# 普通物理甲 測量~~

1.E2. The diameter of our disk-shaped galaxy, the Milky Way, is about D = 7.84 × 10^4 light-years (ly). The distance to the Andromeda galaxy, which is the spiral galaxy nearest to the Milky Way, is about S=2.38 × 10^6 ly. If a scale model represents the Milky Way and Andromeda galaxies as dinner plates P=29 cm in diameter, determine the distance (cm) between the centers of the two plates.

2.E1. One gallon V = 3.96 × 10^(-3) m^3 of paint covers an area of A=29.25 m^2. What is the thickness (μm) of the fresh paint on the wall?

3.M2. One cubic meter 1.00 m^3 of aluminum has a mass of 3520 kg, and the same volume of iron has a mass of 9560 kg. Find the radius (cm) of a solid aluminum sphere that will balance a solid iron sphere of radius R=2.00 cm on an equal-arm balance.

4.M6. Every horizontal cross section of the bottle is circular, but the diameters of the circles have different values. You pour the brightly colored shampoo into the bottle at a constant rate of R=30 cm^3/s. At what rate (cm/s) is its level in the bottle rising at a point where the smallest diameter of the bottle is D=8.08 cm?

5.M4. A highway curve forms a section of a circle. A car goes around the curve as shown in the figure. Its compass shows that the car is initially heading due east. After it travels D = 1025 m, it is heading T= south of east. Find the radius (m) of curvature of its path.

6.D1. Air is blown into a spherical balloon so that, when its radius is R=6 cm, its radius is increasing at the rate 1.06 cm/s. (a) Find the rate (cm^3/s) at which the volume of the balloon is increasing. (b) If this volume flow rate of air entering the balloon is constant, at what rate (cm/s) will the radius be increasing when the radius is 13 cm?

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• 最佳解答

1.Center Dist=29*2.38*10^6/7.84*10^4=29*238/7.84=880(cm)

2.One gallon V = 3.96 × 10^(-3) m^3 of paint covers an area of A=29.25 m^2. What is the thickness t=?μm of the fresh paint on the wall?

t=V/A=3.96/29.25*1000=1.354*10^-4(m)=135.4(μm)

3.One cubic meter of aluminum has a mass of M1=3520 kg, and the same volume of iron has a mass of M2=9560 kg. Find the radius (cm) of a solid aluminum sphere that will balance a solid iron sphere of radius R2=2.00 cm on an equal-arm balance.

D=DensityD1=M1/V=3520/1=3520(kg/m^3)D2=9560/1=9560(kg/m^3)M1=4πD1*R1^3/3, M2=4πD2*R2^3/3M1=M2 => D1*R1^3=D2*R2^3R1^3=D2*R2^3/D1=9560*2^3/3520R1=2*(9560/3520)^1/3=2*2.7159^1/3=2.79(cm)

4.Every horizontal cross section of the bottle is circular, but the diameters of the circles have different values. You pour the brightly colored shampoo into the bottle at a constant rate of R=30 cm^3/s. At what rate (cm/s) is its level in the bottle rising at a point where the smallest diameter of the bottle is D=8.08 cm?

h=R/(πD^2/4)=4R/πD^2=4*30(cm^3/s)/π8.08^2(cm^2)=0.585(cm/s)

5.A highway curve forms a section of a circle. A car goes around the curve as shown in the figure. Its compass shows that the car is initially heading due east. After it travels Dist = 1025 m, it is heading T= south of east. Find the radius (m) of curvature of its path. R=Dist/(π/4)=4Dist/π=4*1025/π=1305(m)or R=4Dist/5π=4*1025/5*π=261(m) if it passes thru one coil.

6.Air is blown into a spherical balloon so that, when its radius is R=6 cm, its radius is increasing at the rate dR/dt=1.06 cm/s. (a) Find the rate (cm^3/s) at which the volume of the balloon is increasing.

V=4πR^3/3dV/dt=4πR^2*dR/dt=4π6^2*1.06=479.53(cm^3/s)

2014-10-21 17:03:25 補充：

(b) If this volume flow rate of air entering the balloon is constant,

at what rate (cm/s) will the radius be increasing when the radius is 13

cm?

dR/dt=(dV/dt)/4πR^2

=479.53/4π13^2

=0.2258(cm/s)

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