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1. A mass m= 0.50 kg is pushed against the end of a horizontal spring, compressing it by an amount d=40 cm from its relaxed position. The spring has spring constant k=15 N/m. The mass is released from rest and slides along a flat surface. The coefficient of kinetic friction between the mass and the surface is 0.25.
a) What is the speed of the mass when it reaches the equilibrium position of the spring?
b) Where does the mass first come to a stop?
2.A soft-drink can contains about 0.35 kg of liquid at 5°C. Drinking this liquid can actually consume some of the fat in the body, since energy is needed to warm the liquid to body temperature (37°C). How many food Calories should the drink have so that it is in perfect balance with the heat needed to warm the liquid (essentially water)?
3.A resting adult of average size converts chemical energy in food into internal energy at the rate of 120 W, called her basal metabolic rate. To stay at a constant temperature, energy must be transferred out of the body at the same rate. Several processes exhaust energy from your body. Usually the most important is thermal conduction into the air in contact with your exposed skin. If you are not wearing a hat, a convection current of warm air rises vertically from your head like a plume from a smokestack. Your body also loses energy by electromagnetic radiation, by your exhaling warm air, and by the evaporation of perspiration. Now consider still another pathway for energy loss: moisture in exhaled breath. Suppose you breathe out 22.0 breaths per minute, each with a volume of 0.600 L. Suppose also that you inhale dry air and exhale air at 37°C containing water vapor with a vapour pressure of 3.20 kPa. The vapor comes from the evaporation of liquid water in your body. Model the water vapour as an ideal gas. Assume its latent heat of evaporation at 37°C is the same as its heat of vaporization at 100°C. Calculate the rate at which you lose energy by exhaling humid air.
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4.High-altitude mountain climbers do not eat snow, but always melt it first with a stove. To see why, calculate the energy absorbed from your body if you:
(a) eat 1.0 kg of –15°C snow which your body warms to body temperature of 37°C;
(b) melt 1.0 kg of –15°C snow using a stove and drink the resulting 1.0 kg of water at 2°C, which your body has to warm to 37°C.
5.An athlete whose mass is 70.0 kg drinks 16 oz (453.6 g) of refrigerated water. The water is at a temperature of 35.0°F.
(a) Ignoring the temperature change of the body that results from the water intake (so that the body is regarded as a reservoir always at 98.6°F), find the entropy increase of the entire system.
(b) What If? Assume that the entire body is cooled by the drink and that the average specific heat of a person is equal to the specific heat of liquid water. Ignoring any other energy transfers by heat and any metabolic energy release, find the athlete’s temperature after she drinks the cold water, given an initial body temperature of 98.6°F. Under these assumptions, what is the entropy increase of the entire system? Compare this result with the one you obtained in part (a).
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