Name: ________________ Class: _______ Work, Mechanical Advantage, and Efficiency 1. A container has a mass of 36 kg. How much does the container weigh? π = 36 ππ π = 9.8 πβππ πΉπ = ? πΉπ = ππ πΉπ = 36 × 9.8 πΉπ = 352.8 π β΄ The container weighs 352.8 π. 2. If you were to lift the container, and place it on the back of a truck, 115 cm high, how much work would you do? πΉπ = 352.8 π π = 115 ππ π = 1.15 π π =? π = πΉπ π = 352.8 × 1.15 π = 405.72 π½ β΄ It should take 405.72 π½ of work to put the container in the truck. 3. If it was a windy day, and it took you 450 J of energy to get the container to the back of the truck, how efficient were you? ππ = 450 π½ ππ = 405.72 π½ πΈππ = ? ππ ππ 405.72 πΈππ = 450 πΈππ = 0.9016 πΈππ = 90.16 % πΈππ = β΄ The process was about 90 % efficient. 4. For the lever shown below, what effort force would be needed to raise the load? ππΏ = 37 ππ ππΈ = 126 ππ πΉπΏ = 283 πΉπΈ = ? ππΏ πΉπΈ = ππΈ πΉπΏ 37 πΉπΈ = 126 283 πΉπΈ 0.294 = 283 πΉπΈ = 0.294 × 283 πΉπΈ = 83.1 π β΄ It should take 83.1 π to lift the load. 5. What is the mechanical advantage of this lever? ππΏ = 37 ππ ππΈ = 126 ππ πΌππ΄ = ? ππΈ ππΏ 126 πΌππ΄ = 37 πΌππ΄ = 3.405 πΌππ΄ = β΄ The mechanical advantage of the lever should be about 3.4. 6. If the larger gear below is turned at a rate of 60 rotations per minute, at what rate would the smaller gear turn? Velocity Ratio Follower Speed #π·πππ£ππ ππππ‘β = 21 #πΉπππππ€ππ ππππ‘β = 7 ππ = ? π·πππ£ππ πππππ = 60 π ππ πΉπππππ€ππ πππππ = ? ππ = 3 #π·πππ£ππ ππππ‘β ππ = #πΉπππππ€ππ ππππ‘β πΉπππππ€ππ πππππ = π·πππ£ππ πππππ × ππ ππ = 7 ππ = 3 πΉπππππ€ππ πππππ = 60 × 3 πΉπππππ€ππ πππππ = 180 π ππ β΄ The small gear turns 3 times faster. β΄ The smaller gear would turn at 180 π ππ. 21 7. For each of the following three simple machines: a. What is the ideal mechanical advantage? b. How much force, ideally, would be needed to move the object? Weight of Box π = 12 ππ π = 9.8 πβππ πΉπ = ? πΉπ = ππ πΉπ = 12 × 9.8 πΉπ = 117.6 π β΄ The container weighs 117.6 π. Ideal Mechanical Advantage β = 1.6 π π = 3.9 π πΌππ΄ = ? Effort Force πΉπΏ = 117.6 π πΉπΈ = ? πΌππ΄ = 2.4375 π πΌππ΄ = β 3.9 πΌππ΄ = 1.6 πΌππ΄ = 2.4375 πΌππ΄ = β΄ The ideal mechanical advantage is about 2.4. Ideal Mechanical Advantage ππ€ = 28 ππ ππ = 6.5 ππ πΌππ΄ = ? πΉπΏ = 156 π πΉπΈ = ? πΌππ΄ = 4.308 ππ€ πΌππ΄ = ππ 28 πΌππ΄ = 6.5 πΌππ΄ = Μ 4.308 πΌππ΄ = β΄ The ideal mechanical advantage is about 4.3. πΉπΏ πΉπΈ πΉπΏ πΉπΈ = πΌππ΄ 117.6 πΉπΈ = 2.4375 πΉπΈ = Μ 48.246 π β΄ It should take about 