A 32 Kg Child Goes Down A Straight Slide Inclined At $38^{\circ}$ Above The Horizontal. The Child Is Acted On By His Weight, The Normal Force From The Slide, And Kinetic Friction.How Large Is The Normal Force Of The Slide On The Child? Express
Introduction
When a child slides down an inclined plane, several forces act on the child, including the normal force from the slide, the child's weight, and kinetic friction. In this article, we will focus on determining the magnitude of the normal force acting on the child as they slide down the inclined plane.
The Forces Acting on the Child
The child is acted on by three main forces:
- Weight (W): The child's weight is the force due to gravity acting on the child. It is equal to the child's mass (m) multiplied by the acceleration due to gravity (g).
- Normal Force (N): The normal force is the force exerted by the slide on the child, perpendicular to the surface of the slide.
- Kinetic Friction (f_k): Kinetic friction is the force opposing the motion of the child down the slide. It is proportional to the normal force and the coefficient of kinetic friction (μ_k).
Resolving the Forces
To determine the normal force, we need to resolve the forces acting on the child into their components. We can do this by using trigonometry and the concept of resolving forces into their x and y components.
Step 1: Resolve the Weight into its Components
The weight (W) of the child can be resolved into its x and y components using the following equations:
W_x = W * sin(θ) W_y = W * cos(θ)
where θ is the angle of the inclined plane (38° in this case).
Step 2: Resolve the Normal Force into its Components
The normal force (N) can also be resolved into its x and y components using the following equations:
N_x = N * sin(θ) N_y = N * cos(θ)
Step 3: Apply Newton's Second Law
Newton's second law states that the net force acting on an object is equal to its mass multiplied by its acceleration. In this case, the net force acting on the child is the sum of the x and y components of the weight and the normal force.
F_net_x = W_x + N_x F_net_y = W_y - N_y
Since the child is moving down the inclined plane, the net force acting on the child in the x-direction is equal to the child's mass multiplied by the acceleration due to gravity multiplied by the sine of the angle of the inclined plane.
F_net_x = m * g * sin(θ)
Step 4: Solve for the Normal Force
We can now solve for the normal force (N) by equating the net force acting on the child in the y-direction to the child's mass multiplied by the acceleration due to gravity multiplied by the cosine of the angle of the inclined plane.
N_y = m * g * cos(θ)
Since the normal force is perpendicular to the surface of the slide, its magnitude is equal to its y-component.
N = N_y
Calculating the Normal Force
Now that we have the equation for the normal force, we can plug in the values for the child's mass (m = 32 kg), the acceleration due to gravity (g = 9.8 m/s^2), and the angle of the inclined plane (θ = 38°) to calculate the magnitude of the normal force.
N = m * g * cos(θ) N = 32 kg * 9.8 m/s^2 * cos(38°) N = 32 kg * 9.8 m/s^2 * 0.788 N = 246.4 N
Conclusion
In this article, we have determined the magnitude of the normal force acting on a 32 kg child as they slide down a straight slide inclined at 38° above the horizontal. The normal force is a critical component of the forces acting on the child, and its magnitude is determined by the child's mass, the acceleration due to gravity, and the angle of the inclined plane. By understanding the normal force, we can gain a deeper appreciation for the complex interactions between the child and the slide.
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: Forces and Newton's laws
- MIT OpenCourseWare: Physics 8.01: Classical Mechanics
- Physics Classroom: Forces and Newton's Laws
A 32 kg Child Goes Down a Straight Slide: Q&A =============================================
Introduction
In our previous article, we explored the forces acting on a 32 kg child as they slide down a straight slide inclined at 38° above the horizontal. We determined the magnitude of the normal force acting on the child, which is a critical component of the forces acting on the child. In this article, we will answer some frequently asked questions related to the forces acting on the child.
Q: What is the normal force, and why is it important?
A: The normal force is the force exerted by the slide on the child, perpendicular to the surface of the slide. It is an important force because it helps to counteract the weight of the child and prevents the child from sinking into the slide.
Q: How is the normal force related to the weight of the child?
A: The normal force is related to the weight of the child through the angle of the inclined plane. As the angle of the inclined plane increases, the normal force decreases, and the weight of the child becomes more significant.
Q: What is the relationship between the normal force and the kinetic friction?
A: The normal force and the kinetic friction are related through the coefficient of kinetic friction (μ_k). The kinetic friction is proportional to the normal force and the coefficient of kinetic friction.
Q: How does the angle of the inclined plane affect the normal force?
A: The angle of the inclined plane affects the normal force by changing the component of the weight that is perpendicular to the surface of the slide. As the angle of the inclined plane increases, the component of the weight that is perpendicular to the surface of the slide decreases, resulting in a decrease in the normal force.
Q: What is the significance of the normal force in real-world applications?
A: The normal force is significant in real-world applications such as designing roller coasters, water slides, and other amusement park attractions. Understanding the normal force is crucial in ensuring the safety and stability of these attractions.
Q: Can you provide an example of how the normal force is used in a real-world application?
A: Yes, consider a roller coaster with a steep drop. The normal force acting on the riders is critical in ensuring their safety. If the normal force is too small, the riders may experience a loss of control, and if it is too large, the riders may experience a jarring impact. The designers of the roller coaster must carefully balance the normal force to ensure a safe and enjoyable experience for the riders.
Q: How can the normal force be measured in a real-world application?
A: The normal force can be measured using a variety of methods, including:
- Force sensors: These sensors can be attached to the surface of the slide or the roller coaster to measure the normal force acting on the child or the riders.
- Accelerometers: These sensors can be attached to the child or the riders to measure their acceleration and calculate the normal force.
- Computer simulations: These simulations can be used to model the motion of the child or the riders and calculate the normal force.
Conclusion
In this article, we have answered some frequently asked questions related to the forces acting on a 32 kg child as they slide down a straight slide inclined at 38° above the horizontal. We have discussed the significance of the normal force, its relationship to the weight of the child, and its impact on the kinetic friction. We have also provided examples of how the normal force is used in real-world applications and discussed methods for measuring the normal force.
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: Forces and Newton's laws
- MIT OpenCourseWare: Physics 8.01: Classical Mechanics
- Physics Classroom: Forces and Newton's Laws