Question

Two forces , one four times as large as the other pull in the same direction on a 10kg mass and impart to it an acceleration of 2.5 m/s ^ 2 ?. If the smaller force is removed , what is the acceleration of the mass?

Answer 1

Let the smaller force be $F$ and the bigger one be $4F$. Since they are pulling in the same direction, the net force is $F+4F = 5F$. Then, according to the Newton's second law:

$$5F = ma_0$$

where $m = 10kg$ is the mass of the object and $a_0 = 2.5m/s$ is its acceleration. Thus, the smaller force is:

$$F = \dfrac{10\cdot 2.5}{5} = 5N$$

If we remove the smaller force, only the $4F$ will be left. Then, using the Newton's second law again, obtain:

$$4F = ma$$

where $a$ is the unknown acceleration with only bigger force left. Thus, obtain:

$$a = \dfrac{4F}{m} = \dfrac{4\cdot 5}{10} = 2m/s^2$$

Answer. $2\space m/s^2$.