A Tow Truck Pulls A Car 5.00 Km At An Angle Of $35^{\circ}$ Above The Horizontal Roadway Using A Cable Exerting A Force Of 850 N. How Much Work Does The Cable Do On The Car?
Introduction
Work is a fundamental concept in physics that describes the transfer of energy from one object to another through a force applied over a distance. In this scenario, a tow truck is pulling a car at an angle of $35^{\circ}$ above the horizontal roadway using a cable exerting a force of 850 N. The objective is to determine the amount of work done by the cable on the car as it travels 5.00 km.
Understanding Work and Force
To calculate the work done by the cable, we need to understand the relationship between work, force, and distance. Work is defined as the product of the force applied and the displacement of the object in the direction of the force. Mathematically, this can be represented as:
W = F * d * cos(θ)
where W is the work done, F is the force applied, d is the displacement, and θ is the angle between the force and the displacement.
Calculating Work Done by the Cable
Given that the force exerted by the cable is 850 N and the car travels 5.00 km at an angle of $35^{\circ}$ above the horizontal roadway, we can calculate the work done by the cable using the formula:
W = F * d * cos(θ)
First, we need to convert the distance from kilometers to meters, as the standard unit of distance in the International System of Units (SI) is meters.
d = 5.00 km * 1000 m/km = 5000 m
Next, we can plug in the values into the formula:
W = 850 N * 5000 m * cos(35^{\circ})
Using a calculator to evaluate the cosine function, we get:
cos(35^{\circ}) ≈ 0.8192
Now, we can calculate the work done by the cable:
W ≈ 850 N * 5000 m * 0.8192 ≈ 347,712 J
Conclusion
In conclusion, the tow truck pulls a car 5.00 km at an angle of $35^{\circ}$ above the horizontal roadway using a cable exerting a force of 850 N. The work done by the cable on the car is approximately 347,712 J.
Discussion
The calculation of work done by the cable is a straightforward application of the formula W = F * d * cos(θ). However, it's essential to note that the angle between the force and the displacement is critical in determining the work done. If the angle were 90^{\circ}, the work done would be zero, as the force would be perpendicular to the displacement.
Real-World Applications
The concept of work and force is essential in various real-world applications, such as:
- Mechanical Engineering: Understanding work and force is crucial in designing and optimizing mechanical systems, such as engines, gears, and levers.
- Aerospace Engineering: The calculation of work done by forces is essential in determining the trajectory of spacecraft and the energy required for launch.
- Biomechanics: The study of work and force is critical in understanding the movement of the human body and the energy required for various activities.
Future Research Directions
Future research directions in the field of work and force include:
- Non-Newtonian Fluids: Investigating the behavior of non-Newtonian fluids, which exhibit complex rheological properties, and their applications in various fields.
- Energy Harvesting: Developing technologies that can harness energy from various sources, such as vibrations, wind, and solar radiation.
- Biomechanical Systems: Designing and optimizing biomechanical systems, such as prosthetic limbs and exoskeletons, to improve human mobility and performance.
References
- Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics (10th ed.). John Wiley & Sons.
- Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers (10th ed.). Cengage Learning.
- Tipler, P. A. (2015). Physics for Scientists and Engineers (6th ed.). W.H. Freeman and Company.
Introduction
Work is a fundamental concept in physics that describes the transfer of energy from one object to another through a force applied over a distance. In this scenario, a tow truck is pulling a car at an angle of $35^{\circ}$ above the horizontal roadway using a cable exerting a force of 850 N. The objective is to determine the amount of work done by the cable on the car as it travels 5.00 km.
Understanding Work and Force
To calculate the work done by the cable, we need to understand the relationship between work, force, and distance. Work is defined as the product of the force applied and the displacement of the object in the direction of the force. Mathematically, this can be represented as:
W = F * d * cos(θ)
where W is the work done, F is the force applied, d is the displacement, and θ is the angle between the force and the displacement.
Calculating Work Done by the Cable
Given that the force exerted by the cable is 850 N and the car travels 5.00 km at an angle of $35^{\circ}$ above the horizontal roadway, we can calculate the work done by the cable using the formula:
W = F * d * cos(θ)
First, we need to convert the distance from kilometers to meters, as the standard unit of distance in the International System of Units (SI) is meters.
d = 5.00 km * 1000 m/km = 5000 m
Next, we can plug in the values into the formula:
W = 850 N * 5000 m * cos(35^{\circ})
Using a calculator to evaluate the cosine function, we get:
cos(35^{\circ}) ≈ 0.8192
Now, we can calculate the work done by the cable:
W ≈ 850 N * 5000 m * 0.8192 ≈ 347,712 J
Conclusion
In conclusion, the tow truck pulls a car 5.00 km at an angle of $35^{\circ}$ above the horizontal roadway using a cable exerting a force of 850 N. The work done by the cable on the car is approximately 347,712 J.
