Power (Mechanical) - Revision history

Tarnie14: /* History */

2018-04-19T01:03:37Z

History

← Older revision		Revision as of 21:03, 18 April 2018
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	The transmission of mechanical power has evolved over the course of the past few centuries. In the 16th century, mechanical power transmission involved systems of push-rods that linked pumps to water wheels. This example is seen further in the late 18th century in German towns where power is transmitted from water wheels to salt wells. This "primitive" is still present in today's day and age, as oil fields transmitting power from pumping engines to pump jacks follow the same principle. Other mediums to transfer mechanical power include hydraulic systems, pneumatic systems, and solid structures such as gears and driveshafts.		The transmission of mechanical power has evolved over the course of the past few centuries. In the 16th century, mechanical power transmission involved systems of push-rods that linked pumps to water wheels. This example is seen further in the late 18th century in German towns where power is transmitted from water wheels to salt wells. This "primitive" is still present in today's day and age, as oil fields transmitting power from pumping engines to pump jacks follow the same principle. Other mediums to transfer mechanical power include hydraulic systems, pneumatic systems, and solid structures such as gears and driveshafts.

	~~A pump can potentially look like this:~~

	~~[[File:pump2.jpg]]~~

	== See also ==		== See also ==

Tarnie14: /* Simple */

2018-04-19T01:03:13Z

Simple

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	===Simple===		===Simple===
			[[File:sleddog.jpg \|border\|right]]
	A certain motor is capable of doing 3000 J of work in 12 s.		A certain motor is capable of doing 3000 J of work in 12 s.
	~~[[File:sleddog.jpg \|border\|right]]~~
	What is the power output of this motor?		What is the power output of this motor?

Tarnie14: /* Simple */

2018-04-19T01:02:40Z

Simple

← Older revision		Revision as of 21:02, 18 April 2018
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	A certain motor is capable of doing 3000 J of work in 12 s.		A certain motor is capable of doing 3000 J of work in 12 s.
			[[File:sleddog.jpg \|border\|right]]
	What is the power output of this motor?		What is the power output of this motor?

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	A weightlifter does 5000 J of work over a time span of 5 seconds. How much power does the weightlifter exert?		A weightlifter does 5000 J of work over a time span of 5 seconds. How much power does the weightlifter exert?
	~~[[File:sleddog.jpg \|border\|right]]~~

	:<math>power = \frac{W}{\Delta t} = \frac{5000 J}{5 s} = 1000 J/s </math>		:<math>power = \frac{W}{\Delta t} = \frac{5000 J}{5 s} = 1000 J/s </math>

Tarnie14: /* Simple */

2018-04-19T01:02:12Z

Simple

← Older revision		Revision as of 21:02, 18 April 2018
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	A weightlifter does 5000 J of work over a time span of 5 seconds. How much power does the weightlifter exert?		A weightlifter does 5000 J of work over a time span of 5 seconds. How much power does the weightlifter exert?
			[[File:sleddog.jpg \|border\|right]]

	:<math>power = \frac{W}{\Delta t} = \frac{5000 J}{5 s} = 1000 J/s </math>		:<math>power = \frac{W}{\Delta t} = \frac{5000 J}{5 s} = 1000 J/s </math>

	It takes a husky 30 s to pull a sled 45 m. Over that time the dig uses a constant force of 50 N. How much power does the husky exert?		It takes a husky 30 s to pull a sled 45 m. Over that time the dig uses a constant force of 50 N. How much power does the husky exert?
	~~[[File:sleddog.jpg \|border\|right]]~~

	:<math>power = \frac{{F}{\Delta r}}{\Delta t} = \frac{{50 N} \cdot {45 m}}{30 s} = \frac{2250 J}{30 s} = 75 J/s </math>		:<math>power = \frac{{F}{\Delta r}}{\Delta t} = \frac{{50 N} \cdot {45 m}}{30 s} = \frac{2250 J}{30 s} = 75 J/s </math>

Tarnie14: /* Examples */

2018-04-19T01:01:54Z

Examples

← Older revision		Revision as of 21:01, 18 April 2018
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	It takes a husky 30 s to pull a sled 45 m. Over that time the dig uses a constant force of 50 N. How much power does the husky exert?		It takes a husky 30 s to pull a sled 45 m. Over that time the dig uses a constant force of 50 N. How much power does the husky exert?
			[[File:sleddog.jpg \|border\|right]]

