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)
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)
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)
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)
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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