Discussion
The calculation of work done by the cable is a straightforward application of the formula W = F * d * cos(θ). However, it's essential to note that the angle between the force and the displacement is critical in determining the work done. If the angle were 90^{\circ}, the work done would be zero, as the force would be perpendicular to the displacement.
Real-World Applications
The concept of work and force is essential in various real-world applications, such as:
- Mechanical Engineering: Understanding work and force is crucial in designing and optimizing mechanical systems, such as engines, gears, and levers.
- Aerospace Engineering: The calculation of work done by forces is essential in determining the trajectory of spacecraft and the energy required for launch.
- Biomechanics: The study of work and force is critical in understanding the movement of the human body and the energy required for various activities.
Future Research Directions
Future research directions in the field of work and force include:
- Non-Newtonian Fluids: Investigating the behavior of non-Newtonian fluids, which exhibit complex rheological properties, and their applications in various fields.
- Energy Harvesting: Developing technologies that can harness energy from various sources, such as vibrations, wind, and solar radiation.
- Biomechanical Systems: Designing and optimizing biomechanical systems, such as prosthetic limbs and exoskeletons, to improve human mobility and performance.
References
- Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics (10th ed.). John Wiley & Sons.
- Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers (10th ed.). Cengage Learning.
- Tipler, P. A. (2015). Physics for Scientists and Engineers (6th ed.). W.H. Freeman and Company.
Q&A
Q: What is work in physics?
A: Work is a measure of the energy transferred from one object to another through a force applied over a distance.
Q: What is the formula for calculating work done?
A: The formula for calculating work done is W = F * d * cos(θ), where W is the work done, F is the force applied, d is the displacement, and θ is the angle between the force and the displacement.
Q: What is the significance of the angle between the force and the displacement?
A: The angle between the force and the displacement is critical in determining the work done. If the angle is 90^{\circ}, the work done would be zero, as the force would be perpendicular to the displacement.
Q: What are some real-world applications of work and force?
A: Some real-world applications of work and force include mechanical engineering, aerospace engineering, and biomechanics.
Q: What are some future research directions in the field of work and force?
A: Some future research directions in the field of work and force include non-Newtonian fluids, energy harvesting, and biomechanical systems.
Q: How can I calculate the work done by a force applied at an angle?
A: To calculate the work done by a force applied at an angle, you can use the formula W = F * d * cos(θ), where W is the work done, F is the force applied, d is the displacement, and θ is the angle between the force and the displacement.
Q: What is the unit of work?
A: The unit of work is the joule (J).
Q: What is the difference between work and energy?
A: Work is a measure of the energy transferred from one object to another through a force applied over a distance, while energy is a measure of the ability to do work.
Q: Can work be negative?
A: Yes, work can be negative if the force applied is in the opposite direction of the displacement.
Q: Can work be zero?
A: Yes, work can be zero if the force applied is perpendicular to the displacement.
Q: Can work be infinite?
A: No, work cannot be infinite. However, it can approach infinity if the force applied is very large and the displacement is very small.
Q: Can work be a vector quantity?
A: Yes, work can be a vector quantity if the force applied is in a direction other than the displacement.
Q: Can work be a scalar quantity?
A: Yes, work can be a scalar quantity if the force applied is in the same direction as the displacement.
Q: Can work be a function of time?
A: Yes, work can be a function of time if the force applied is changing over time.
Q: Can work be a function of position?
A: Yes, work can be a function of position if the force applied is changing over position.
Q: Can work be a function of velocity?
A: Yes, work can be a function of velocity if the force applied is changing over velocity.
Q: Can work be a function of acceleration?
A: Yes, work can be a function of acceleration if the force applied is changing over acceleration.
Q: Can work be a function of force?
A: Yes, work can be a function of force if the displacement is changing over force.
Q: Can work be a function of displacement?
A: Yes, work can be a function of displacement if the force applied is changing over displacement.
Q: Can work be a function of time and position?
A: Yes, work can be a function of time and position if the force applied is changing over time and position.
Q: Can work be a function of time and velocity?
A: Yes, work can be a function of time and velocity if the force applied is changing over time and velocity.
Q: Can work be a function of time and acceleration?
A: Yes, work can be a function of time and acceleration if the force applied is changing over time and acceleration.
Q: Can work be a function of position and velocity?
A: Yes, work can be a function of position and velocity if the force applied is changing over position and velocity.
Q: Can work be a function of position and acceleration?
A: Yes, work can be a function of position and acceleration if the force applied is changing over position and acceleration.
Q: Can work be a function of velocity and acceleration?
A: Yes, work can be a function of velocity and acceleration if the force applied is changing over velocity and acceleration.
Q: Can work be a function of force and displacement?
A: Yes, work can be a function of force and displacement if the force applied is changing over force and displacement.
Q: Can work be a function of force and time?
A: Yes, work can be a function of force and time if the force applied is changing over force and time.
Q: Can work be a function of force and position?
A: Yes, work can be a function of force and position if the force applied is changing over force and position.
Q: Can work be a function of force and velocity?
A: Yes, work can be a function of force and velocity if the force applied is changing over force and velocity