Importance of Power and Work

Oct 13, 2025 by recoveryshake.com 76 views

Understanding the Problem

To determine the time required for a 15,000 W engine to do 1,800,000 J of work, we need to use the formula that relates power, work, and time. The formula is given by:

Power (P) = Work (W) / Time (t)

where P is the power in watts (W), W is the work done in joules (J), and t is the time in seconds (s).

Given Values

We are given the following values:

Power (P) = 15,000 W
Work (W) = 1,800,000 J

Solving for Time

We can rearrange the formula to solve for time (t):

t = W / P

Substituting the given values, we get:

t = 1,800,000 J / 15,000 W

Calculating Time

Now, we can calculate the time required:

t = 120 s

Conclusion

Therefore, the time required for a 15,000 W engine to do 1,800,000 J of work is 120 s.

Comparison with Options

Let's compare our answer with the given options:

A. 0.008 s: This is much too short a time.
B. 8 s: This is also too short a time.
C. 120 s: This matches our calculated answer.
D. 1,785,000 s: This is much too long a time.

Final Answer

The final answer is C. 120 s.

Additional Information

To further understand the concept, let's consider a real-world example. Suppose you have a 15,000 W electric motor that you want to use to lift a heavy load. If the motor can do 1,800,000 J of work, how long will it take to lift the load? Using the formula, we can calculate the time required:

t = W / P

t = 1,800,000 J / 15,000 W

t = 120 s

Therefore, it will take 120 seconds (or 2 minutes) for the motor to lift the load.

Importance of Power and Work

Power and work are two fundamental concepts in physics that are closely related. Power is the rate at which work is done, and work is the product of force and distance. In this problem, we used the formula to relate power, work, and time. Understanding these concepts is crucial in many real-world applications, such as designing engines, motors, and other machines.

Real-World Applications

The concept of power and work has many real-world applications, including:

Engine Design: When designing engines, engineers need to consider the power output and work done by the engine. This is crucial in determining the efficiency and performance of the engine.
Motor Design: Similarly, when designing motors, engineers need to consider the power output and work done by the motor. This is crucial in determining the efficiency and performance of the motor.
Energy Efficiency: Understanding power and work is also crucial in determining energy efficiency. For example, a more efficient engine or motor will do more work with less power, resulting in better energy efficiency.

Conclusion

In conclusion, the time required for a 15,000 W engine to do 1,800,000 J of work is 120 s. This problem demonstrates the importance of understanding power and work in physics and their real-world applications.

Q: What is power, and how is it related to work?

A: Power is the rate at which work is done. It is measured in watts (W) and is calculated as the work done per unit time. The formula for power is:

P = W / t

where P is the power, W is the work done, and t is the time.

Q: What is work, and how is it related to force and distance?

A: Work is the product of force and distance. It is measured in joules (J) and is calculated as the force applied to an object multiplied by the distance over which the force is applied.

W = F × d

where W is the work done, F is the force applied, and d is the distance.

Q: How is power related to energy?

A: Power is the rate at which energy is transferred or converted. It is measured in watts (W) and is calculated as the energy transferred per unit time.

P = E / t

where P is the power, E is the energy transferred, and t is the time.

Q: What is the difference between power and energy?

A: Power is the rate at which energy is transferred or converted, while energy is the total amount of energy transferred or converted. Power is measured in watts (W), while energy is measured in joules (J).

Q: How is power used in real-world applications?

A: Power is used in a wide range of real-world applications, including:

Engine Design: Power is used to design engines that can produce a certain amount of work.
Motor Design: Power is used to design motors that can produce a certain amount of work.
Energy Efficiency: Power is used to determine the energy efficiency of a system or device.
Electrical Systems: Power is used to design electrical systems that can supply a certain amount of power to a load.

Q: What is the unit of power?

A: The unit of power is the watt (W).

Q: What is the unit of work?

A: The unit of work is the joule (J).

Q: How is power related to torque and rotational speed?

A: Power is related to torque and rotational speed by the formula:

P = τ × ω

where P is the power, τ is the torque, and ω is the rotational speed.

Q: What is the difference between instantaneous power and average power?

A: Instantaneous power is the power at a specific instant in time, while average power is the power over a period of time.

Q: How is power used in electrical systems?

A: Power is used in electrical systems to determine the amount of power that can be supplied to a load. It is also used to design electrical systems that can supply a certain amount of power to a load.

Q: What is the importance of power in physics?

A: Power is an important concept in physics because it is used to describe the rate at which work is done. It is also used to determine the energy efficiency of a system or device.

Q: How is power related to energy storage?

