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Mechanical Power

What can you remember from P3 in Y11? Definition Formula Derived Units Actual units. Mechanical Power. To understand how to successfully complete mechanical power problems To apply these skills to the slightly more involved questions at AS. Mechanical Power.

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Mechanical Power

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  1. What can you remember from P3 in Y11? • Definition • Formula • Derived Units • Actual units Mechanical Power

  2. To understand how to successfully complete mechanical power problems To apply these skills to the slightly more involved questions at AS Mechanical Power Book Reference : Pages 153-154

  3. Some further thoughts on work done from last lesson.... Mechanical Power • Two people each shifting boxes up a flight of stairs... One at a full sprint, while the other takes all day. Currently, through our view of work done, we would calculate the work done by each to be the same • Clearly this conflicts with our everyday definition of “working hard”

  4. Definition : • Power is defined as the rate of energy transfer • Formula : • Power = Energy • Time • And when energy is transferred by a force doing work... • Power = Work done • time taken to do that work • Units: • Derived : Js-1 = called Watts (capital W) Mechanical Power

  5. Worked Example: A person with a mass of 48kg (480N) climbs a flight of stairs with a height of 10m in 12s Power = Work done time taken to do that work Power = 480N x 10m 12s Power = 400W Mechanical Power

  6. Looking at the power Equation again: Power = Work done time taken to do that work Power = Force x distance moved etc... t However, d/t is a very familiar concept..... Power = Force x velocity Engine Power

  7. Engines produce motive power. A powered vehicle can be found in different scenarios: • Moving at constant speed & height • Moving & gaining speed • Moving & gaining height • No reason why we couldn’t mix and match! Engine Power

  8. Moving at constant speed & height • All of the resistive forces, (friction, air resistance etc) are equal and opposite to the motive force. • The work done by the engine is lost to the surroundings (heat, sound etc) • PowerEngine = ForceResistive x velocity Engine Power Scenario 1

  9. Moving & gaining speed • The motive force from the engine exceeds the resistive forces. We have an unbalanced force and so we accelerate • The work done by the engine is the sum of the energy lost to surrounding and the gain in kinetic energy due to the increase in speed • PowerEngine = ForceResistive x velocity + K.E gain per sec • Note K.E. = ½mv2 coming soon..... Engine Power Scenario 2

  10. Moving & gaining height • If we are driving up an incline we are gaining height.... If we are gaining height we are gaining gravitational potential energy (GPE) • The work done by the engine is the sum of the energy lost to the surroundings and the gain in gravitational potential energy • PowerEngine = ForceResistive x velocity + GPE gain per sec • Note G.P.E. = mgh coming soon..... Engine Power Scenario 3

  11. Show that a juggernaut lorry with an output power of 264kW moving at a constant speed of 70 mph (31 m/s). What are the resistive forces experienced? • PowerEngine = ForceResistive x velocity • ForceResistive = PowerEngine / velocity • ForceResistive = 264,000 / 31 • ForceResistive = 8516N Worked example

  12. Power is the rate of energy transfer and can be calculated using: • Power = Work done • time taken to do that work • When powered motion is involved we can use: • Power = Force x velocity • This can be applied to scenarios with either constant level velocity or where there are gains in kinetic energy and/or potential energy due to increases in velocity and height respectively. Summary

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