Question

When a certain force is applied to the 1-kg standard mass its acceleration is 5.0 m/s^2. When the same force is applied to another object its acceleration is one-fifth as much. The mass of the object is:_____

Answer 1

Mass of the object = 5 kg.

Step-by-step explanation:

Given:

Object 1:

Mass of the given object,
`m_1` = 1 kg

Acceleration of the object,
`a_1` = 5.0 m/s^2

Object 2:

Acceleration of the object,
`a_2` =
`((1)/(5))^t^h * a_1`

`a_2=(1)/(5) * 5`

`a_2=1 m.s^-^2`

We have to find the mass of the object 2.

Let the mass be
`m_2` .

Now we will find the force on object 1 using Newton's second law .

⇒
`F_1=m_1(a_1)`

⇒
`F_1=1(5)` kg.ms^-2

⇒
`F_1=5` N

According to the question.

The same force is applied to object 2.

So,

⇒
`F_1=F_2= 5\ N`

⇒
`F_2=m_2(a_2)`

⇒ Re-arranging.

⇒
`m_2=(F_1)/(a_2)`

⇒ Plugging the values.

⇒
`m_2=(5\ kg.m.s^-^2)/(1\ m.s^-^2)`

⇒
`m_2= 5` kg.

The mass of the object where same force is applied is 5 kg.