Question

Applying a constant net force to an object causes it to accelerate at 10 m/s2. What will the acceleration of the object be if (a) the force is doubled, (b) the mass is halved, (c) the force is doubled and the mass is doubled, (d) the force is doubled and the mass is halved, (e) the force is halved, (f) the mass is doubled, (g) the force is halved and the mass is halved, and (h) the force is halved and the mass is doubled?

Answer 1

According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. Doubling the force or halving the mass will result in a doubling of the acceleration, while doubling the mass or halving the force will result in a halving of the acceleration.

Step-by-step explanation:

According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.

So, if the force is doubled, the acceleration of the object will also double (a).

If the mass is halved, the acceleration will be doubled (b).

If the force is doubled and the mass is doubled, the acceleration will stay the same as the force and mass cancel each other out (c). If the force is doubled and the mass is halved, the acceleration will be quadrupled (d).

If the force is halved, the acceleration will be halved (e). If the mass is doubled, the acceleration will be halved (f).

If the force is halved and the mass is halved, the acceleration will stay the same (g).

If the force is halved and the mass is doubled, the acceleration will be quartered (h).

Answer 2

Step-by-step explanation:

`F=ma`

The force is directly proportional to mass and acceleration.

a) If force is doubled then acceleration is doubled.

b) If mass is halved then acceleration of the will increase if the force is constant.

c) If the force is doubled and the mass is doubled then acceleration is halved.

`F_1=m_1a_1\\\Rightarrow a_1=(F_1)/(m_1)`

`2F_1=2(2m_1)a_2\\\Rightarrow F_1=2m_1a_2\\\Rightarrow a_2=(F_1)/(2m_1)`

Dividing the equation

`(a_1)/(a_2)=((F_1)/(m_1))/((F_1)/(2m_1))\\\Rightarrow a_2=(1)/(2)a_1`

d) If the force is doubled and the mass is halved then acceleration is doubled

`F_1=m_1a_1\\\Rightarrow a_1=(F_1)/(m_1)`

`2F_1=2((m_1)/(2))a_2\\\Rightarrow a_2=2(F_1)/(m_))\\\Rightarrow a_2=(F_1)/(2m_1)`

e) If the force is halved then the acceleration is halved.

f) If the mass is doubled then the acceleration is halved keeping the constant force

g) If the force is halved and the mass is halved then the acceleration is doubled

`F_1=m_1a_1\\\Rightarrow a_1=(F_1)/(m_1)`

`(1)/(2)F_1=(1)/(2)((m_1)/(2))a_2\\\Rightarrow a_2=2(F_1)/(m_1)`

h) If the force is halved and the mass is doubled then the acceleration is halved.

`F_1=m_1a_1\\\Rightarrow a_1=(F_1)/(m_1)`

`(1)/(2)F_1=(1)/(2)(2m_1)a_2\\\Rightarrow a_2=(F_1)/(2m_1)`