Lon CAPA 1 Solutions F 2018 PDF

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Lon Capa Solutions for Fall 2018...

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CAPA #1 Solutions (1a) Bicyclists in the Tour de France reach speeds of 38.8 miles per hour (mi/h) on flat sections of the road. What is the speed in kilometers per hour (km/h)? (b) What is the speed in meters per second (m/s)?

3

(2) An auditorium measures 39.0 m x 17.0 m x 15.0 m. The density of air is 1.20 kg/m . (a) What is the volume of the room in cubic feet? (1 m = 3.28 ft) (b) What is the weight of air in the room in pounds? (1 kg = 2.20 lb)

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(6)

(7) The corners of a square lie on a circle of diameter 0.35 m. Each side of the square has length L. Find L.

(8) The average blood volume in the human body is about 6 L. A typical blood sample contains about 5,500,000 red blood cells per cubic millimetre (mm3). Estimate how many red blood cells you have in your body. (1 L = 10-3 m3, 1 m = 1000 mm). Enter only the exponent of your answer: e.g. if your answer is 1×10n, enter only the integer n. - Volume of blood = V = 6 L - Density of blood cells = ρ = 5,500,000 cells/mm3 - Number of cells in the body = N = ρ V 10!! m! ! = 6L ∙ = 6×10!! m! L 1000 mm cells ∙ ! = 5.5×10 1m mm!

!

!

! = 5.5×10!"

cells 1×10! mm! ∙ = 5.5×10 mm! 1 m! !

cells m!

∴ ! = 6×10!! m! ∙ 5.5×10!"

!"##$ !!

The correct exponent is n = 13.

= 3.3×10!" cells.

(9) How many grams of aluminum are required to make a hollow spherical shell having an inner radius of 5.45 cm and an outer radius of 5.47 cm? The density (ρ) of aluminum is 2.70 g/cm3. - Inner radius = Ri - Outer radius = Ro - Mass = M = ρV 4 Volume of a sphere = ! = !! ! 3 Volume of a ℎ!""!# sphere = !! − !! =

4 4 ! 4 ! !!! − !!! = ! !!! − !!! 3 3 3

4 ∴ ! = ! ∙ ! !!! − !!! 3

!

! = 2.70 g/cm! ∙ ! ! 5.47 cm

!

− 5.45 cm

!

= 20.2 g

(10) One cubic meter (1.00 m^3) of aluminum has a mass of 2.70E+3 kg, and 1.00 m^3 of copper has a mass of 8.92E+3 kg. Find the radius of an aluminum sphere whose mass is the same as that of a copper sphere of radius 1.80 cm.

• To find the radius of the aluminum sphere with the same mass as the copper sphere:

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(12) A woman wishing to know the height of a mountain measures the angle of elevation of the mountaintop as 12.1 deg. After walking 0.98 km closer to the mountain on level ground, she finds the angle to be 14.4 deg. Find the height of the mountain.

• after she moves closer:

• combine equations 1 and 2 to solve for h:

(13) An aerialist on a high platform holds on to a trapeze attached to a support by an 8 m cord. Just before he jumps off the platform, the cord makes an angle alpha of 41.9 deg with the vertical. He jumps, swings down, then back up, releasing the trapeze at the instant it is 0.93 m below its initial height. Calculate the angle theta that the trapeze cord makes with the vertical at this instant.

• split the problem into two triangles:

• Before swing:

• After swing:

(14) The magnitudes of four displacement vectors shown in the drawing are A = 15.7 m, B = 10.5 m, C = 12.0 m, and D = 24.7 M. Determine the magnitude for the resultant vector that occurs when these vectors are added together.

• We first need to split each vector into x and y components, being careful of signs:

• Example:

• Now add all x components and all y components:

• The magnitude of the resulting vector is:...