Select The Correct Answer.How Much Work Will A Machine With A Power Rating Of $1.1 \times 10^3$ Watts Do In 2.0 Hours?A. $1.5 \times 10^6$ Joules B. \$2.1 \times 10^6$[/tex\] Joules C. $4.0 \times 10^6$
Introduction
In physics, work and power are two fundamental concepts that are often used interchangeably, but they have distinct meanings. Work is the transfer of energy from one object to another through a force applied over a distance, while power is the rate at which work is done. In this article, we will explore the relationship between work and power, and use a real-world example to illustrate how to calculate the work done by a machine.
What is Work?
Work is defined as the product of the force applied to an object and the distance over which the force is applied. Mathematically, work (W) is represented as:
W = F * d
where F is the force applied and d is the distance over which the force is applied.
What is Power?
Power is the rate at which work is done. It is defined as the work done per unit time. Mathematically, power (P) is represented as:
P = W / t
where W is the work done and t is the time over which the work is done.
The Relationship Between Work and Power
The relationship between work and power is given by the equation:
W = P * t
This equation shows that work is equal to the product of power and time. In other words, the work done by a machine is equal to the power rating of the machine multiplied by the time over which the machine operates.
Example Problem
A machine has a power rating of 1.1 x 10^3 watts. How much work will the machine do in 2.0 hours?
To solve this problem, we need to use the equation W = P * t. We are given the power rating of the machine (P = 1.1 x 10^3 watts) and the time over which the machine operates (t = 2.0 hours). We need to convert the time from hours to seconds, since the power rating is given in watts (which is a unit of power in joules per second).
1 hour = 3600 seconds
Therefore, 2.0 hours = 2.0 x 3600 = 7200 seconds
Now, we can plug in the values into the equation W = P * t:
W = (1.1 x 10^3 watts) x (7200 seconds)
W = 7.92 x 10^6 joules
Therefore, the machine will do 7.92 x 10^6 joules of work in 2.0 hours.
Conclusion
In conclusion, work and power are two fundamental concepts in physics that are related by the equation W = P * t. The work done by a machine is equal to the power rating of the machine multiplied by the time over which the machine operates. In this article, we used a real-world example to illustrate how to calculate the work done by a machine. We hope that this article has provided a clear understanding of the relationship between work and power.
Answer
The correct answer is A. 7.92 x 10^6 joules.
Discussion
This problem is a great example of how to apply the concept of work and power in a real-world scenario. The machine's power rating is given in watts, which is a unit of power in joules per second. To calculate the work done by the machine, we need to convert the time from hours to seconds and then plug in the values into the equation W = P * t.
Additional Resources
For more information on work and power, check out the following resources:
Related Topics
Energy and Work
Energy is the ability to do work. It is a measure of the amount of work that can be done by an object. There are several types of energy, including kinetic energy, potential energy, and thermal energy.
Power and Energy
Power is the rate at which work is done. It is defined as the work done per unit time. Energy is the ability to do work. It is a measure of the amount of work that can be done by an object.
Work and Energy
Work is the transfer of energy from one object to another through a force applied over a distance. Energy is the ability to do work. It is a measure of the amount of work that can be done by an object.
References
- Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. John Wiley & Sons.
- Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.
Work and Power: Q&A =====================
Q: What is the difference between work and power?
A: Work is the transfer of energy from one object to another through a force applied over a distance, while power is the rate at which work is done.
Q: How is work calculated?
A: Work (W) is calculated as the product of the force applied (F) and the distance over which the force is applied (d): W = F * d.
Q: How is power calculated?
A: Power (P) is calculated as the work done (W) divided by the time over which the work is done (t): P = W / t.
Q: What is the relationship between work and power?
A: The relationship between work and power is given by the equation: W = P * t.
Q: How is the work done by a machine calculated?
A: The work done by a machine is calculated by multiplying the power rating of the machine by the time over which the machine operates: W = P * t.
Q: What is the unit of work?
A: The unit of work is the joule (J).
Q: What is the unit of power?
A: The unit of power is the watt (W).
Q: Can you give an example of how to calculate the work done by a machine?
A: Yes, let's say a machine has a power rating of 1.1 x 10^3 watts and operates for 2.0 hours. To calculate the work done by the machine, we need to convert the time from hours to seconds and then plug in the values into the equation W = P * t.
1 hour = 3600 seconds
Therefore, 2.0 hours = 2.0 x 3600 = 7200 seconds
Now, we can plug in the values into the equation W = P * t:
W = (1.1 x 10^3 watts) x (7200 seconds)
W = 7.92 x 10^6 joules
Therefore, the machine will do 7.92 x 10^6 joules of work in 2.0 hours.
Q: What is the difference between kinetic energy and potential energy?
A: Kinetic energy is the energy of motion, while potential energy is the energy of position.
Q: Can you give an example of how to calculate the kinetic energy of an object?
A: Yes, let's say an object has a mass of 5.0 kg and a velocity of 10.0 m/s. To calculate the kinetic energy of the object, we need to use the equation: K = (1/2) * m * v^2.
K = (1/2) * (5.0 kg) * (10.0 m/s)^2
K = 250 J
Therefore, the kinetic energy of the object is 250 J.
Q: What is the difference between thermal energy and other forms of energy?
A: Thermal energy is the energy of heat, while other forms of energy include kinetic energy, potential energy, and electrical energy.
Q: Can you give an example of how to calculate the thermal energy of an object?
A: Yes, let's say an object has a mass of 2.0 kg and a temperature of 20.0°C. To calculate the thermal energy of the object, we need to use the equation: Q = m * c * ΔT.
Q = (2.0 kg) * (1000 J/kg°C) * (20.0°C - 0.0°C)
Q = 40000 J
Therefore, the thermal energy of the object is 40000 J.
Q: What is the difference between electrical energy and other forms of energy?
A: Electrical energy is the energy of electricity, while other forms of energy include kinetic energy, potential energy, and thermal energy.
Q: Can you give an example of how to calculate the electrical energy of an object?
A: Yes, let's say an object has a charge of 5.0 C and a voltage of 10.0 V. To calculate the electrical energy of the object, we need to use the equation: E = Q * V.
E = (5.0 C) * (10.0 V)
E = 50 J
Therefore, the electrical energy of the object is 50 J.