Question

A block with a mass m1 is hit by a force of magnitude F which causes the block to have an acceleration of magnitude a. If a second block of mass m2 is hit by the same force of magnitude F which causes the block to have an acceleration of magnitude 2a, then which of these could be the two masses? A) m1= 200kg ; m2= 100kgB) m1= 50kg ; m2= 25 kgC) m1= 100kg ; m2= 50kgD)m1= 10kg ; m2= 50kgE)Any of these

Answer 1

We are given that a force "F" accelerates an object of mass "m1". According to Newton's second law, this can be represented by the following equation:

`F=m_1a`

Now, we are given that a second object of mass "m2" is accelerated by "2a" using the same force. Using Newton's second law we get:

`F=m_2(2a)`

Now, we will divide both equations, we get:

`(F)/(F)=(m_1a)/(m_2(2a))`

Now, we simplify by canceling put the "F" and the "a":

`1=(m_1)/(2m_2)`

Now, we multiply both sides by "2m2", we get:

`2m_2=m_1`

Therefore, the first mass must be twice the second mass.

The options that meet this condition are:

`m_1=200kg,m_2=100kg\text{ }`
`m_1=50kg,m_2=25kg`
`m_1=100kg,m_2=50kg`