You have been hired to design a spring-launched roller coaster that will carry two passengers per car. The car goes up a 10-m-high hill, then descends 20 m to the track's lowest point. You've determined that the spring can be compressed a maximum of 2.1 m and that a loaded car will have a maximum mass of 450 kg. For safety reasons, the spring constant should be 14% larger than the minimum needed for the car to just make it over the top. Part A What spring constant should you specify? Express your answer to two significant figures and include the appropriate units. View Available Hint(s) k= Submit 01 Part B μA Value Previous Answers XIncorrect: Try Again: 4 attempts remaining НА Value What is the maximum speed of a 350 kg car if the spring is compressed the full amount? Express your answer to two significant figures and include the appropriate units. View Available Hint(s) A N A m @ O ? Units ?

You have been hired to design a spring-launched roller coaster that will carry two passengers per car. The car goes up a 10-m-high hill, then descends 20 m to the track's lowest point. You've determined that the spring can be compressed a maximum of 2.1 m and that a loaded car will have a maximum mass of 450 kg. For safety reasons, the spring constant should be 14% larger than the minimum needed for the car to just make it over the top. Part A What spring constant should you specify? Express your answer to two significant figures and include the appropriate units. View Available Hint(s) k= Submit 01 Part B μA Value Previous Answers XIncorrect: Try Again: 4 attempts remaining НА Value What is the maximum speed of a 350 kg car if the spring is compressed the full amount? Express your answer to two significant figures and include the appropriate units. View Available Hint(s) A N A m @ O ? Units ?

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter8: Conservation Of Energy

Section: Chapter Questions

Problem 75PQ: At 220 m, the bungee jump at the Verzasca Dam in Locarno, Switzerland, is one of the highest jumps...

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Concept explainers

Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest. 

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You have been hired to design a spring-launched
roller coaster that will carry two passengers per car.
The car goes up a 10-m-high hill, then descends
20 m to the track's lowest point. You've determined
that the spring can be compressed a maximum of
2.1 m and that a loaded car will have a maximum
mass of 450 kg. For safety reasons, the spring
constant should be 14% larger than the minimum
needed for the car to just make it over the top.
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Part A
What spring constant should you specify?
Express your answer to two significant figures and include the appropriate units.
▸ View Available Hint(s)
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k= Value
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Part B
DELL
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Previous Answers
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What is the maximum speed of a 350 kg car if the spring is compressed the full amount?
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At 220 m, the bungee jump at the Verzasca Dam in Locarno, Switzerland, is one of the highest jumps on record. The length of the elastic cord, which can be modeled as having negligible mass and obeying Hookes law, has to be precisely tailored to each jumper because the margin of error at the bottom of the dam is less than 10.0 m. Kristin prepares for her jump by first hanging at rest from a 10.0-m length of the cord and is observed to stretch the rope to a total length of 12.5 m. a. What length of cord should Kristin use for her jump to be exactly 220 m? b. What is the maximum acceleration she will experience during her jump?
A block of mass 0.250 kg is placed on top of a light, vertical spring of force constant 5 000 N/m and pushed downward so that the spring is compressed by 0.100 m. After the block is released from rest, it travels upward and then leaves the spring. To what maximum height above the point of release does it rise?
Why is the following situation impossible? In a new casino, a supersized pinball machine is introduced. Casino advertising boasts that a professional basketball player can lie on top of the machine and his head and feet will not hang off the edge! The ball launcher in the machine sends metal balls up one side of the machine and then into play. The spring in the launcher (Fig. P6.60) has a force constant of 1.20 N/cm. The surface on which the ball moves is inclined = 10.0 with respect to the horizontal. The spring is initially compressed its maximum distance d = 5.00 cm. A ball of mass 100 g is projected into play by releasing the plunger. Casino visitors find the play of the giant machine quite exciting.
Tarzan grabs a vine hanging vertically from a tall tree when he is running at 9.0 m/s. (a) How high can he swing upward? (b) Does the length of the vine affect this height?
A block of mass 0.500 kg is pushed against a horizontal spring of negligible mass until the spring is compressed a distance x (Fig. P7.79). The force constant of the spring is 450 N/m. When it is released, the block travels along a frictionless, horizontal surface to point , the bottom of a vertical circular track of radius R = 1.00 m, and continues to move up the track. The blocks speed at the bottom of the track is = 12.0 m/s, and the block experiences an average friction force of 7.00 N while sliding up the track. (a) What is x? (b) If the block were to reach the top of the track, what would be its speed at that point? (c) Does the block actually reach the top of the track, or does it fall off before reaching the top?
Assume that the force of a bow on an arrow behaves like the spring force. In aiming the arrow, an archer pulls the bow back 50 cm and holds it in position with a force of 150 N. If the mass of the arrow is 50 g and the “spring” is massless, what is the speed of the arrow immediately after it leaves the bow?
Check Your Understanding When the length of the spring in Example 8.3 changes from an initial value of 22.0 cm to a final value, the elastic potential energy it contributes changes by 0.0800 J. Find the final length.
Consider a block of mass 0.200 kg attached to a spring of spring constant 100 N/m. The block is placed on a frictionless table, and the other end of the spring is attached to the wall so that the spring is level with the table. The block is then pushed in so that the spring is compressed by 10.0 cm. Find the speed of the block as it crosses (a) the point when the spring is not stretched, (b) 5.00 cm to the left of point in (a), and (c) 5.00 cm to the right of point in (a).
(a) What is the power output in watts and horsepower of a 70.0-kg sprinter who accelerates from rest to 10.0 m/s in 3.00 s? (b) Considering the amount of power generated, do you think a well-trained athlete could do this repetitively for long periods of time?
A block is placed on top of a vertical spring, and the spring compresses. Figure P8.24 depicts a moment in time when the spring is compressed by an amount h. a. To calculate the change in the gravitational and elastic potential energies, what must be included in the system? b. Find an expression for the change in the systems potential energy in terms of the parameters shown in Figure P8.24. c. If m = 0.865 kg and k = 125 N/m, find the change in the systems potential energy when the blocks displacement is h = 0.0650 m, relative to its initial position. FIGURE P8.24
An inclined plane of angle = 20.0 has a spring of force constant k = 500 N/m fastened securely at the bottom so that the spring is parallel to the surface as shown in Figure P6.61. A block of mass m = 2.50 kg is placed on the plane at a distance d = 0.300 m from the spring. From this position, the block is projected downward toward the spring with speed v = 0.750 m/s. By what distance is the spring compressed when the block momentarily comes to rest?
A 100 — kg man is skiing across level ground at a speed of 8.0 m/s when he comes to the small slope 1.8 m higher than ground level shown in the following figure. (a) If the skier coasts up the bill, what is his speed when he reaches the top plateau? Assume friction between the snow and skis is negligible. (b) What is his speed when he reaches the upper level if an 80 — N frictional force acts on the skis?