Log Ride (object sliding down a circularly curved slope). In an amusement park ride, a boat moves slowly in a narrow channel of water. It then passes over a slope into a pool below as shown. The water in the channel ensures that there is very little friction. A B P Дх On this particular ride, the slope (the black arc through points A and B) is a circular curve of radius R, centered on point P. The dotted line shows the boat's trajectory. At some point B along the slope, the boat (and the water falling with it) will separate from the track and fall freely as shown. Note that the pond is level with point P. Considering the boat as a particle, assume it starts from rest at point A and slides down the slope without friction. a) Determine the angle dsep at which the boat will separate from the track. b) Determine the horizontal distance Ax (from point P) at which the boat strikes the pond surface. c) Determine the impact speed v, and impact angle 0. Hints: Derive a formula giving the maximum speed vmax at which the boat can stay on the track, in terms of the angle p. (Circular kinematics.) Derive a formula for the speed v of the boat as it traverses the circular slope, in terms of the angle p. (Conservation of energy.)

Log Ride (object sliding down a circularly curved slope). In an amusement park ride, a boat moves slowly in a narrow channel of water. It then passes over a slope into a pool below as shown. The water in the channel ensures that there is very little friction. A B P Дх On this particular ride, the slope (the black arc through points A and B) is a circular curve of radius R, centered on point P. The dotted line shows the boat's trajectory. At some point B along the slope, the boat (and the water falling with it) will separate from the track and fall freely as shown. Note that the pond is level with point P. Considering the boat as a particle, assume it starts from rest at point A and slides down the slope without friction. a) Determine the angle dsep at which the boat will separate from the track. b) Determine the horizontal distance Ax (from point P) at which the boat strikes the pond surface. c) Determine the impact speed v, and impact angle 0. Hints: Derive a formula giving the maximum speed vmax at which the boat can stay on the track, in terms of the angle p. (Circular kinematics.) Derive a formula for the speed v of the boat as it traverses the circular slope, in terms of the angle p. (Conservation of energy.)

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Gravitational force

In nature, every object is attracted by every other object. This phenomenon is called gravity. The force associated with gravity is called gravitational force. The gravitational force is the weakest force that exists in nature. The gravitational force is always attractive.

Acceleration Due to Gravity

In fundamental physics, gravity or gravitational force is the universal attractive force acting between all the matters that exist or exhibit. It is the weakest known force. Therefore no internal changes in an object occurs due to this force. On the other hand, it has control over the trajectories of bodies in the solar system and in the universe due to its vast scope and universal action. The free fall of objects on Earth and the motions of celestial bodies, according to Newton, are both determined by the same force. It was Newton who put forward that the moon is held by a strong attractive force exerted by the Earth which makes it revolve in a straight line. He was sure that this force is similar to the downward force which Earth exerts on all the objects on it.

Question

Log Ride (object sliding down a circularly curved slope).
In an amusement park ride, a boat moves slowly in a narrow channel of water. It then passes over a
slope into a pool below as shown. The water in the channel ensures that there is very little friction.
A
B.
R
C
Ax
On this particular ride, the slope (the black arc through points A and B) is a circular curve of radius R,
centered on point P. The dotted line shows the boat's trajectory. At some point B along the slope, the
boat (and the water falling with it) will separate from the track and fall freely as shown. Note that the
pond is level with point P.
Considering the boat as a particle, assume it starts from rest at point A and slides down the slope
without friction.
a) Determine the angle psep at which the boat will separate from the track.
b) Determine the horizontal distance Ax (from point P) at which the boat strikes the pond surface.
c) Determine the impact speed v, and impact angle 0.
Hints:
Derive a formula giving the maximum speed vmax at which the boat can stay on the track, in
terms of the angle p. (Circular kinematics.)
Derive a formula for the speed v of the boat as it traverses the circular slope, in terms of the
angle ø. (Conservation of energy.)

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