Question

When a constant force is applied to an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object
with mass 4 kg, the acceleration of the object is 5 m/s. When the same force acts upon another object, its acceleration is 2 m/s.. What is the mass of this
object?

Answer 1

Answer: The mass of the object is 10 kg

Step-by-step explanation:

According to Newton's second law of motion, the force $F$ applied to an object with mass $m$ is directly proportional to its acceleration $a$:

$F=ma$ (1)

If we isolate $a$:

$a=\frac{F}{m}$ (2) This means the acceleration of the object varies inversely with its mass

Now, we are given the following data to calculate a constant force using (1):

$m_{1}=4 kg$

$a_{1}=5 m/s^{2}$

$F=m_{1}a_{1}$ (3)

$F=(4 kg)(5 m/s^{2)$ (4)

$F=20 N$ (5)

If we apply this same force calulated in (4) in another object with an acceleration of $a_{2}=2 m/s^{2}$, its mass $m_{2}$ will be:

$F=m_{2}a_{2}$ (6)

$20 N=m_{2}2 m/s^{2}$ (7)

Finding  $m_{2}$:

$m_{2}=10 kg$ This is the mass of the object