Two Children Are Pulling And Pushing A 30.0 Kg Sled. The Child Pulling The Sled Is Exerting A Force Of 12.0 N At A $45^{\circ}$ Angle. The Child Pushing The Sled Is Exerting A Horizontal Force Of 8.00 N. There Is A Force Of Friction Of 5.00

Introduction

In this article, we will explore a classic physics problem involving two children pulling and pushing a sled. We will use the principles of physics to determine the net force acting on the sled and the resulting acceleration. This problem is a great example of how to apply the concepts of force, friction, and Newton's laws of motion to real-world scenarios.

The Problem

Two children are pulling and pushing a 30.0 kg sled. The child pulling the sled is exerting a force of 12.0 N at a $45^{\circ}$ angle. The child pushing the sled is exerting a horizontal force of 8.00 N. There is a force of friction of 5.00 N acting opposite to the direction of motion. We need to find the net force acting on the sled and the resulting acceleration.

Breaking Down the Forces

To solve this problem, we need to break down the forces acting on the sled into their components. We can use trigonometry to find the horizontal and vertical components of the force exerted by the child pulling the sled.

Horizontal Component of the Pulling Force

The horizontal component of the pulling force is given by:

$$F_{\text{pull, horizontal}} = F_{\text{pull}} \cos \theta$$

where $F_{\text{pull}}$ is the magnitude of the pulling force (12.0 N) and $\theta$ is the angle of the pulling force (45°).

$$F_{\text{pull, horizontal}} = 12.0 \cos 45^{\circ} = 8.49 \text{ N}$$

Vertical Component of the Pulling Force

The vertical component of the pulling force is given by:

$$F_{\text{pull, vertical}} = F_{\text{pull}} \sin \theta$$

$$F_{\text{pull, vertical}} = 12.0 \sin 45^{\circ} = 8.49 \text{ N}$$

Net Horizontal Force

The net horizontal force acting on the sled is the sum of the horizontal components of the pulling and pushing forces, minus the force of friction.

$$F_{\text{net, horizontal}} = F_{\text{pull, horizontal}} + F_{\text{push, horizontal}} - F_{\text{friction}}$$

$$F_{\text{net, horizontal}} = 8.49 + 8.00 - 5.00 = 11.49 \text{ N}$$

Net Vertical Force

The net vertical force acting on the sled is the sum of the vertical components of the pulling and pushing forces.

$$F_{\text{net, vertical}} = F_{\text{pull, vertical}} + F_{\text{push, vertical}}$$

Since there is no vertical force acting on the sled, the net vertical force is zero.

Net Force

The net force acting on the sled is the vector sum of the net horizontal and vertical forces.

$$F_{\text{net}} = \sqrt{F_{\text{net, horizontal}}^2 + F_{\text{net, vertical}}^2}$$

$$F_{\text{net}} = \sqrt{11.49^2 + 0^2} = 11.49 \text{ N}$$

Acceleration

The acceleration of the sled is given by Newton's second law:

$$a = \frac{F_{\text{net}}}{m}$$

where $m$ is the mass of the sled (30.0 kg).

$$a = \frac{11.49}{30.0} = 0.383 \text{ m/s}^2$$

Conclusion

In this article, we used the principles of physics to solve a classic problem involving two children pulling and pushing a sled. We broke down the forces acting on the sled into their components, found the net horizontal and vertical forces, and calculated the resulting acceleration. This problem is a great example of how to apply the concepts of force, friction, and Newton's laws of motion to real-world scenarios.

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.

Further Reading

• For more information on the concepts of force, friction, and Newton's laws of motion, see the references listed above.
• For more practice problems on physics, see the following resources:
  • Khan Academy: Physics
  • MIT OpenCourseWare: Physics
  • Physics Classroom: Problems and Solutions
    Two Children Pulling and Pushing a Sled: A Physics Problem - Q&A ===========================================================

Introduction

In our previous article, we explored a classic physics problem involving two children pulling and pushing a sled. We used the principles of physics to determine the net force acting on the sled and the resulting acceleration. In this article, we will answer some common questions related to this problem.

Q: What is the purpose of breaking down the forces into their components?

A: Breaking down the forces into their components is necessary to find the net force acting on the sled. By finding the horizontal and vertical components of the pulling force, we can determine the net horizontal and vertical forces acting on the sled.

Q: Why is the force of friction important in this problem?

A: The force of friction is important in this problem because it opposes the motion of the sled. Without the force of friction, the sled would accelerate indefinitely. However, with the force of friction, the sled will accelerate until it reaches a steady speed.

Q: Can the children pull the sled faster if they exert a greater force?

A: Not necessarily. While a greater force may result in a greater acceleration, it also increases the force of friction. If the force of friction is too great, it may counteract the pulling force, resulting in no net acceleration.

Q: What is the relationship between the mass of the sled and its acceleration?

A: According to Newton's second law, the acceleration of an object is inversely proportional to its mass. This means that a greater mass will result in a smaller acceleration, assuming the same net force.

Q: Can the children push the sled faster if they exert a greater force?

A: Yes, if the force is exerted in the same direction as the motion of the sled. However, if the force is exerted in the opposite direction, it will actually slow down the sled.

Q: What is the significance of the angle of the pulling force?

A: The angle of the pulling force affects the horizontal and vertical components of the force. A greater angle will result in a greater vertical component, which may counteract the pulling force.

Q: Can the children pull the sled faster if they work together?

A: Yes, if they exert their forces in the same direction. However, if they exert their forces in opposite directions, it may actually slow down the sled.

Conclusion

In this article, we answered some common questions related to the problem of two children pulling and pushing a sled. We hope that this Q&A article has provided a better understanding of the concepts involved in this problem.

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.

Further Reading

• For more information on the concepts of force, friction, and Newton's laws of motion, see the references listed above.
• For more practice problems on physics, see the following resources:
  • Khan Academy: Physics
  • MIT OpenCourseWare: Physics
  • Physics Classroom: Problems and Solutions