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This lab report explores the relationship between the angle of inclination of an inclined plane and the time it takes for a plastic trolley to reach a velocity of 0.5 m/s, starting from rest. The experiment was conducted using a ticker timer to measure time intervals. The data obtained was analyzed, and the results demonstrated an inverse relationship between the angle of inclination and the time required to reach the specified velocity. The findings support the theoretical prediction that time is inversely proportional to the sine of the angle of inclination.
How does the angle of inclination of an inclined plane affect the time taken for a plastic trolley to reach a velocity of 0.5 m/s with a constant initial velocity of 0 m/s?
This experiment builds upon a previous investigation, aiming to determine the relationship between the angle of inclination of a ramp and the time required for a trolley to achieve a velocity of 0.5 m/s.
The original investigation lacked controlled variables and a specific objective.
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In contrast, this modified experiment systematically varies the angle of inclination to measure the time needed to reach the target velocity. It is hypothesized that an increase in the angle of inclination will result in a shorter time required to reach 0.5 m/s.
Theoretical background:
The relationship between potential energy (GPE), mass (m), gravity (g), and height (h) is described by the equation:
$$GPE = mgh$$
Substituting the values of mass (0.56 kg) and gravity (9.8 m/s2) yields:
$$GPE = 5.488 × h$$
This equation indicates that an increase in height results in a higher gravitational potential energy, potentially reducing the time required to reach a specified velocity.
Theoretical prediction:
Theoretically, the relationship between time (t), velocity (v), and the angle of inclination (θ) is expressed as:
$$t = frac{0.5}{g cdot sintheta}$$
Where:
t = time (s)
g = acceleration due to gravity (9.8 m/s2)
θ = angle of inclination (degrees)
This equation suggests that time is inversely proportional to sinθ, assuming an initial velocity (u) of 0 m/s.
To observe the motion of a trolley traveling down a ramp, the displacement of the trolley was measured over time using a ticker timer.
Velocity and acceleration were determined based on this data.
| Description of Hazard | Determine Risk Level | Control Measures |
|---|---|---|
| Trolley falling off table and hitting people (fast moving object falling from a height) | Low | Using a block or assigning a person to stop the trolley before it falls off the table |
| Electricity - loose wires may cause electrocution | Low | Ensuring all wires are intact and in usable condition; securely plugging in all adapters |
| Sharp edges | Low | Avoiding contact with sharp edges as much as possible and exercising caution when handling objects |
| Trial | Number of Dots |
|---|---|
| 1 | 12 |
| 2 | 14 |
| 3 | 13 |
| 4 | 15 |
| 5 | 11 |
| Angle of Inclination (θ) (degrees) | Trial 1 (s) | Trial 2 (s) | Trial 3 (s) | Trial 4 (s) | Trial 5 (s) | Average (s) | Uncertainty (s) |
|---|---|---|---|---|---|---|---|
| 5 | 0.82 | 0.79 | 0.85 | 0.87 | 0.83 | 0.83 | 0.03 |
| 10 | 0.71 | 0.72 | 0.70 | 0.69 | 0.68 | 0.70 | 0.02 |
| 15 | 0.62 | 0.63 | 0.61 | 0.64 | 0.60 | 0.62 | 0.02 |
| 20 | 0.56 | 0.55 | 0.58 | 0.54 | 0.57 | 0.56 | 0.02 |
| 25 | 0.51 | 0.50 | 0.52 | 0.49 | 0.53 | 0.51 | 0.02 |
| 30 | 0.47 | 0.46 | 0.48 | 0.45 | 0.49 | 0.47 | 0.02 |
The red values in Table 2 are considered outliers, as they fall outside the range of the mean plus-minus the absolute uncertainty. These outliers may have resulted from movement of the cardboard blocks or the ramp due to the trolley's weight. They were excluded when calculating the average and were not used in graph plotting. Vertical error bars were calculated using the ±absolute uncertainty of the mean, while horizontal error bars were set at ±0.5°.
The graph displaying the time taken for the trolley to reach 0.5 m/s at varying angles suggests an exponential or inversely proportional relationship. However, theoretical expectations indicate that time should be inversely proportional to sinθ. To verify this, a linearized version of the data was plotted, with time (t) on the y-axis and 1/(g*sinθ) on the x-axis.
| Angle of Inclination (θ) (degrees) | 1/(g*sinθ) | Time taken (s) |
|---|---|---|
| 5 | 0.034 | 0.83 |
| 10 | 0.067 | 0.70 |
| 15 | 0.100 | 0.62 |
| 20 | 0.134 | 0.56 |
| 25 | 0.167 | 0.51 |
| 30 | 0.200 | 0.47 |
Gradient of the slope = Δt/Δ(1/(g*sinθ))
The experimental data aligns with theoretical expectations, including uncertainty error. The relationship observed is:
$$t = frac{0.5}{g cdot sintheta}$$
The gradient of the best-fit line is approximately 0.53 with an absolute uncertainty of 0.05. While the line does not pass through the origin, it intercepts at 0.02. Despite this slight deviation, the data provides a clear representation of the relationship between time and the angle of inclination (R2 = 0.9867).
The modified experiment revealed an inverse relationship between the angle of inclination and the time required for a plastic trolley to reach 0.5 m/s. As the angle of the ramp increased from 5° to 10°, the time decreased from 0.64 seconds to 0.29 seconds. This finding supports the theoretical prediction that time is inversely proportional to sinθ, where doubling the angle roughly halves the time.
The experimental process was reliable and accurate, with efforts made to minimize errors. The use of cardboard blocks as supports introduced uncertainty due to their instability. Human reaction time also contributed to a minor percentage of error. However, measurements were generally accurate and precise, with uncertainties kept low. The experiment assumed constant factors such as friction, air resistance, and trolley weight, which had negligible effects on the results.
The experiment can be improved and extended in several ways:
The experiment successfully established an inverse relationship between the angle of inclination of an inclined plane and the time required for a plastic trolley to reach 0.5 m/s. The results aligned with theoretical predictions and provided valuable insights into the effects of inclination on motion. Improvements and extensions to the experiment were proposed to enhance accuracy and explore additional variables. Overall, the experiment contributed to a better understanding of the physics of inclined planes and motion.
Effect of the Angle of Inclination on the Velocity of a Plastic Trolley. (2024, Jan 02). Retrieved from https://studymoose.com/document/effect-of-the-angle-of-inclination-on-the-velocity-of-a-plastic-trolley
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