Question 2.CE.2: A very light plastic bag hangs from a light spring. The spri......
Measuring forces
A very light plastic bag hangs from a light spring. The spring is not stretched. We place one golf ball into the bag and observe that the spring stretches to a new length. We add a second ball and observe that the spring stretches twice as far. We add a third ball and observe that the spring stretches three times as far. How can we use this experiment to develop a method to measure the magnitude of a force?
Sketch and translate First, draw sketches to represent the four situations as shown below. On each sketch, carefully show the change in the length of the spring. Choose the bag with the golf balls as the system and analyze the forces exerted in each case.
Simplify and diagram Assume that Earth exerts the same force on each ball \overrightarrow{F} _{E on IB} independent of the presence of other balls. Thus, the total force exerted by Earth on the three ball system is three times greater than the force exerted on the one-ball system. Draw a force diagram for each case. Assume that in each case the spring exerts a force on the system \overrightarrow{F} _{S on \# B} that is equal in magnitude and opposite in direction to the force that Earth exerts on the system \overrightarrow{F} _{E on \# B} so that the sum of the forces exerted on the system with a number # of golf balls is zero.
Try it yourself: Represent the relation between the force that the spring exerts on the bag with a number # of golf balls (F_{S on \# B} ) and spring stretch (y) with an F-versus-y graph. Draw a trendline.
Answer: Based on the graph’s trendline, we see that the spring elongates until the force it exerts on the system object balances the force that Earth exerts on it.
