Question

An object with mass M is subjected to a force of 100 newtons and accelerates at rate A. How much force would be needed to make mass M accelerate at 4A?

Please explain because I do not understand!

Answer 1

Newton's second law of motion relates force (\(F\)), mass (\(M\)), and acceleration (\(a\)) through the equation \(F = M \cdot a\). Here, you are given that a force of \(100 \, \text{newtons}\) results in an acceleration \(A\).

So, the initial force (\(F_1\)) applied to the object is given by \(F_1 = M \cdot A\).

Now, you want to find the force (\(F_2\)) needed to make the same mass (\(M\)) accelerate at \(4A\). According to Newton's second law, \(F_2 = M \cdot (4A)\).

Substitute the expression for \(F_1\) into \(F_2\):

\[F_2 = M \cdot (4A) = 4 \cdot (M \cdot A) = 4 \cdot F_1\]

So, the force needed to make mass \(M\) accelerate at \(4A\) is four times the force needed for an acceleration of \(A\). In this case, \(4 \cdot 100 \, \text{newtons} = 400 \, \text{newtons}\).