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Concept explainers
(a)
The expression for
(a)
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Answer to Problem 8.82CP
The expression for
Explanation of Solution
Given info: The length of the string is
The diagram is shown below.
Figure I
The formula to calculate the horizontal displacement is,
Here,
The formula to calculate the work done by the wind force is,
Here,
Substitute
The formula to calculate the gravitational potential energy of the ball is,
Here,
From the law of conservation of energy,
Here,
Substitute
Square the above expression on both sides to find
Substitute
Conclusion:
Therefore, the expression for
(b)
The value of
(b)
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Answer to Problem 8.82CP
The value of
Explanation of Solution
Given info: The length of the string is
From part (a), the expression for
Substitute
Conclusion:
Therefore, the value of
(c)
The value of
(c)
![Check Mark](/static/check-mark.png)
Answer to Problem 8.82CP
The value of
Explanation of Solution
Given info: The length of the string is
From part (a), the expression for
Substitute
Conclusion:
Therefore, the value of
(d)
The value of
(d)
![Check Mark](/static/check-mark.png)
Answer to Problem 8.82CP
The value of
Explanation of Solution
Given info: The length of the string is
From part (a), the expression for
In the above expression, the height of the ball is directly proportional to the square of the magnitude of force as the force increases then the height of the ball also increases but in the given case, the value of force is approach to zero then the height of the ball also approach to zero.
Conclusion:
Therefore, the value of
(e)
The value of
(e)
![Check Mark](/static/check-mark.png)
Answer to Problem 8.82CP
The value of
Explanation of Solution
Given info: The length of the string is
From part (a), the expression for
Substitute
Conclusion:
Therefore, the value of
(f)
The equilibrium height of the ball as a function of
(f)
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Answer to Problem 8.82CP
The equilibrium height of the ball as a function of
Explanation of Solution
Given info: The length of the string is
The given diagram is shown below.
Figure II
The diagram is shown below.
Figure III
From the figure the equilibrium height of the ball is,
Here,
From the figure II,
Substitute
Substitute
Conclusion:
Therefore, the equilibrium height of the ball as a function of
(g)
The value of equilibrium height of the ball
(g)
![Check Mark](/static/check-mark.png)
Answer to Problem 8.82CP
The value of equilibrium height of the ball
Explanation of Solution
Given info: The length of the string is
From part (a), the expression for equivalent height of the ball in terms of
Substitute
Conclusion:
Therefore, the value of equilibrium height of the ball
(h)
The value of equilibrium height of the ball
(h)
![Check Mark](/static/check-mark.png)
Answer to Problem 8.82CP
The value of equilibrium height of the ball
Explanation of Solution
Given info: The length of the string is
From part (a), the expression for equivalent height of the ball in terms of
Substitute
Conclusion:
Therefore, the value of equilibrium height of the ball
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Chapter 8 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
- 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 P8.24arrow_forwardA Eric is twirling a ball of mass m = 0.150 kg attached to a lightweight string in a vertical circle. If the total energy of the system is conserved, by what factor does the tension on the string increase at the bottom compared with the top of the circle?arrow_forwardA small block of mass m = 200 g is released from rest at point along the horizontal diameter on the inside of a frictionless, hemispherical bowl of radius R = 30.0 cm (Fig. P7.45). Calculate (a) the gravitational potential energy of the block-Earth system when the block is at point relative to point . (b) the kinetic energy of the block at point , (c) its speed at point , and (d) its kinetic energy and the potential energy when the block is at point . Figure P7.45 Problems 45 and 46.arrow_forward
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- A bead with a hole through it slides on a wire track. The wire is threaded through the hole in the bead, and the bead slides without friction around a loop-the-loop (see figure below). The bead is released from rest at a height h = 3.70R.arrow_forwardA slingshot, consisting of a leather pouch attached to two rubber bands which are tied to the prongs of a wooden Y- shaped frame, is used to shoot a pebble horizontally. When the slingshot is stretched by a distance d, it gives the pebble speed v. What speed does it give the same pebble when it is stretched to distance 3d?arrow_forwardYou have a new internship, where you are helping to design a new freight yard for the train station in your city. There will be a number of dead-end sidings where single cars can be stored until they are needed. To keep the cars from running off the tracks at the end of the siding, you have designed a combination of two coiled springs as illustrated in Figure P7.41. When a car moves to the right in the figure and strikes the springs, they exert a force to the left on the car to slow it down. Both springs are described by Hooke's law and have spring constants k1= 1600 N/m and k2 = 3400 N/m. After the first spring compresses by a distance of d = 30.0 cm, the second spring acts with the first to increase the force to the left on the car in Figure P7.41.When the spring with spring constant k2 compresses by 50.0 cm, the coils of both springs are pressed together, so that the springs can no longer compress. A typical car on the siding has a mass of 6000 kg. When you present your design to…arrow_forward
- A 5.00 - kg block is set into motion up an inclined plane with an initial speed of υi = 8.00 m/s (Fig. P8.23). The block comes to rest after traveling d= 3.00 m along the plane, which is inclined at an angle of θ=30.0° to the horizontal.For this motion, determine (a) the change in the block's Kinetic energy, (b) the change in the potential energy if the block-Earth system, and (c) the friction force exerted on the block (assumed to be constant). (d) What is the coefficient of kinetic friction?arrow_forwardA mother pushes her child on a swing so that his speed is 9.1 m/s at the lowest point of his path. The swing is attached to a point 2.05 m above the child’s center of mass when the swing is motionless. a. What is the magnitude of the force that the child exerts on the seat at the lowest point if his mass is 16 kg in N?arrow_forwardA particle of mass 0.500 kg is shot from Pas shown in Figure P8.10. The particle has an initial velocity v, with a horizontal component of 30.0 m/s. The particle rises to a maximum height of 20.0 m above P. Using the law of conservation of energy, determine (a) the vertical com- ponent of v;, (b) the work done by the gravitational force on the particle during its motion from Pto B, and (c) the horizontal and the vertical components of the velocity vector when the particle reaches B. 20.0 m 60.0 marrow_forward
- Principles 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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