48.2 π to move the box. πΉπΏ πΉπΈ πΉπΏ πΉπΈ = πΌππ΄ 156 πΉπΈ = 4.308 πΉπΈ = Μ 36.214 π β΄ It should take about 36.2 π to lift the load. Effort Force Ideal Mechanical Advantage ππ’πππππ‘ π ππππ = 6 ππ’ππππ π ππππ = 1 πΌππ΄ = ? # ππ’πππππ‘ π ππππ # π ππππ ππ’ππππ 6 πΌππ΄ = 1 πΌππ΄ = 6 β΄ The ideal mechanical advantage is 6. πΌππ΄ = Effort Force πΉπΏ = 3240 π πΉπΈ = ? πΌππ΄ = 6 πΉπΏ πΉπΈ πΉπΏ πΉπΈ = πΌππ΄ 3240 πΉπΈ = 6 πΉπΈ = 540 π πΌππ΄ = β΄ It should take 540 π to lift the load. 8. The following system combines a variety of simple machines. The box is to travel up a ramp. There is a cable used to raise the box up the ramp, that cable moves through a variety of pulleys. The pulley system is attached to a winch. a. What is the mechanical advantage of this system? b. How much force, ideally, should you need to use to move the box? c. If the box moves to the top of the ramp by turning the crank arm with a force of 15 N, how efficient is the system? * Note, this is a level 4 question, do what you can, but understand that not all students will be able to get a full solution. However, everyone should attempt it. IMA - Ramp β = 1.4 π π = 3.6 π πΌππ΄π = ? π β 3.6 πΌππ΄π = 1.4 πΌππ΄π = Μ 2.571 πΌππ΄π = IMA - System Because the three simple machines are used one after the other, they need to be multiplied, as each simple machine applies its mechanical advantage to the next. IMA - Pulleys ππ’πππππ‘ π ππππ = 3 ππ’ππππ π ππππ = 1 πΌππ΄π = ? # ππ’πππππ‘ π ππππ # π ππππ ππ’ππππ 3 πΌππ΄π = 1 πΌππ΄π = 3 πΌππ΄π = πΌππ΄π = πΌππ΄π × πΌππ΄π × πΌππ΄π πΌππ΄π = 2.571 × 3 × 3.231 πΌππ΄π = Μ 24.923 β΄ The ideal mechanical advantage of the system is about 24.9. IMA β Winch (W&A) π·π€ = 21 × 2 π·π€ = 42 ππ π·π = 13 ππ πΌππ΄π = ? π·π€ π·π 42 = 13 = Μ 3.231 πΌππ΄π = πΌππ΄π πΌππ΄π Load Force (Straight Lift) π = 15.3 ππ π = 9.8 πβππ πΉπ = ? πΉπ = ππ πΉπ = 15.3 × 9.8 πΉπ = 149.94 π β΄ To lift the container without the system it would take 149.94 π. Question 8 Continued Effort Force πΉπΏ = 149.94 π πΉπΈ = ? πΌππ΄ = 24.923 πΉπΏ πΉπΈ πΉπΏ πΉπΈ = πΌππ΄ 149.94 πΉπΈ = 24.923 πΉπΈ = Μ 6.016 π πΌππ΄ = β΄ It should take about 6.0 π to lift the load with the system. Actual Mechancial Advantage πΉπΏ = 149.94 π πΉπΈ = 15 π π΄ππ΄π = ? System Efficiency πΌππ΄π = 24.923 π΄ππ΄π = 9.996 πΈπππ = ? πΉπΏ π΄ππ΄π = πΉπΈ 149.94 π΄ππ΄π = 15 π΄ππ΄π = 9.996 πΈπππ = π΄ππ΄ πΌππ΄ 9.996 πΈπππ = 24.923 πΈπππ = Μ 0.401 πΈπππ = Μ 40% β΄ The system is 40% efficient.
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