Question

1-1 Suppose you want to make a scale model of a hydrogen atom. You choose, for the nucleus, a small ball bearing with a radius of 1.5 mm. The radius of the hydrogen atom is 0.529 × 10−10 m and the radius of the nucleus is 1.2 × 10−15 m.

(a) What would be the radius of the model?

(b) Suppose that now you want to make a scale model of the solar system using the same ball bearing as in part (a) to represent the sun. How far from it would you place a sphere representing the earth? (Center to center distance please.) The radius of the sun is 6.96 × 108 m, and the radius of the earth is 6.37 × 106 m. The distance between the sun and the earth is 1.496 × 1011 m.

(c) What would be the radius of the sphere representing the earth in part (b)?

(a) 50, 99 m

(b) 0.200, 0.500 m

(c) 1.00 × 10−5 , 2.00 × 10−5 m.

1-2. (a) Atoms are typically spaced about 0.2 nm apart. At that spacing, how many atoms would be found in a line 4.96 inches long?

(b) How many kg of water are in 3.90 cubic inches (in^3 )?

(a) 1.0 × 108 , 8.0 × 108

(b) 0.010, 0.099 kg

1-3. A garden plot must have a central planting area of length 13 m and width 8 m. There is to be a sidewalk around its edge of width w. If the total area, planting area plus sidewalk area, is 142 m2 , what is the sidewalk width w in meters?

[0.70, 1.60 m]

2-1. Consider the following formula: x = A cos(Bt^2 ). “x” is in meters and “t” is in seconds.

(a) Which of the following must be the units of A?

1/m, m/rad, m/s2 , m, m s2

(b) Which one of the following is the least acceptable units for B?

degree/s2 , m/s2 , rad/s2 , rev/s2 .

2-2. Kim has a metal casting company which makes commemorative coins. She has 0.12 cubic meters of silver which she needs to make into 8.3E+04 coins of thickness 2 mm. If she uses all of the silver, what is the diameter in centimeters of each coin? [2.50, 3.60 cm]

2-3. When two sticks are laid end-to-end they cover a length of 8.32 feet. One stick is 2.60 feet longer than the other. What is the length of the shorter stick in feet? [2.50, 4.00 ft]

2-4. A surveyor measures the distance across a straight river by the following method: Starting directly across from a tree on the opposite bank, she walks 100 m along the river bank to establish a base line. Then she sights across to the tree. The angle between her baseline and the tree is 37.7 degrees. How wide is the river? [50.0, 90.0 m]

2-5. A dog searching for a bone walks 3.50 m south, then 8.20 m at an angle 25.3 degrees north of east, and finally 15.0 m west.

(a) What is the magnitude of the dog’s total displacement?

(b) What is the direction of the dog’s total displacement where directly east is taken as zero degrees and counter-clockwise is positive?

(a) 7.00, 9.00 m

(b) 160.0, 190.0 degrees

Answer 1

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