Advanced Engineering Mathematics
6th Edition
ISBN: 9781284105902
Author: Dennis G. Zill
Publisher: Jones & Bartlett Learning
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Chapter 3.8, Problem 3E
To determine
The equation of motion.
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Practical Question:
An object is moving horizontally with the speed of 50 m/s. When the
object at the height of 2 km, an object free fall from the aircraft.
Determine the type of the motion and explain
A. Free fall motion
B. Floating motion
C. Horizontal motion
D. Projectile motion
A Ferris wheel at a theme park rotates in an anticlockwise direction at a constant rate. People enter the cars of the Ferris wheel from a platform which is above ground level. The Ferris wheel does not stop at any time. The Ferris wheel has 16 cars, spaced evenly around the circular structure. A spider attached itself to the point P on the side of car C when the point P was at its lowest point at time 1.00 pm. The height, h metres, of the point P above ground level, at time t hours after 1.00 pm is given by h(t)=62+60 sin(((5t-1)pi)/2) a) Write down the maximum height, in metres, of the point P above ground level. b)Write down the minimum height, in metres, of the point P above ground level. c) At what time, after 1.00 pm, does point P first return to its lowest point? d)Find the time, after 1.00 pm, when P first reaches a height of 92 metres above ground level. e)Find the number of minutes during one rotation that P is at least 92 metres above ground level.
A mass attached to a spring oscillates upward and downward. The length L of the spring after t seconds is given by the function L = 20 – 2.5 cos(4nt), where L is measured in centimeters (see the figure).
Equilibrium
position
(a) Sketch the graph of this function for 0sts 5.
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Chapter 3 Solutions
Advanced Engineering Mathematics
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- Force Tyler and his cousin Kelly have attached a rope to the branch of a tree and tied a board to the other end to form a swing. Tyler sits on the board while his cousin pushes him through an angle of 25.5 and holds him there. If Tyler weighs 95.5 pounds, find the magnitude of the force Kelly must push with horizontally to keep Tyler in static equilibrium. See Figure 13.arrow_forwardForce Tyler and his cousin Kelly have attached a rope to the branch of a tree and tied a board to the other end to form a swing. Tyler sits on the board while his cousin pushes him through an angle of 25.5 and holds him there. If Tyler weighs 95.5 pounds, find the magnitude of the force Kelly must push with horizontally to keep Tyler in static equilibrium. See Figure 1. Figure 1arrow_forwardEXAMPLE 1 A dam has the shape of a trapezoid shown in the top figure. The height is 30 m and the width is 60 m at the top and 30 m at the bottom. Find the force on the dam due to hydrostatic pressure if the water level is 2 m from the top of the dam. SOLUTION We choose a vertical x-axis with origin at the surface of the water and directed downward as in the middle figure. The depth of the water is 28 m, so we divide the interval [0, 28] into subintervals of equal length with endpoints x; and we choose x E [X; - 1, x]. The ith horizontal strip of the dam is approximated by a rectangle with height Ax and width wi, where, from similar triangles in the bottom figure, a 15 Xị or a = 24 - Xj 30 2 2 and so - 2(1 ]-) - 54 wj = 2(15 + a) = If Aj is the area of the ith strip, then Aj z WiAx = If Ax is small, then the pressure P; on the ith strip is almost constant and we can use this equation to write Pi x 1000gx;" The hydrostatic force F; acting on the ith strip is the product of the pressure…arrow_forward
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- A certain mass stretches one spring rigid support Ū m Need Help? lb 3 The first mass is set aside, and a mass weighing 12 pounds is attached to the double-spring arrangement, and the system is set in motion. If the period of motion is z/10 second, determine how much the first mass weighs. (Use g = 32 ft/s2 for the acceleration due to gravity.) Read It foot and another spring. 1/13 foot. The two springs are then attached in parallel to a common rigid support in the manner shown in the figure below. Watch Itarrow_forwardSpring work a. It takes 50 J of work to stretch a spring 0.2 m from its equilibrium position. How much work is needed to stretch it an additional 0.5 m? b. It takes 50 N of force to stretch a spring 0.2 m from its equilibrium position. How much work is needed to stretch it an additional 0.5 m?arrow_forwardA mass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. Initially, the mass is released from rest from a point 2 inches below the equilibrium position. Find the equation of motion. (Use g = 32 ft/s² for the acceleration due to gravity.) x(t) = ft Need Help? Read It Watch Itarrow_forward
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