Spring Launcher Force vs Cart Mass
Diagram 1.

Source: https://homework.study.com/explanation/the-ball-launcher-in-a-pinball-machine/
Real-World Phenomenon
A cart is launched using the same spring launcher on a smooth track. With the launcher set to a stronger setting, the cart speeds up more. But when extra mass is added to the cart, the cart speeds up less, even when the launcher setting stays the same.
When an object’s motion changes, it is because a net force acts on it. Net force is the sum of all forces acting on an object. If the forces are balanced, the net force is $0 \text{ N}$ and the object’s motion does not change. If forces are unbalanced, the net force is not zero and the object’s motion changes by speeding up, slowing down, or changing direction.
In this investigation, a spring launcher provides a forward push on a cart. The cart is on a smooth track, so friction is small compared to the launcher force. That means the launcher provides most of the net force during the push. We measure how the cart’s motion changes by measuring acceleration, which tells how quickly the cart’s speed increases.
Newton’s Second Law explains how force and mass work together: the acceleration of an object depends on the net force acting on it and the mass of the object. If the net force increases while mass stays the same, acceleration increases. If the mass increases while the net force stays the same, acceleration decreases. This happens because mass is related to inertia, the tendency of an object to resist changes in motion. A cart with more mass has more inertia, so it requires more net force to produce the same acceleration.
Diagram 2.
Source: https://www.chegg.com/homework-help/questions-and-answers/frictionless-cart-mass-m-attached-spring-spring-constant
In Table 1, we test the same cart mass with different launcher force settings. In Table 2, we repeat the same force settings but add mass to the cart. If the data show that stronger launcher forces produce larger accelerations and added mass reduces acceleration at the same force, that provides evidence that change in motion depends on both the sum of forces and the mass.
Table 1.
Launcher Force (N) | Mass (kg) | Acceleration (m/s$^2$) | Mass (kg) | Acceleration (m/s$^2$) |
|---|
1 | 1 | 1 | 2 | 0.5 |
2 | 1 | 2 | 2 | 1 |
3 | 1 | 3 | 2 | 1.5 |
4 | 1 | 4 | 2 | 2 |
Graph of Information - Figure 1.

Graph of Information - Figure 2.
