086 – The operation of a hoist

Educational Goals

This laboratory activity is designed to help students achieve the following educational objectives:

Understanding Pulley Systems and Mechanical Advantage

• Investigate how a 5-strand pulley system reduces the input force required to lift a load, using the ratio Fg/F≈number of strands.
• Apply Newton’s second law to derive equilibrium conditions for loads lifted at constant velocity.

Energy Transformations and Efficiency

• Calculate mechanical work ($F\Delta x$) and gravitational potential energy ($mgh$) to analyze energy conservation.
• Determine the energy efficiency (R=Ep/W​​×100%) of the pulley system and identify sources of energy loss.

Experimental Design and Data Analysis

• Use dynamometers and rulers to measure force, displacement, and height, ensuring precision in calculations.
• Plot force ratios and efficiency trends to visualize theoretical vs. experimental results.

Real-World Applications

• Relate pulley mechanics to engineering systems (e.g., cranes, elevators) and discuss trade-offs between force reduction and energy dissipation.

Collaborative and Safety Skills

• Work in teams to assemble pulley systems and synchronize measurements.
• Adhere to safety protocols when handling weights and tensioned ropes.

Protocol

1. Suspend a weight of 1 N to the assembly of moving pulleys.
2. Approach one hand to the end of the dynamometer in order to lift the load at a constant speed.
3. The force indicated by the dynamometer is recorded in the results table.
4. Repeat steps 1 and 2 eight more times, each time increasing the suspended weight by 1 N.
5. For each of the tests, calculate the ratio of the weight of the load Fg to the driving force F required.
6. Apply Newton’s second law to the load to obtain a relationship between weight and tension in the rope.
7. Calculate the mechanical work that was performed to lift the load to a height of 20 cm at a constant speed.
8. Determine the amount of potential energy acquired by the charge.
9. Determine the energy efficiency of the hoist.

Anticipated Outcomes

Quantitative Results

• Force Ratio: For a 5-strand pulley, Fg/F​​≈5. Example:

• • • From Lab 8: Fg=2.00 N, $\text{N}$ → $5.0$.
    • From Lab 9: Fg=9.8 N (1.00 kg mass), $\text{N}$ → $4.45$.
• Mechanical Work and Energy:
  • • Work input: W=FΔx=2.20 N×1.0 m=2.2J.
    • Potential energy: Ep=mgh=1.00 kg×9.8 N/kg×0.200 m=1.96 J.
    • Efficiency: R=1.96 J/2.20 J ×100%≈89%.

Qualitative Observations

• Smaller input forces are required for heavier loads due to mechanical advantage.
• Efficiency decreases slightly with heavier loads due to increased friction.

Graphical Analysis

• Force vs. Load: A linear plot of Fg vs. F confirms proportionality, with deviations due to pulley friction (e.g. data shows Fg/F​​ ranges from 4.7–5.0).
• Efficiency Trends: Efficiency remains high (~85–90%) but never reaches 100% due to energy losses.

Error Analysis

• Systematic errors: Non-negligible pulley weight (e.g. 0.40–1.85 N force discrepancies).
• Random errors: ±0.1 N dynamometer precision, ±0.5 cm ruler inaccuracies.

Conceptual Understanding

• Mechanical Advantage: Derived from equilibrium $=5T,$where tension $T=F$.
• Energy Loss: Friction in pulley axles and work done against pulley weight explain R<100.

Summary of Assignment by Grade Range

Grades 6–8

Focus:

• Introduction to simple machines and force reduction.

Tasks:

• Assemble a 5-strand pulley and measure input/output forces.
• Observe how pulling 1 m of rope lifts a load 0.2 m.
• Discuss real-world applications (e.g., theater curtains, construction cranes).

Expected Outcomes:

• Recognize pulleys as force multipliers.
• Practice tabulating Fg​, F, and Δx.
• Identify energy losses as “wasted effort.”

Grades 9–10

Focus: Quantitative analysis of mechanical advantage and energy.

Tasks:

• Calculate Fg/F​​, $W$, and Ep​ for each trial.
• Plot Fg/F vs. Fg​ to verify proportionality.
• Use W=FΔx and Ep=mgh to compare input/output energy.

Expected Outcomes:

• Derive Fg=5T from Newton’s second law.
• Explain efficiency losses using energy conservation.
• Propose improvements to reduce friction (e.g., lubricated pulleys).

Grades 11–12

Focus:

• Advanced error analysis and system optimization.

Tasks:

• Calculate frictional work: $.$
• Redesign the system using ball-bearing pulleys or lighter materials.

Expected Outcomes:

• Write lab reports with error margins and regression analysis.
• Evaluate economic impacts of pulley efficiency in industrial settings.
• Propose experiments testing dynamic loads or variable strand counts.

Safety and Extensions Safety:

• Secure pulleys to prevent slippage; avoid jerking ropes under tension.

Extensions:

• Test 3-strand vs. 5-strand pulley efficiency.
• Integrate digital sensors for real-time force/displacement tracking.
• Explore regenerative systems (e.g., storing dissipated energy).

Laboratory essentials

Instruments

Hoist

Weights (1 to 9N)

Dynamometer

50cm ruler

Products