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SIN练习题1

SIN练习题1答案及解析

（答案：C）解析：

This is a straightforward s = (1/2)a t² problem, to ease students into the exam. It's easy to calculate the time to get to Lovelon, and each light year represents 1 light-year = 365 days/year x 24 hours/day x 3600 seconds/hour x 3 x 10⁸ m/s = 9.46 x 10¹⁵ m.If Romeo travels all the way there at 15 m/s², then 10 light-years will take him a time given by 10 x 9.46 x 10¹⁵ = 1/2 x 15 (time)² giving 1.123 x 10⁸ seconds, or 3.56 years, and he will be moving at 16.85 x 10⁸ m/s, which in Startrek language is Warp 5.6! This won't do him much good of course, because he will pass Lovelon at this speed. Romeo has to travel half-way to Lovelon, 5 light-years, then reverse his rockets to decelerate for another 5 light years at 15 m/s², so that he arrives at low speed for docking. This splits the journey exactly in half, due to the obvious symmetry of the motion. At the half-way point he'll be moving at 11.9 x 10⁸ m/s, which is near enough Warp 4!

SIN练习题第2题

2.An overweight acrobat, "weighing" in at 115 kg, wants to perform a single hand stand. He tries to cheat by resting one foot against a smooth frictionless vertical wall. The horizontal force there is 130 N. What is the magnitude of the force exerted by the floor on his hand?

(A) 1134 (B) 1257 (C) 997 (D) 1119 (E) 1127

SIN练习题2答案及解析

（答案：A）解析：

The acrobat has a force acting on his hand that we resolve into two perpendicular components: the vertical one is the reaction to the weight (115 x 9.8 N = 1127 N) and the horizontal one balances the 130 N force from the wall. These two forces give a resultant force F of
F = √(11272 + 1302) = 1134 N (A).

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SIN练习题第3题

3.For each breath that you take, how many of the air molecules would also have been breathed by the patron saint of Physics, Sir Isaac Newton during his lifetime (1642-1727)?
The atmosphere is about 8 km high, and the molecules in the air each occupy a space representing a little cubic box about 33.3 x 10 ^-9 m along a side. The earth's radius is 6.37 x 10⁶ m.
Make reasonable assumptions for any data that you need!

(A) 6 (B) 6 X 10³ (C) 6 X 106 (D) 6 X 109 (E) 6 X 1012

SIN练习题3答案及解析

（答案：D）解析：If each breath of Sir Isaac's (and ours) is about 1 litre = 10^-3 m³, and they are 3 seconds apart, then in 1727-1642=85 years, he will have had 85 x 365 x 24 x 3600 /3 = 8.93 x 10⁸ breaths, for a total volume of 8.93 x 10⁵ m³. We will assume that the air mixes well enough that we do not have to worry about air being breathed twice.
The total volume of the atmosphere is 4 R_E 2 h, where R_E is the Earth's radius, and h is the height of the atmosphere, giving 4.08 x 10¹⁸ m³. The fraction of air molecules ever breathed by the patron saint of Physics is thus 8.93 x 10⁵ / 4.08 x 10¹⁸ = 2.19 x 10^-13.
The number of molecules in each breath of ours is the density 1/(3.3 x 10^-9)³ = 2.78 x 10²⁵ m^-3, multiplied by the volume of each breath, 10^-3 m³, or 2.78 x 10²² molecules. Multiplying by the fraction breathed by Newton, each breath of ours has about 6.08 x 10⁹ molecules also breathed by him (D). Since we have about 9 x 10⁸ breaths, each breath of ours has about 7 molecules also breathed by Isaac Newton.

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SIN练习题第4题

4.The ice storm this winter in the province of Quebec strained many wires to the breaking point. In a particular situation, the transmission pylons are separated by 500 m of wire. The top grounding wire is 15° from the horizontal at the pylons, as in the diagram, and has a diameter of 1.5 cm. The steel wire has a density of 7860 kg/m³. When ice (density 900 kg/m³) built up on the wire to a total diameter of 10.0 cm, the wire snapped. What was the breaking stress (force/unit area) in N/m² in the wire at the breaking point?
You may assume the ice has no strength.

(A) 7.4 X 107 (B) 4.4 X 108 (C) 2.6 X 106 (D) 1.15 X 107 (E) 6.7 X 108

SIN练习题4答案及解析

答案：（B）   解析如下

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SIN练习题第5题

5.Romeo is landing back on Earth to claim his bride, Juliet. His spaceship is descending vertically at 50 m/s and he is 500m up when he throws a bouquet of Lovelon flowers horizontally (from his point of view) out of his ship to land near Juliet, who is waiting at the dockport, 40 m from his landing spot. How fast must Romeo throw his flowers in m/s so that they land at Juliet's feet? (Lovelon flowers are very slippery, and do not experience air resistance. They can also absorb quite a shock on landing and still look fresh!).

(A) 1.96 (B) 2.52 (C) 4.00 (D) 5.24 (E) 6.44

SIN练习题5答案及解析

答案：E；解析如下

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SIN练习题第6题

6.A teenager is downloading pirated, compressed songs in MP3 format from the Internet. Each song is about 3 minutes long when played, and needs about 2.9 megabytes of computer storage. To fill a CD requires about 70 minutes of music. If a 56K modem is being used which gives on average about 30 kilobits/sec of data flow, how many minutes does it take to download a full CD's worth of songs, ignoring setup times and filename entries? A byte represents 8 bits.

(A) 301 (B) 203 (C) 187 (D) 38 (E) 14

SIN练习题第6题答案解析

答案：A；解析如下：

With each song being 3 minutes long, there are 23.33 songs on a 70-minute CD. This requires a total storage of 2.9 megabytes x 23.33 = 67.67 megabytes. The modem processes about 30 kilobits/sec, which is 3.75 kilobytes/sec. At this rate, 67.67 megabytes will take (67.67x10⁶)/(3750) = 18045 seconds or 301 minutes (A) or 5.01 hours!

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