Question

1. if you double the net force acting on an object but keep its mass the same, what happens to the acceleration?

a. it stays the same.
b. it is cut in half.
c. it doubles.
d. it quadruples.

you are pushing two shopping carts with the same amount of force. cart a is empty, and cart b is full of groceries (triple the mass of cart a). which statement is true?
a. cart b will accelerate faster.
b. cart a will accelerate three times faster than cart b.
c. both carts will have the same acceleration.
d. cart b will not move at all

an objects mass is tripled while the net force acting on it remains constant, how will its acceleration change?
it will remain the same
it will triple as well
it will be nine time smaller
it will be one third the original acceleration

two objects, one with a mass of 5 kg and one with a mass of 10 kg, are pushed with the same force. which one will have a greater acceleration?
they will have the same acceleration
the 5 kg object
acceleration does not depend on mass
the 10 kg object

Explanation:

Step1: Recall Newton's 2nd Law

$F = ma$, rearranged to $a = \frac{F}{m}$

Step2: Analyze first question

Original: $a_1 = \frac{F}{m}$. New: $a_2 = \frac{2F}{m} = 2a_1$

Step3: Analyze second question

Let $m_A = m$, $m_B = 3m$, $F_A=F_B=F$. $a_A=\frac{F}{m}$, $a_B=\frac{F}{3m}=\frac{1}{3}a_A$

Step4: Analyze third question

Original: $a_1 = \frac{F}{m}$. New: $a_2 = \frac{F}{3m} = \frac{1}{3}a_1$

Step5: Analyze fourth question

$F$ is equal. $a_1=\frac{F}{5}$, $a_2=\frac{F}{10}$. $a_1 > a_2$

Answer:

1. c. It doubles.
2. b. Cart A will accelerate three times faster than Cart B.
3. it will be one third the original acceleration
4. the 5 kg object