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Concept explainers
Review. In 1887 in Bridgeport, Connecticut, C. J. Belknap built the water slide shown in Figure P8.77. A rider on a small sled, of total mass 80.0 kg, pushed off to start at the top of the slide (point Ⓐ) with a speed of 2.50 m/s. The chute was 9.76 m high at the top and 543 m long. Along its length, 72.5 small wheels made friction negligible. Upon leaving the chute horizon-tally at its bottom end (point ©), the rider skimmed across the water of Long Island Sound for as much as 50 m, “skipping along like a flat pebble,” before at last coming to rest and swimming ashore, pulling his sled after him. (a) Find the speed of the sled and rider at point © (b) Model the force of water friction as a constant retarding force acting on a particle. Find the magnitude of the
(a)
![Check Mark](/static/check-mark.png)
The speed of the sled and rider at point
Answer to Problem 8.77AP
The speed of the sled and rider at point
Explanation of Solution
Given info: The speed at point
The formula to calculate the kinetic energy at point
Here,
The formula to calculate the initial gravitational potential energy at point
Here,
The formula to calculate the gravitational potential energy at point
Here,
The formula to calculate the kinetic energy at point
Here,
The formula to calculate the energy at point
Here,
Substitute
The formula to calculate the energy at point
Here,
Substitute
Apply the law of conservation of energy at point
Here,
Substitute
Rearrange the above formula for
Substitute
Take the approximation.
Conclusion:
Therefore, the speed of the sled and rider at point
(b)
![Check Mark](/static/check-mark.png)
The magnitude of the friction force the water exerts on the sled.
Answer to Problem 8.77AP
The magnitude of the friction force the water exerts on the sled is
Explanation of Solution
Given info: The speed at point
The free body diagram is shown below.
Figure II
The formula to calculate the work done by the friction force at point
Here,
The formula to calculate the energy at point
Here,
Substitute
The formula to calculate the energy at point
Here,
Substitute
Apply the law of conservation of energy at point
Here,
Substitute
Rearrange the above formula for
Substitute
Thus, the value of work done by the frictional force is
From the above figure, the displacement is
Substitute
Thus, the frictional force acts on point
The formula to calculate the normal force is,
Here,
Substitute
Thus, the value of normal force is
The formula to calculate the magnitude of the force the water exerts on the sled is,
Here,
Substitute
Conclusion:
Therefore, the magnitude of the friction force the water exerts on the sled is
(c)
![Check Mark](/static/check-mark.png)
The magnitude of the force the chute exerts on the sled at point
Answer to Problem 8.77AP
The magnitude of the force the chute exerts on the sled at point
Explanation of Solution
Given info: The speed at point
From the above figure,
The formula to calculate the force exerted by the weight of the chute is,
Here,
The formula to calculate the force acting at point
Here,
The acceleration is 0 at point
The formula to calculate the force at the point
Here,
Substitute
Substitute
Conclusion:
Therefore, the magnitude of the force the chute exerts on the sled at point
(c)
![Check Mark](/static/check-mark.png)
The magnitude of the force the chute exerts on the sled at point
Answer to Problem 8.77AP
The magnitude of the force the chute exerts on the sled at point
Explanation of Solution
Given info: The speed at point
From the above figure,
The formula to calculate the centripetal force exerted at point
Here,
The formula to calculate the weight of chute at point
Here,
The formula to calculate the force at the point
Here,
Substitute
Substitute
Conclusion:
Therefore, the magnitude of the force the chute exerts on the sled at point
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Chapter 8 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
- A string under a tension of 59.0 N is used to whirl a rock in a hortzontal circle of radius 2.45 m at a speed of 20.1 m/s on a frictionless surface as shown in the figure below. As the string is pulled in, the speed of the rock increases. When the string on the table is 1.00 m long and the speed of the rock is 50.5 m/s, the string breaks. What is the breaking strength, in newtons, of the string? Need Help?arrow_forwardTab sLk A printing press has a roller 17 inches in diameter. A point on the roller's surface moves at a speed of 85 feet per second. What is the roller's angular speed? The roller's angular speed is radians per second. (Round your answer to the nearest hundredth.) Esc I 1 Q A 91°F Sunny 261 N @ 2 W S Alt X 3E D C STR 4 F C FS do 5 % T V OL G 6 B F7 H W & 7 P U N J 8 +00 8 F9 1 k M F10 ( 9 K O V LO F11 O L P All + 99+ F12 . V Parrow_forwardA 100 kg cart goes around the inside of a vertical loop of a roller coaster. The radius of the loop is 3 m and the cart moves at a speed of 6 m/s at the top. What is the force exerted by the track on the cart at the top of the loop?arrow_forward
- The answer is supposed to be v=2.56m/s but I'm not sure how to write out the problem.arrow_forwardThe puck in the figure below has a mass of 0.160 kg. Its original distance from the center of rotation is 40.0 cm, and it moves with a speed of 60.0 cm/s. The string is pulled downward 15.0 cm through the hole in the frictionless table. Determine the work done on the puck. (Hint: Consider the change of kinetic energy of the puck.)arrow_forwardNow Chandra and Darcel decide to try a problem. Suppose that the height of the incline is h = 16.0 m. Find the speed at the bottom for each of the following objects. solid sphere m/s spherical shell m/s hoop cylinder m/s m/s In a race, which object would win?arrow_forward
- A certain string just breaks when it is under 23 N of tension. A boy uses this string to rotate a 660 g stone in a horizontal circle of radius 2.0 m. The boy continuously increases the speed of the stone. At approximately what speed will the string break? (Hint: you may assume that the string is about to break and it hasn't broken yet). O 8.35 m/s O 0.264 m/s O 69.7 m/s O0.0143 m/sarrow_forwardThe puck in the figure below has a mass of 0.120 kg. The distance of the puck from the center of rotation is originally 39.0 cm, and the puck is sliding with a speed of 80.0 cm/s. The string is pulled downward 18.0 cm through the hole in the frictionless table. Determine the work done on the puck. (Suggestion: Consider the change of kinetic energy.)arrow_forwardA thin 105 g disk with a diameter of 7.00 cm rotates about an axis through its center with 0.615 J of kinetic energy. What is the speed (in m/s) of a point on the rim?arrow_forward
- To test the speed of a bullet, you create a pendulum by attaching a 5.80 kg wooden block to the bottom of a 1.60 m long, 0.800 kg rod. The top of the rod is attached to a frictionless axle and is free to rotate about that point. You fire a 10 g bullet into the block, where it sticks, and the pendulum swings out to an angle of 39.0°. What was the speed of the bullet?arrow_forwardTwo hangers are attached by a string to a vertically mounted pulley system as shown. One disk is bigger than the other, and the disks are attached to each other such that they rotate together. The axle has negligible friction. The mass of the large disk is 1200 grams and the radius is 11 cm. The mass of the small disk is 400 grams and the radius is 4 cm. The high hanger has a mass of 200 grams and starts 80 cm above the ground. The lower mass starts on the ground and has a mass of 100 grams. The hangers are released from rest. What is the velocity of the 200 gram hanger when it hits the floor?arrow_forwardMalar is playing with a toy car track set and has made a vetical loop she wants to send a 150-gram car around. She has a hill for the car to roll down and if she releases it from a height of 24 cm above the top of the loop, which has a radius of 20 cm, it goes around the loop and exits with a speed of 3.12 m/s. How much energy was lost due to friction (between the car and the sides of the track, and the car's axels) during the entire trip? Hint: You don't have any details about the time while the car is going down the hill or through the loop, so you don't know how fast it is going at the top of the loop.arrow_forward
- Physics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
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