Answer: The mass of the object is 10 kg
Step-by-step explanation:
According to Newton's second law of motion, the force [tex]F[/tex] applied to an object with mass [tex]m[/tex] is directly proportional to its acceleration [tex]a[/tex]:
[tex]F=ma[/tex] (1)
If we isolate [tex]a[/tex]:
[tex]a=\frac{F}{m}[/tex] (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):
[tex]m_{1}=4 kg[/tex]
[tex]a_{1}=5 m/s^{2}[/tex]
[tex]F=m_{1}a_{1}[/tex] (3)
[tex]F=(4 kg)(5 m/s^{2)[/tex] (4)
[tex]F=20 N[/tex] (5)
If we apply this same force calulated in (4) in another object with an acceleration of [tex]a_{2}=2 m/s^{2}[/tex], its mass [tex]m_{2}[/tex] will be:
[tex]F=m_{2}a_{2}[/tex] (6)
[tex]20 N=m_{2}2 m/s^{2}[/tex] (7)
Finding [tex]m_{2}[/tex]:
[tex]m_{2}=10 kg[/tex] This is the mass of the object