	:<math>power = \frac{{F}{\Delta r}}{\Delta t} = \frac{{50 N} \cdot {45 m}}{30 s} = \frac{2250 J}{30 s} = 75 J/s </math>		:<math>power = \frac{{F}{\Delta r}}{\Delta t} = \frac{{50 N} \cdot {45 m}}{30 s} = \frac{2250 J}{30 s} = 75 J/s </math>

Tarnie14: /* Difficult */

2018-04-19T00:55:46Z

Difficult

← Older revision		Revision as of 20:55, 18 April 2018
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	A bicyclist is going up an inclined slope with an angle <math> \alpha </math> = 2.9 degrees by a uniform speed of 27 km/h. The magnitude of the air resistance force is given by <math> F_{odp} = kv^2 </math> kgs/m where the numerical value of <math> k = 0.3 </math> if the unit of the speed is m/s and the unit of the resistance force is the newton (N). The mass of the bicyclist including the bike is 70 kg. Do not consider the rolling resistance. '''(a)''' What forward force exerted on the bike by the road is needed to make the bicyclist move with constant speed? '''(b)''' How much work does the bicyclist do when riding a distance of 1200 m? '''(c)''' What is the power of the bicyclist during the ride? Assume there is no loss of mechanical energy.		A bicyclist is going up an inclined slope with an angle <math> \alpha </math> = 2.9 degrees by a uniform speed of 27 km/h. The magnitude of the air resistance force is given by <math> F_{odp} = kv^2 </math> kgs/m where the numerical value of <math> k = 0.3 </math> if the unit of the speed is m/s and the unit of the resistance force is the newton (N). The mass of the bicyclist including the bike is 70 kg. Do not consider the rolling resistance. '''(a)''' What forward force exerted on the bike by the road is needed to make the bicyclist move with constant speed? '''(b)''' How much work does the bicyclist do when riding a distance of 1200 m? '''(c)''' What is the power of the bicyclist during the ride? Assume there is no loss of mechanical energy.
			[[File:Bike_power.JPG \|border\|right]]
	:<math> F_g </math> = weight		:<math> F_g </math> = weight
	:N = normal force exerted on the bike by the road		:N = normal force exerted on the bike by the road
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	'''(c)''' <math> power = F\cdot v = (51.6 N)(7.5 m/s) = 387 J/s </math>		'''(c)''' <math> power = F\cdot v = (51.6 N)(7.5 m/s) = 387 J/s </math>

	~~[[File:Bike_power.JPG \|border\|right]]~~

	'''Difficult problems will require a multitude of forces to be found before calculating the work. These can be tricky so make sure to draw a free body diagram.'''		'''Difficult problems will require a multitude of forces to be found before calculating the work. These can be tricky so make sure to draw a free body diagram.'''

Tarnie14: /* Difficult */

2018-04-19T00:55:21Z

Difficult

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	'''(c)''' <math> power = F\cdot v = (51.6 N)(7.5 m/s) = 387 J/s </math>		'''(c)''' <math> power = F\cdot v = (51.6 N)(7.5 m/s) = 387 J/s </math>

			[[File:Bike_power.JPG \|border\|right]]

	'''Difficult problems will require a multitude of forces to be found before calculating the work. These can be tricky so make sure to draw a free body diagram.'''		'''Difficult problems will require a multitude of forces to be found before calculating the work. These can be tricky so make sure to draw a free body diagram.'''

