdot \frac{F}{m} = \frac{a_1}{2}\).
Hence, when the mass is doubled at constant force, the acceleration is halved.
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