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Chapter 4: Q21P (page 166)
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?
The density of the material is .
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Young鈥檚 modulus for aluminum is . The density of aluminum is , and the mass of one mole is 27g. If we model the interactions of neighbouring aluminum atoms as though they were connected by spring, determine the approximate spring constant of such a spring. Repeat this analysis for lead is: Young鈥檚 modulus for Lead and the density of lead is , and the mass of one mole is 207g. Make a note of these results, which we will use for various purposes later on. Note that aluminum is a rather stiff material, whereas lead is quite soft.
A 3 kgblock measures5 cm by 10 cm by 20cm. When it slides on a 10cm by 20 cmface, it moves with constant speed when pulled horizontally by a force whose magnitude 3N is. How big a horizontal force must be applied to pull it with constant speed of it slides on a 5 cm by 20 cm face?
You hang a heavy ball with a mass of 14 kg from a gold wire 2.5 m long that is 2 mm in diameter. You measure the stretch of the wire, and find that the wire stretched 0.00139 m. (a) Calculate Young鈥檚 modulus for the wire. (b) The atomic mass of gold is 197 g/mole, and the density of gold is. Calculate the interatomic spring stiffness for gold.
Two blocks of mass m1 and m3 , connected by a rod of mass m2 , are sitting on a low friction surface, and you push to the left on the right block (mass m1 ) with a constant force of magnitude F(Figure 4.57).
(a) What is the acceleration of the blocks?
(b) What is the vector force exerted by the rod on the block of mass m3 ? ( is approximately equal to the compression force in the rod near its left end.)What is the vector forceexerted by the rod on the block of massm1? is approximately equal to the compression force in the rod near its right end.)
(c) Suppose that instead of pushing on the right block (mass m1 ), you pull to the left on the left block (mass m3) with a constant force of magnitude F . Draw a diagram illustrating this situation. Now what is the vector force exerted by the rod on the block of mass m3?
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.
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