3.4 Power
3 min read•january 29, 2023
Daniella Garcia-Loos
Daniella Garcia-Loos
Power and Work vs Time
is essentially the rate of change of energy/work in a system. While this key concept is quite brief, is a topic explored not just in the realm of mechanics. is typically used in reference to electricity but it can refer to even the simplest scenarios like walking up the stairs. The units for are typically Watts or Joules/seconds.
Here are the two main formulas for :
Here you can see above that can be the slope in a Work vs Time graph or an Energy vs Time graph, which may be useful for FRQs! Let's take a look at one of those graphs!
Taken from New York State Library System
Work won't always be a straight line, sometimes it may be a constant horizontal line, and it can also be negative! Just be aware that is the slope.
It can also be simplified into the equation below:
We must remember our formula from kinematics and simplify
Here are some key takeaways about :
is defined as the rate at which work is done or energy is transferred. Mathematically, is represented as the derivative of work with respect to time (P = dW/dt)
is also defined as the dot product of the force and velocity (P = F.v)
The unit of is the Joule per second (J/s) or the watt (W)
In physics, work and are scalar quantities and their direction is not considered.
can be calculated for both conservative and .
In a conservative system, the is zero when the object is at a position of .
In a nonconservative system, may not be zero even when the object is at a position of .
can be calculated for various types of systems such as electrical, mechanical, thermodynamic, and more.
The of a system is defined as the ratio of the output to the input .
The maximum of a system is determined by the laws of thermodynamics.
can be calculated for different types of systems such as electrical, mechanical, thermodynamic, and more.
The of a system is defined as the ratio of the output to the input .
The maximum of a system is determined by the laws of thermodynamics.
In mechanical systems, can be calculated as the product of the and the (P = T.w)
In electrical systems, can be calculated as the product of the current and the voltage (P = I.V)
In thermodynamic systems, can be calculated as the product of the heat flow and the temperature difference (P = Q.ΔT)
In case of a cyclic process the net work done is zero, thus the net is also zero.
Practice Questions
1. A large household air conditioner may consume 15.0 kW of . What is the cost of operating this air conditioner 3.00 h per day for 30.0 d if the cost of electricity is $0.110 per kW · h? (Taken from Lumen Learning)
Answer:
Multiply the cost of electricity per hour by the maximum consumption to find the cost per hour
$15 * 0.110 = 1.65$
Then multiply by the amount of usage per day and the amount of days
$1.65 330 = 148.5$
$149
2. Calculate the output needed for a 950-kg car to climb a 2.00º slope at a constant 30.0 m/s while encountering wind resistance and friction totaling 600 N. (Taken from Lumen Learning)
Answer:
Key Terms to Review (7)
Angular velocity
: Angular velocity refers to the rate at which an object rotates around a fixed axis. It is measured in radians per second and represents how quickly an object is spinning.Efficiency
: Efficiency refers to how effectively a system or process converts input energy into useful output energy without wasting any energy as heat or other forms of loss. It is often expressed as a percentage.Non-conservative forces
: Non-conservative forces are external forces that do work on an object, causing a change in its mechanical energy. These forces depend on the path taken by the object and not just its initial and final positions.Power
: Power is the rate at which work is done or energy is transferred. It measures how quickly a task can be completed.Stable equilibrium
: Stable equilibrium refers to a state where an object remains at rest or returns to its original position after being slightly displaced. In this state, any small disturbance causes a restoring force that brings the object back to its equilibrium position.Torque
: Torque is the measure of how effectively a force can cause an object to rotate. It depends on the magnitude of the force, the distance from the axis of rotation, and the angle between the force and lever arm.Watt (W)
: The watt is the unit of power in the International System of Units (SI). It measures the rate at which work is done or energy is transferred.3.4 Power
3 min read•january 29, 2023
Daniella Garcia-Loos
Daniella Garcia-Loos
Power and Work vs Time
is essentially the rate of change of energy/work in a system. While this key concept is quite brief, is a topic explored not just in the realm of mechanics. is typically used in reference to electricity but it can refer to even the simplest scenarios like walking up the stairs. The units for are typically Watts or Joules/seconds.
Here are the two main formulas for :
Here you can see above that can be the slope in a Work vs Time graph or an Energy vs Time graph, which may be useful for FRQs! Let's take a look at one of those graphs!
Taken from New York State Library System
Work won't always be a straight line, sometimes it may be a constant horizontal line, and it can also be negative! Just be aware that is the slope.
It can also be simplified into the equation below:
We must remember our formula from kinematics and simplify
Here are some key takeaways about :
is defined as the rate at which work is done or energy is transferred. Mathematically, is represented as the derivative of work with respect to time (P = dW/dt)
is also defined as the dot product of the force and velocity (P = F.v)
The unit of is the Joule per second (J/s) or the watt (W)
In physics, work and are scalar quantities and their direction is not considered.
can be calculated for both conservative and .
In a conservative system, the is zero when the object is at a position of .
In a nonconservative system, may not be zero even when the object is at a position of .
can be calculated for various types of systems such as electrical, mechanical, thermodynamic, and more.
The of a system is defined as the ratio of the output to the input .
The maximum of a system is determined by the laws of thermodynamics.
can be calculated for different types of systems such as electrical, mechanical, thermodynamic, and more.
The of a system is defined as the ratio of the output to the input .
The maximum of a system is determined by the laws of thermodynamics.
In mechanical systems, can be calculated as the product of the and the (P = T.w)
In electrical systems, can be calculated as the product of the current and the voltage (P = I.V)
In thermodynamic systems, can be calculated as the product of the heat flow and the temperature difference (P = Q.ΔT)
In case of a cyclic process the net work done is zero, thus the net is also zero.
Practice Questions
1. A large household air conditioner may consume 15.0 kW of . What is the cost of operating this air conditioner 3.00 h per day for 30.0 d if the cost of electricity is $0.110 per kW · h? (Taken from Lumen Learning)
Answer:
Multiply the cost of electricity per hour by the maximum consumption to find the cost per hour
$15 * 0.110 = 1.65$
Then multiply by the amount of usage per day and the amount of days
$1.65 330 = 148.5$
$149
2. Calculate the output needed for a 950-kg car to climb a 2.00º slope at a constant 30.0 m/s while encountering wind resistance and friction totaling 600 N. (Taken from Lumen Learning)
Answer:
Key Terms to Review (7)
Angular velocity
: Angular velocity refers to the rate at which an object rotates around a fixed axis. It is measured in radians per second and represents how quickly an object is spinning.Efficiency
: Efficiency refers to how effectively a system or process converts input energy into useful output energy without wasting any energy as heat or other forms of loss. It is often expressed as a percentage.Non-conservative forces
: Non-conservative forces are external forces that do work on an object, causing a change in its mechanical energy. These forces depend on the path taken by the object and not just its initial and final positions.Power
: Power is the rate at which work is done or energy is transferred. It measures how quickly a task can be completed.Stable equilibrium
: Stable equilibrium refers to a state where an object remains at rest or returns to its original position after being slightly displaced. In this state, any small disturbance causes a restoring force that brings the object back to its equilibrium position.Torque
: Torque is the measure of how effectively a force can cause an object to rotate. It depends on the magnitude of the force, the distance from the axis of rotation, and the angle between the force and lever arm.Watt (W)
: The watt is the unit of power in the International System of Units (SI). It measures the rate at which work is done or energy is transferred.
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