Hanging mass and Car Lab

 ZiTong Cheng

For this experiment, we first shot the video of the car's movement, then obtained the speed of the car through the video analysis software, then established the motion model and calculated the equation through desmos to obtain our estimate, and then wrote all the data in the table for comparison.

The data we get:

and the distance the hanging mass moved before it hits the ground is d = 0.275 +/- 0.01 m.

Questions：

1. Comparison Between Predicted and Measured Velocity:

When the hanging mass varied, the measured velocity was relatively close to the predicted velocity, but there was a 6-10% difference in most cases. The discrepancy became more noticeable as the hanging mass increased. Similarly, when the mass of the car changed, the measured values deviated from the predictions by around 15% in some cases. While most of the measurements were reasonably close to the initial predictions, the differences could be attributed to factors such as friction, irregularities on the track, slight errors during release, and possible human error in the video analysis. In addition, I personally think that due to the small measurement data, our inevitable errors have a greater impact on the experimental data, so I think any error below 15% is acceptable.

% different

2. Does the Launch Velocity Depend on the Car’s Mass, the Mass of the Hanging Object, and the Falling Distance? Is There a Combination of Distance and Hanging Mass Where the Car’s Mass Has Little Effect on Its Launch Velocity?

The launch velocity does depend on the car’s mass. A heavier car accelerates more slowly due to increased inertia, resulting in a lower velocity. The mass of the hanging object also plays a significant role—heavier masses exert a greater pulling force, leading to higher velocities. Additionally, the distance the object falls is crucial, as a longer distance allows more potential energy to be converted into kinetic energy, thereby increasing the car’s velocity.
In some scenarios, when the hanging mass is sufficiently large and the falling distance is long enough, the additional energy can compensate for the increased car mass, making the car’s mass less significant in determining the final velocity.

3. If the Same Mass Block Falls Through the Same Distance but the Car’s Mass Changes, Does the Force That the String Exerts on the Car Change? Is the Force Exerted by the String Always Equal to the Weight of the Hanging Object?

The force that the string exerts on the car changes when the car’s mass is altered. Increasing the car’s mass reduces the system’s acceleration, which decreases the net force exerted by the string. The force exerted by the string equals the weight of the hanging object only when the system is at rest or in equilibrium. During motion, due to acceleration, the force exerted by the string is generally less than the weight of the hanging object.

4. Is the Frictional Force the Same Whether or Not the String Exerts a Force on the Car? Does This Agree with Your Initial Prediction?

The frictional force is not the same whether or not the string exerts a force on the car, which does not fully align with the initial prediction. The frictional force depends on the system’s conditions, including the mass of the hanging object and the falling distance. While the string pulls the car, friction opposes the motion, but once the hanging mass hits the ground, the car continues moving due to inertia, with friction gradually slowing it down. As a result, the frictional force can vary at different stages, leading to some deviations from initial expectations.