Question

FIGURE shows an acceleration-versus-force graph for a 200 g object. What force values go in the blanks on the horizontal scale?

Short answer

(a) F= 1 N

(b) F= 2 N

Step-by-step solution

Step 1.Given information

here graph is given which shows an acceleration-versus-force graph for a 200 g object. and when you show the graph the value of force is missing so using Newton second law find the value of force in horizontal scale.

Step 2 

Newton second Law say that force is directly proportional to rate of change of momentum

$$\begin{gathered} F\alpha \frac{d\overrightarrow{p}}{dt} \\ F=m\frac{dv}{dt} \\ F=ma...........\left(1\right) \end{gathered}$$

Step 3 

Consider the first condition where mass is 0.2 kg and acceleration 5 m/s²

substitute value of mass and acceleration in equation (1)

$$\begin{gathered} F_1=m{a}_1 \\ {F}_1=0.2kg\times 5m/s^2 \\ {F}_1=1N \end{gathered}$$

Step 4 

Consider the first condition where mass is 0.2 kg and acceleration 10 m/s²

substitute value of mass and acceleration in equation (1)

$$\begin{gathered} F_2=m{a}_2 \\ {F}_2=0.2kg\times 10m/s^2 \\ {F}_2=2N \end{gathered}$$

Therefor, two forces value are 1 N and 2 N.