Tarnie14: /* Difficult */

2018-04-19T00:55:01Z

Difficult

← Older revision		Revision as of 20:55, 18 April 2018
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	A bicyclist is going up an inclined slope with an angle <math> \alpha </math> = 2.9 degrees by a uniform speed of 27 km/h. The magnitude of the air resistance force is given by <math> F_{odp} = kv^2 </math> kgs/m where the numerical value of <math> k = 0.3 </math> if the unit of the speed is m/s and the unit of the resistance force is the newton (N). The mass of the bicyclist including the bike is 70 kg. Do not consider the rolling resistance. '''(a)''' What forward force exerted on the bike by the road is needed to make the bicyclist move with constant speed? '''(b)''' How much work does the bicyclist do when riding a distance of 1200 m? '''(c)''' What is the power of the bicyclist during the ride? Assume there is no loss of mechanical energy.		A bicyclist is going up an inclined slope with an angle <math> \alpha </math> = 2.9 degrees by a uniform speed of 27 km/h. The magnitude of the air resistance force is given by <math> F_{odp} = kv^2 </math> kgs/m where the numerical value of <math> k = 0.3 </math> if the unit of the speed is m/s and the unit of the resistance force is the newton (N). The mass of the bicyclist including the bike is 70 kg. Do not consider the rolling resistance. '''(a)''' What forward force exerted on the bike by the road is needed to make the bicyclist move with constant speed? '''(b)''' How much work does the bicyclist do when riding a distance of 1200 m? '''(c)''' What is the power of the bicyclist during the ride? Assume there is no loss of mechanical energy.
	~~[[File:Bike_power.JPG \|border\|right]]~~
	:<math> F_g </math> = weight		:<math> F_g </math> = weight
	:N = normal force exerted on the bike by the road		:N = normal force exerted on the bike by the road

Tarnie14: /* Difficult */

2018-04-19T00:52:14Z

Difficult

← Older revision		Revision as of 20:52, 18 April 2018
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	A bicyclist is going up an inclined slope with an angle <math> \alpha </math> = 2.9 degrees by a uniform speed of 27 km/h. The magnitude of the air resistance force is given by <math> F_{odp} = kv^2 </math> kgs/m where the numerical value of <math> k = 0.3 </math> if the unit of the speed is m/s and the unit of the resistance force is the newton (N). The mass of the bicyclist including the bike is 70 kg. Do not consider the rolling resistance. '''(a)''' What forward force exerted on the bike by the road is needed to make the bicyclist move with constant speed? '''(b)''' How much work does the bicyclist do when riding a distance of 1200 m? '''(c)''' What is the power of the bicyclist during the ride? Assume there is no loss of mechanical energy.		A bicyclist is going up an inclined slope with an angle <math> \alpha </math> = 2.9 degrees by a uniform speed of 27 km/h. The magnitude of the air resistance force is given by <math> F_{odp} = kv^2 </math> kgs/m where the numerical value of <math> k = 0.3 </math> if the unit of the speed is m/s and the unit of the resistance force is the newton (N). The mass of the bicyclist including the bike is 70 kg. Do not consider the rolling resistance. '''(a)''' What forward force exerted on the bike by the road is needed to make the bicyclist move with constant speed? '''(b)''' How much work does the bicyclist do when riding a distance of 1200 m? '''(c)''' What is the power of the bicyclist during the ride? Assume there is no loss of mechanical energy.
	[[File:~~wikipic1~~.~~png~~ \|border\|right]]		[[File:Bike_power.JPG \|border\|right]]
	:<math> F_g </math> = weight		:<math> F_g </math> = weight
	:N = normal force exerted on the bike by the road		:N = normal force exerted on the bike by the road
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	:<math> F = F_gsin\alpha + F_{odp} = mgsin\alpha + kv^2 </math> ~~[[File:wikipic2.png \|border\|right]]~~		:<math> F = F_gsin\alpha + F_{odp} = mgsin\alpha + kv^2 </math>

Tarnie14: /* References */

2018-04-19T00:36:50Z

References

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	<https://physicstasks.eu/280/bicyclist-going-uphill>. <br>		<https://physicstasks.eu/280/bicyclist-going-uphill>. <br>
	<https://en.wikipedia.org/wiki/Power_(physics)>. <br>		<https://en.wikipedia.org/wiki/Power_(physics)>. <br>
	<https://en.wikipedia.org/wiki/Power_transmission#Mechanical_power>		<https://en.wikipedia.org/wiki/Power_transmission#Mechanical_power><br>
	<https://en.wikibooks.org/wiki/General_Mechanics/Work_and_Power>		<https://en.wikibooks.org/wiki/General_Mechanics/Work_and_Power>

	[[Category:Energy]]		[[Category:Energy]]