To calculate the uncertainty in the calculated potential and kinetic energy values shown in the table, let's analyze the quantities involved.

1. Uncertainty in Potential Energy

The potential energy $PE$ is given by: $PE = m \cdot g \cdot h$ where:

• $m$ is the mass of the object (assumed constant, so its uncertainty can be considered negligible if not given),
• $g$ is the gravitational constant ($9.81 \, \text{m/s}^2$, usually with negligible uncertainty),
• $h$ is the height with uncertainty.

Given the uncertainty in height $\Delta h = 0.01 \, \text{m}$, the uncertainty in potential energy $\Delta PE$ can be calculated using: $\Delta PE = PE \cdot \frac{\Delta h}{h}$

2. Uncertainty in Kinetic Energy

The kinetic energy $KE$ is given by: $KE = \frac{1}{2} m v^2$ where:

• $v$ is the velocity with uncertainty.

The uncertainty in kinetic energy $\Delta KE$ due to the uncertainty in velocity $\Delta v = 0.001 \, \text{m/s}$ can be calculated as: $\Delta KE = KE \cdot \frac{2 \Delta v}{v}$

If you provide the mass $m$ or any further information about it, I can help compute the exact uncertainties for each potential and kinetic energy value. Let me know if you want the calculations with hypothetical values.

Would you like more details on each step?

Related Questions

1. What is the effect of doubling the height uncertainty on the potential energy uncertainty?
2. How does changing the mass affect the uncertainty in kinetic energy?
3. Can gravitational constant variations impact the potential energy uncertainty in different locations?
4. How would a greater uncertainty in velocity impact the total energy uncertainty?
5. What are other methods to reduce uncertainties in energy calculations?

Tip

When calculating uncertainties, focus on the major sources of error to simplify analysis, especially when some quantities have negligible uncertainties.