A: Power is related to energy storage by the formula:

P = E / t

where P is the power, E is the energy stored, and t is the time.

Q: What is the difference between power and energy storage?

A: Power is the rate at which energy is transferred or converted, while energy storage is the total amount of energy stored in a system or device.

Q: How is power used in mechanical systems?

A: Power is used in mechanical systems to determine the amount of work that can be done by a machine or device. It is also used to design mechanical systems that can produce a certain amount of work.

Q: What is the importance of power in mechanical systems?

A: Power is an important concept in mechanical systems because it is used to describe the rate at which work is done. It is also used to determine the energy efficiency of a system or device.

Q: How is power related to thermodynamics?

A: Power is related to thermodynamics by the formula:

P = Q / t

where P is the power, Q is the heat transferred, and t is the time.

Q: What is the difference between power and thermodynamics?

A: Power is the rate at which energy is transferred or converted, while thermodynamics is the study of the relationships between heat, work, and energy.

Q: How is power used in thermodynamic systems?

A: Power is used in thermodynamic systems to determine the amount of work that can be done by a system or device. It is also used to design thermodynamic systems that can produce a certain amount of work.

Q: What is the importance of power in thermodynamic systems?

A: Power is an important concept in thermodynamic systems because it is used to describe the rate at which work is done. It is also used to determine the energy efficiency of a system or device.

Q: How is power related to electrical engineering?

A: Power is related to electrical engineering by the formula:

P = V × I

where P is the power, V is the voltage, and I is the current.

Q: What is the difference between power and electrical engineering?

A: Power is the rate at which energy is transferred or converted, while electrical engineering is the study of the design and application of electrical systems.

Q: How is power used in electrical engineering?

A: Power is used in electrical engineering to determine the amount of power that can be supplied to a load. It is also used to design electrical systems that can supply a certain amount of power to a load.

Q: What is the importance of power in electrical engineering?

A: Power is an important concept in electrical engineering because it is used to describe the rate at which energy is transferred or converted. It is also used to determine the energy efficiency of a system or device.

Q: How is power related to mechanical engineering?

A: Power is related to mechanical engineering by the formula:

P = F × v

where P is the power, F is the force, and v is the velocity.

Q: What is the difference between power and mechanical engineering?

A: Power is the rate at which energy is transferred or converted, while mechanical engineering is the study of the design and application of mechanical systems.

Q: How is power used in mechanical engineering?

A: Power is used in mechanical engineering to determine the amount of work that can be done by a machine or device. It is also used to design mechanical systems that can produce a certain amount of work.

Q: What is the importance of power in mechanical engineering?

A: Power is an important concept in mechanical engineering because it is used to describe the rate at which work is done. It is also used to determine the energy efficiency of a system or device.

Q: How is power related to civil engineering?

A: Power is related to civil engineering by the formula:

P = Q × h

where P is the power, Q is the flow rate, and h is the head.

Q: What is the difference between power and civil engineering?

A: Power is the rate at which energy is transferred or converted, while civil engineering is the study of the design and application of infrastructure systems.

Q: How is power used in civil engineering?

A: Power is used in civil engineering to determine the amount of work that can be done by a system or device. It is also used to design infrastructure systems that can produce a certain amount of work.

Q: What is the importance of power in civil engineering?

A: Power is an important concept in civil engineering because it is used to describe the rate at which work is done. It is also used to determine the energy efficiency of a system or device.

Q: How is power related to aerospace engineering?

A: Power is related to aerospace engineering by the formula:

P = m × g × h

where P is the power, m is the mass, g is the acceleration due to gravity, and h is the height.

Q: What is the difference between power and aerospace engineering?

A: Power is the rate at which energy is transferred or converted, while aerospace engineering is the study of the design and application of aerospace systems.

Q: How is power used in aerospace engineering?

A: Power is used in aerospace engineering to determine the amount of work that can be done by a system or device. It is also used to design aerospace systems that can produce a certain amount of work.

Q: What is the importance of power in aerospace engineering?

A: Power is an important concept in aerospace engineering because it is used to describe the rate at which work is done. It is also used to determine the energy efficiency of a system or device.

Q: How is power related to nuclear engineering?

A: Power is related to nuclear engineering by the formula:

P = Q × t

where P is the power, Q is the heat transferred, and t is the time.

Q: What is the difference between power and nuclear engineering?

A: Power is the rate at which energy is transferred or converted, while nuclear engineering is the study of the design and application of nuclear systems.

Q: How is power used in nuclear engineering?

A: Power is used in nuclear engineering to determine the amount of work that can be done by a system or device. It is also used to design nuclear systems that can produce a