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Chapter 4: Q25P (page 166)
If a chain of 50identical short springs linked end to end has a stiffness of 270N/m, what is the stiffness of one short spring?
The stiffness of the one short spring is .
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Forty-five identical springs are placed side by side (in parallel) and connected to a large massive block. The stiffness of the 45-spring combination is 20,250N/m. What is the stiffness of one of the individual springs?
For a vertical spring-mass oscillator that is moving up and down, which of the following statements are true? (More than one statement may be true.) (a) At the lowest point in the oscillation, the momentum is zero. (b) At the lowest point in the oscillation, the rate of change of the momentum is zero. (c) At the lowest point in the oscillation, (d) At the lowest point in the oscillation, (e) At the lowest point in the oscillation, .
If in a certain material whose atoms are in a cubic array the interatomic distance is and the mass of one atom is , what be the density of this material?
In the approximation that the Earth is a sphere of uniform density, it can be shown that the gravitational force it exerts on a mass m inside the Earth at a distance r from the center is , where R is the radius of the Earth. (Note that at the surface, the force is indeed mg, and at the center it is zero). Suppose that there were a hole drilled along a diameter straight through the Earth, and the air were pumped out of the hole. If an object is released from one end of the hole, how long will it take to reach the other side of the Earth? Include a numerical result.
The period of a particular spring-mass oscillator is when the amplitude is . (a) what would be the period if we doubled the mass? (b) What would be the period if we replaced the original spring with a spring that is twice as stiff (keeping the original mass)? (c) What would be the period if we cut the original spring in half and use just one of the pieces (keeping the original mass)? (d) What would be the period if we increased the amplitude of the original system to , so that the total distance traveled in one period is twice as large? (e) What would be the period if we took the original system to a massive planet where ?
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