A Sled With A Mass Of 8 Kg Is Pulled At A 50-degree Angle With A Force Of 20 N. The Force Of Friction Acting On The Sled Is 2.4 N. What Is The Acceleration Of The Sled And The Normal Force Acting On It, To The Nearest Tenth?A. $a = 1.3 \,
Introduction
In this problem, we are given a sled with a mass of 8 kg that is being pulled at a 50-degree angle with a force of 20 N. Additionally, the force of friction acting on the sled is 2.4 N. Our goal is to calculate the acceleration of the sled and the normal force acting on it, to the nearest tenth.
Calculating the Acceleration
To calculate the acceleration of the sled, we need to consider the forces acting on it. The force of 20 N is being applied at a 50-degree angle, which means it has both horizontal and vertical components. We can resolve this force into its horizontal and vertical components using trigonometry.
The horizontal component of the force is given by:
F_horizontal = F * cos(θ)
where F is the magnitude of the force (20 N) and θ is the angle (50 degrees).
F_horizontal = 20 * cos(50°) F_horizontal = 20 * 0.6428 F_horizontal = 12.856 N
The vertical component of the force is given by:
F_vertical = F * sin(θ)
F_vertical = 20 * sin(50°) F_vertical = 20 * 0.7660 F_vertical = 15.320 N
Now, we can calculate the net force acting on the sled in the horizontal direction. The force of friction is acting in the opposite direction, so we subtract it from the horizontal component of the force:
F_net = F_horizontal - F_friction F_net = 12.856 N - 2.4 N F_net = 10.456 N
We can now use Newton's second law to calculate the acceleration of the sled:
F_net = m * a
where m is the mass of the sled (8 kg) and a is the acceleration.
a = F_net / m a = 10.456 N / 8 kg a = 1.303 N/kg a = 1.3 m/s^2
Calculating the Normal Force
To calculate the normal force acting on the sled, we need to consider the vertical forces acting on it. The vertical component of the force is 15.320 N, and the weight of the sled is given by:
W = m * g
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
W = 8 kg * 9.8 m/s^2 W = 78.4 N
The normal force is the sum of the vertical component of the force and the weight of the sled:
N = F_vertical + W N = 15.320 N + 78.4 N N = 93.72 N
Conclusion
In this problem, we calculated the acceleration of a sled with a mass of 8 kg that is being pulled at a 50-degree angle with a force of 20 N. We also calculated the normal force acting on the sled. The acceleration of the sled is 1.3 m/s^2, and the normal force is 93.72 N.
Discussion
This problem is a classic example of a physics problem that involves resolving forces into their components and using Newton's laws to calculate the acceleration of an object. The concept of normal force is also important in understanding the forces acting on an object in contact with a surface.
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.
Additional Resources
- Khan Academy: Physics
- MIT OpenCourseWare: Physics
- Physics Classroom: Forces and Newton's Laws
A Sled with a Mass of 8 kg: Calculating Acceleration and Normal Force ===========================================================
Q&A: Frequently Asked Questions
Q: What is the acceleration of the sled?
A: The acceleration of the sled is 1.3 m/s^2.
Q: How do I calculate the acceleration of the sled?
A: To calculate the acceleration of the sled, you need to consider the forces acting on it. The force of 20 N is being applied at a 50-degree angle, which means it has both horizontal and vertical components. You can resolve this force into its horizontal and vertical components using trigonometry. Then, you can use Newton's second law to calculate the acceleration of the sled.
Q: What is the normal force acting on the sled?
A: The normal force acting on the sled is 93.72 N.
Q: How do I calculate the normal force acting on the sled?
A: To calculate the normal force acting on the sled, you need to consider the vertical forces acting on it. The vertical component of the force is 15.320 N, and the weight of the sled is given by the product of its mass and the acceleration due to gravity. The normal force is the sum of the vertical component of the force and the weight of the sled.
Q: What is the force of friction acting on the sled?
A: The force of friction acting on the sled is 2.4 N.
Q: How does the force of friction affect the acceleration of the sled?
A: The force of friction acts in the opposite direction of the force applied to the sled, which means it reduces the net force acting on the sled. As a result, the acceleration of the sled is also reduced.
Q: What is the angle at which the force is applied?
A: The angle at which the force is applied is 50 degrees.
Q: How does the angle of the force affect the acceleration of the sled?
A: The angle of the force affects the horizontal and vertical components of the force. The horizontal component of the force is given by the product of the force and the cosine of the angle, while the vertical component of the force is given by the product of the force and the sine of the angle. As a result, the angle of the force affects the acceleration of the sled.
Q: What is the mass of the sled?
A: The mass of the sled is 8 kg.
Q: How does the mass of the sled affect the acceleration of the sled?
A: The mass of the sled affects the acceleration of the sled through Newton's second law. The acceleration of the sled is given by the net force acting on it divided by its mass. As a result, the mass of the sled affects the acceleration of the sled.
Conclusion
In this article, we have answered some frequently asked questions about the problem of a sled with a mass of 8 kg that is being pulled at a 50-degree angle with a force of 20 N. We have discussed the acceleration of the sled, the normal force acting on it, and the effect of the force of friction and the angle of the force on the acceleration of the sled.
Discussion
This article is a continuation of the previous article, where we calculated the acceleration of the sled and the normal force acting on it. In this article, we have answered some frequently asked questions about the problem, which should help readers understand the concepts involved.
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.
Additional Resources
- Khan Academy: Physics
- MIT OpenCourseWare: Physics
- Physics Classroom: Forces and Newton's Laws