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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

A system consists of a vertical spring with force constant k = 1 250 N/m, length L = 1.50 m, and object of mass m = 5.00 kg attached to the end (Fig. P13.76). The object is placed at the level of the point of attachment with the spring unstretched, at position yi = L, and then it is released so that it swings like a pendulum. (a) Write Newton’s second law symbolically for the system as the object passes through its lowest point. (Note that at the lowest point, r = Lyf.) (b) Write the conservation of energy equation symbolically, equating the total mechanical energies at the initial point and lowest point. (c) Find the coordinate position of the lowest point (d) Will this pendulum’s period be greater or less than the period of a simple pendulum with the same mass m and length L? Explain.

images

Figure P13.76

a)

To determine
The Newton’s second law symbolically for the system as the object passes through its lowest point.

Explanation

Given info: The force constant of the spring is 1250Nm-1 . The length of the spring is 1.50m . The mass of the object is 5.00kg .

The system is shown in the figure.

When the spring passes through the vertical position, it is moving through a circular arc of radius Lyf .

The stretch in the spring yf must be negative for the spring to be stretched at its lowest point and exerting an upward tension force.

The required centripetal force will be supplied by gravity as well as the spring

b)

To determine
The conservation of energy equation symbolically, equating the total mechanical energy at the initial point to the lowest point.

c)

To determine
The coordinate position of the lowest point.

d)

To determine
Whether the period of the pendulum is greater or less than the periof of a simple pendulum with the same mass and length.

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