Chapter 2: Q 875865 2 4 (page 81)
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Short Answer
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Chapter 2: Q 875865 2 4 (page 81)
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Two metal rods are made of different elements. The interatomic spring stiffness of element A is three times larger than the interatomic spring stiffness for element B. The mass of an atom of element A is three times greater than the mass of an atom of element B. The atomic diameters are approximately the same for A and B. What is the ratio of the speed of sound in rod A to the speed of sound in rod B?
(1)You push on a spring whose stiffness is 11 N/m, compressing it until it is 2.5 cm shorter than its relaxed length. What is the magnitude of the force the spring now exerts on your hand?
(2) A different spring is 0.17 m long when it is relaxed.
(a) When a force of magnitude 250 N is applied, the spring becomes 0.24 m long. What is the stiffness of this spring?
(b) This spring is compressed so that length is 0.15 m. What magnitude of the force is required to do this?
A cart rolls with low friction on a track. A fan is mounted on the cart, and when the fan is turned on, there is a constant force acting on the cart. Three different experiments are performed:
(a) Fan off: The cart is originally at rest. You give it a brief push, and it coasts a long distance along the track in the +x direction, slowly coming to a stop.
(b) Fan forward: The fan is turned on, and you hold the cart stationary. You then take your hand away, and the cart moves forward, in the +x direction. After traveling a long distance along the track, you quickly stop and hold the cart.
(c) Fan backward: The fan is turned on facing the 鈥渨rong鈥 way, and you hold the cart stationary. You give it a brief push, and the cart moves forward, in the +x direction, slowing down and then turning around, returning to the starting position, where you quickly stop and hold the cart. Figure 2.57 displays four graphs of px (numbered 1鈥4), the x component of momentum, vs. time. The graphs start when the cart is at rest, and end when the cart is again at rest. Match the experiment with the correct graph.
Question: 400g of boiling water (temperature 1000 , specific heat 4.2J/K/gare poured into an aluminium pan whose mass is 600g and initial temperature (the specific heat of aluminium is . After a short time, what is the temperature of the water? Explain. What simplifying assumptions did you have to make?
(a)On a piece of graph paper, draw the vector . Put the tail of the vector at the origin.
(b)Calculate the magnitude of.
(c)Calculate, the unit vector pointing in the direction of.
(d)On the graph, draw. Put the tail of the vector at so you can compareand.
(e)Calculate the product of the magnitudetimes the unit vector,.
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