Question

according to newtons second law of motion, how much force will be required to accelerate an object at the same rate if its mass is doubled?

a. four times the amount of force is needed.
b. twice the amount of force will be required.
c. half the amount of force will be required.
d. no change in the amount of force is needed.

Explanation:

Step1: Recall Newton's second - law formula

Newton's second - law is $F = ma$, where $F$ is force, $m$ is mass and $a$ is acceleration.

Step2: Analyze the case of doubled mass

Let the initial mass be $m_1=m$, initial force be $F_1 = m_1a=ma$, and the new mass $m_2 = 2m$. Since the acceleration $a$ remains the same, the new force $F_2=m_2a=(2m)a = 2(ma)$. So $F_2 = 2F_1$.

Answer:

B. Twice the amount of force will be required.