Q1) A capstan is a rotating drum or cylinder over which a rope or cord slides to
ID: 2257784 • Letter: Q
Question
Q1) A capstan is a rotating drum or cylinder over which a rope or cord slides to provide a great amplification of the rope's tension while keeping both ends free (Figure 1) . Since the added tension in the rope is due to friction, the capstan generates thermal energy.
figure 1 link : http://session.masteringphysics.com/problemAsset/1006856/16/36898.jpg
Part A
If the difference in tension (T0?T?) between the two ends of the rope is 520N and the capstan has a diameter of 10.0cm and turns once in 0.90s, find the rate Pthermal at which thermal energy is being generated. Give a numerical answer, in watts, rounded to the nearest 10 W
Part B
If the capstan is made of iron (with a specific heat capacity Ciron=470J/(kg??C) and has a mass of 6.00kg, at what rate d?/dt does its temperature rise? Assume that the temperature in the capstan is uniform and that all the thermal energy generated flows into it.
Note that ? is a temperature.
Give a numerical answer, in degrees Celsius per second, rounded to two significant figures.
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Q2) Just about everyone at one time or another has been burned by hot water or steam. This problem compares the heat input to your skin from steam as opposed to hot water at the same temperature.
Assume that water and steam, initially at 100?C, are cooled down to skin temperature, 34?C, when they come in contact with your skin. Assume that the steam condenses extremely fast. We will further assume a constant specific heat capacity c=4190J/(kg?K)for both liquid water and steam.
How much heat H1is transferred to the skin by 25.0 g of steam onto the skin? The latent heat of vaporization for steam is L=2.256
A capstan is a rotating drum or cylinder over which a rope or cord slides to provide a great amplification of the rope's tension while keeping both ends free (Figure 1). Since the added tension in the rope is due to friction, the capstan generates thermal energy. if the difference in tension (T0?T?) between the two ends of the rope is 520N and the capstan has a diameter of 10.0cm and turns once in 0.90s, find the rate Pthermal at which thermal energy is being generated. Give a numerical answer, in watts, rounded to the nearest 10 W if the capstan is made of iron (with a specific heat capacity Ciron=470J/(kg??C) and has a mass of 6.00kg, at what rate d?/dt does its temperature rise? Assume that the temperature in the capstan is uniform and that all the thermal energy generated flows into it. Note that ? is a temperature. Give a numerical answer, in degrees Celsius per second, rounded to two significant figures. Just about everyone at one time or another has been burned by hot water or steam. This problem compares the heat input to your skin from steam as opposed to hot water at the same temperature. Assume that water and steam, initially at 100?C, are cooled down to skin temperature, 34?C, when they come in contact with your skin. Assume that the steam condenses extremely fast. We will further assume a constant specific heat capacity c =4190J/(kg?K)for both liquid water and steam. How much heat H 1 is transferred to the skin by 25.0 g of steam onto the skin? The latent heat of vaporization for steam is L =2.256 times 106J/kg. Express the heat transferred, in joules, to three significant figures. A picture window has dimensions of 1.40 m times 2.50 mand is made of glass 5.90mm thick. On a winter day, the outside temperature is -20.0?C , while the inside temperature is a comfortable 19.5?C. At what rate is heat being lost through the window by conduction? Express your answer using three significant figures. At what rate would heat be lost through the window if you covered it with a 0.750 mm-thick layer of paper (thermal conductivity 0.0500 W/m?K)? Express your answer using three significant figures.Explanation / Answer
1.
A) Power P is a product of force F applied to a speed v. We have
P=Fv
F=T=540N
v= piD/t
P=F pi D/t= 540 pi 0.1/0.9
P=190 W
B) Q=mC(T2-T1)
Heat rise per second
Q/t=P=mC(T2-T1)/t
(T2-T1)/t= P/(mC)=190/(6.00 x 470)=
(T2-T1)/t=0.0674 degC/sec
2.
The creation of steam involves a huge amount of energy know as the "Latent Heat of Vaporization" that is the heat absorbed when a substance changes phase from liquid to gas. To heat water takes about 1 BTU/lb per Deg F so heating water from 0F to 212F takes about 212 BTU's, but once it reaches 212 F it take about 1,000 BTU more to vaporize it, no change in temperature, still at 212 F. When steam burns your skin it must remove that same 1,000 BTU to condense the steam back to a liquid before the temperature falls.
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