Question

a net force is applied to an object. which statement correctly describes the relationship between the net force, mass, and acceleration? (1 point) a greater acceleration results in a greater mass as long as the net force stays constant. a greater net force results in a lesser acceleration as long as the mass stays constant. a greater net force results in a greater acceleration as long as the mass stays constant. a greater acceleration results in a lesser mass as long as the net force stays constant. remaining attempts : 3

Explanation:

According to Newton's second law of motion, \(F = ma\) (where \(F\) is the net force, \(m\) is the mass, and \(a\) is the acceleration). When \(m\) is constant (\(m=\frac{F}{a}\)), \(F\) and \(a\) are directly proportional. When \(F\) is constant (\(F = ma\Rightarrow m=\frac{F}{a}\)), \(m\) and \(a\) are inversely proportional.

• For the first option: From \(m=\frac{F}{a}\) (when \(F\) is constant), a greater \(a\) gives a smaller \(m\), so this option is wrong.
• For the second option: From \(a=\frac{F}{m}\) (when \(m\) is constant), a greater \(F\) gives a greater \(a\), so this option is wrong.
• For the third option: From \(a=\frac{F}{m}\) (when \(m\) is constant), a greater \(F\) gives a greater \(a\), so this option is correct.
• For the fourth option: From \(m=\frac{F}{a}\) (when \(F\) is constant), a greater \(a\) gives a smaller \(m\), which is a correct mathematical relationship from the formula, but the first - option misstates the relationship (it says "a greater acceleration results in a greater mass" which is wrong), while this option correctly states "a greater acceleration results in a lesser mass as long as the net force stays constant"

Answer:

A greater net force results in a greater acceleration as long as the mass stays constant; A greater acceleration results in a lesser mass as long as the net force stays constant.