Question

An object experiencing a constant force accelerates at $10\mathrm{m}/{\mathrm{s}}^2$. What will the acceleration of this object be if

a. The force is doubled? Explain.

b. The mass is doubled?

c. The force is doubled and the mass is doubled?

Short answer

(a) As the force is doubled, acceleration is doubled

$a_{4\mathrm{bands}}=2a_{2\mathrm{bands}}=2\left(1.2\mathrm{m}/{\mathrm{s}}^2\right)=2.4\mathrm{m}/{\mathrm{s}}^2$

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

$a=\frac{1}{2}\left(a_{2\text{bands}}\right)=\frac{1}{2}\left(1.2\mathrm{m}/{\mathrm{s}}^2\right)=0.60\mathrm{m}/{\mathrm{s}}^2$

(c) When both the force and the mass are doubled, the acceleration becomes,

$$\begin{gathered} a^{\text{'}}=2F/2m \\ =F/m{a}^{\text{'}} \\ =a \end{gathered}$$

Step-by-step solution

Part (a) Step 1: Given Information

The acceleration of the object is $10\mathrm{m}/{\mathrm{s}}^2$.

Part (a) Step 2: Calculation

When the force is doubled, the acceleration will also double. The mass of the object is constant. Hence the acceleration value will increase to $20\mathrm{m}/{\mathrm{s}}^2.$

Part (b) Step 1: Given Information

The acceleration of the object is $10\mathrm{m}/{\mathrm{s}}^2$.

Part (b) Step 2: Calculation

Since mass and acceleration are inversely proportional to each other, hence when mass is increased, the acceleration will decrease. Therefore, as the mass is doubled, for the same force the acceleration will be reduced by half. Hence the new value of acceleration will be $5\mathrm{m}/{\mathrm{s}}^2.$

Part (c) Step 1: Given information

The acceleration of the object is $10\mathrm{m}/{\mathrm{s}}^2.$

Part (c) Step 2: Calculation

The force acting on an object is equal to the product of its mass and acceleration as$F=ma$, where $F$is the force, $m$is the mass and $a$ is the acceleration. Therefore, the expression for acceleration is $a=F/m$. When both the force and the mass are doubled, the acceleration becomes, $$\begin{gathered} a^{\text{'}}=2F/2m \\ =F/m{a}^{\text{'}} \\ =a \end{gathered}$$

Hence under the given conditions, the acceleration remains unchanged and its value is again $10\mathrm{m}/{\mathrm{s}}^2.$