Concept explainers
The reason for the given situation in the problem is not possible.
Answer to Problem 54P
The speed of the child is too large, so static friction does not have the strength to keep the child in place on the incline. Hence the situation is impossible.
Explanation of Solution
Assume that, the friction points up the incline, the net force is directed left towards the centre of the circular path in which the child travels, and a
Free body diagram of the child is shown in Figure.
Write the expression for net force in the horizontal direction, from the free body diagram.
Here,
Write the expression for net force in the horizontal direction, from the free body diagram.
Here,
Multiply equation (I) by
Multiply equation (II) by
Add equation (III) and (IV), and solve for
Multiply equation (I) by
Multiply equation (II) by
Add equation (VI) and (VII), and solve for
Equation (V) and (VIII) are consistent only when
Use equation (V) and (VIII) in
Here,
Use
Here,
If
Conclusion:
Substitute,
Since, the speed of the child is too large, so static friction does not have the strength to keep the child in place of the incline. Hence the situation is impossible.
Want to see more full solutions like this?
Chapter 5 Solutions
Principles of Physics: A Calculus-Based Text
- A 70 kg person is sitting on a bathroom scale while riding on a Ferris Wheel. The Ferris Wheel has a radius of 9 m. The scale reads 900 N when the person is at the bottom of the motion. Find the person's speed.arrow_forwardYou are designing the section of a roller coaster ride shown in the figure. Previous sections of the ride give the train a speed of 15.5 m/s at the top of the incline, which is h = 36.7 m above the ground. As any good engineer would, you begin your design with safety in mind. Your local government's safety regulations state that the riders' centripetal acceleration should be no more than n = 1.77 g at the top of the hump and no more than N = 5.37 g at the bottom of the loop. For this initial phase of your design, you decide to ignore the effects of friction and air resistance. (Figure not to scale) What is the minimum radius Rhump you can use for the semi-circular hump? Rhump = What is the minimum radius Roop you can use for the vertical loop? Roop= R₁000 m marrow_forwardYou are designing the section of a roller coaster ride shown in the figure. Previous sections of the ride give the train a speed of 10.7 m/s at the top of the incline, which is h=37.5 m above the ground. As any good engineer would, you begin your design with safety in mind. Your local government's safety regulations state that the riders' centripetal acceleration should be no more than n=1.73 g at the top of the hump and no more than N=5.45 gat the bottom of the loop. For this initial phase of your design, you decide to ignore the effects of friction and air resistance. (Figure not to scale)What is the minimum radius Rhump you can use for the semi-circular hump?What is the minimum radius Rloop you can use for the vertical loop?arrow_forward
- You are designing the section of a roller coaster ride shown in the figure. Previous sections of the ride give the train a speed of 10.7 m/s at the top of the incline, which is h = 36.7 m above the ground. As any good engineer would, you begin your design with safety in mind. Your local government's safety regulations state that the riders' centripetal acceleration should be no more than n = 1.85 g at the top of the hump and no more than N = 5.53 g at the bottom of the loop. For this initial phase of your design, you decide to ignore the effects of friction and air resistance. (Figure not to scale) h Roop terms of use contact us help about us privacy policy careersarrow_forwardYou are designing the section of a roller coaster ride shown in the figure. Previous sections of the ride give the train a speed of 11.3 m/s at the top of the incline, which is h = 37.5 m above the ground. As any good engineer would, you begin your design with safety in mind. Your local government's safety regulations state that the riders' centripetal acceleration should be no more than N = 5.37 g at the top of the hump and no more than N = 5.37 g at the bottom of the loop. For this initial phase of your design, you decide to ignore the effects of friction and air resistance. (Figure not to scale)arrow_forwardA 40 kg person is sitting on a bathroom scale while riding on a Ferris Wheel. The person's speed is 6 m/s. The scale reads 300 N when the person is at the top of the motion. Find the radius of the Ferris Wheel. Use g = 10 m/s/s.arrow_forward
- In 1956, Frank Lloyd Wright proposed the construction of a mile-high building in Chicago. Suppose the building had been constructed. Ignoring Earth’s rotation, find the change in your weight if you were to ride an elevator from the street level, where you weigh 600 N, to the top of the building.arrow_forwardOn the International Space Station an object with mass m = 440 g is attached to a massless string of length L = 0.61 m. The string can handle a tension of T = 5.8 N before breaking. The object undergoes uniform circular motion, being spun around by the string horizontally.What is the maximum speed v the mass can have before the string breaks? Give your answer in units of m/s.arrow_forwardAn 80 kg person riding a Ferris wheel moves in a vertical circular trajectory of radius 6 m. As the person reaches the lowest point, a scale that the person is sitting on reads 920 N. There is nothing else in contact with the person. The person's speed is ____ m/s.arrow_forward
- Luther is designing a roller coaster for an amusement park. At one point, the roller coaster will enter a horizontal loop at a speed of 31.8 m/s. If Luther does not want the centripetal acceleration to exceed 29.0 m/s2, what is the minimum radius of the horizontal loop?arrow_forwardA spaceship travels in a circular orbit around a planet. It applies a sudden thrust and increases its speed by a factor f. If the goal is to change the orbit from a circle to a parabola, what should f be if the thrust points in the tangential direction? Is your answer any different if the thrust points in some other direction? What is the distance of closest approach if the thrust points in the radial direction?arrow_forwardA roller coaster consists of a car attached underneath a thin rail in the shape shown in the figure. The rail loops are circular and there is no friction between the carriage and the rail. The car is represented by the red block and the gray dotted line is a visualization of a part of the path that the car follows. (a) What is the minimum speed v_0 that the car must have at the bottom of the loop system for its centripetal acceleration to satisfy a_c = g at the top of the large loop? Write your answer in terms of R, g (b) Will that speed be the same for the condition a_c = g to hold at the top of the small loop? Show why?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning