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PHYSICS 1

FAP0015

Questions & Answers to Physics I Assignments Chapter 1
11. What, roughly, is the percent uncertainty in the volume of a spherical beach ball whose radius is r = 2.86 ± 0.09 m? Answer: To find the approximate uncertainty in the volume, calculate the volume for the specified radius, the minimum radius, and the maximum radius. Subtract the extreme volumes. The uncertainty in the volume is then half this variation in volume. 3 Vspecified = 4 π rspecified = 4 π ( 2.86 m ) = 9.80 × 101 m3 3 3 3 3 Vmin = 4 π rmin = 4 π ( 2.77 m ) = 8.903 × 101 m3 3 3 3 3 4 4 Vmax = 3 π rmax = 3 π ( 2.95 m ) = 10.754 × 101 m3 3

ΔV =

1 2

(Vmax − Vmin ) = 12 (10.754 × 101 m3 − 8.903 × 101 m3 ) = 0.926 × 101 m3 ΔV Vspecified = 0.926 × 101 m 3 9.80 × 101 m 3 × 100 = 9.418 ≈ 9 %

The percent uncertainty is

19. Express the following sum 1.80 m + 142.5 cm + 5.34 × 10 5 μm. Answer:

with

the

correct

number

of

significant

figures:

To add values with significant figures, adjust all values so that their units are all the same.

1.80 m + 142.5 cm + 5.34 × 105 μ m = 1.80 m + 1.425 m + 0.534 m = 3.759 m = 3.76 m When adding, the final result is to be no more accurate than the least accurate number used. In this case, that is the first measurement, which is accurate to the hundredths place.

27. Estimate how long it would take one person to mow a football field using an ordinary home lawn mower. Assume the mower moves with a 1 km h speed, and has a 0.5 m width. Answer: The dimension of a football field (FIFA specification) is 64 meters by 100 meters. The mower has a cutting width of 0.5 meters. Thus the distance the mower has to move is

d=

Area of field 6400 m 2 = = 12800 m = 12.8 km Width of mower 0.5 m

At a speed of 1 km/hr, then it will take about 12.8 h to mow the field.

51. The diameter of the Moon is 3480 km. What is the volume of the Moon? How many Moons would be needed to create a volume equal to that of Earth? Answer: The volume of a sphere is found by V = 4/3 πr3.

3 4 VMoon = 3 π RMoon = 4 π 1.74 × 10 6 m 3

(

)

3

= 2.21 × 1019 m 3
3

VEarth VMoon

3 π REarth ⎛ REarth ⎞ ⎛ 6.38 × 106 m ⎞ = 4 =⎜ ⎟ =⎜ ⎟ = 49.3 3 π RMoon ⎝ RMoon ⎠ ⎝ 1.74 × 106 m ⎠ 3 . 4 3

3

Thus it would take about 49.3 Moons to create a volume equal to that of the Earth.

Jan2011

PHYSICS 1

FAP0015

Chapter 2
13. An airplane travels 3100 km at a speed of 790 km/h and then encounters a tailwind that boosts its speed to 990 km/h for the next 2800 km. What was the total time for the trip? What was the average speed of the plane for this trip? Answer: The average speed for each segment of the trip is given by v = For the first segment, Δt1 = d1 v1 = 3100 km 790 km h = 3.924 h .

d Δt

, so Δt =

d v

for each segment.

For the second segment, Δt 2 =

d2 v2

=

2800 km 990 km h

= 2.828 h .

Thus the total time is Δt tot = Δt1 + Δt 2 = 3.924 h + 2.828 h = 6.752 h ≈ 6.8 h . The average speed of the plane for the entire trip is v = 19. = 873.8 ≈ 8.7 ×10 km h . Δttot 6.752 h A sports car moving at constant speed travels 110 m in 5.0 s. If it then brakes and comes to a stop in 4.0 s, what is its acceleration in m/s2? Express the answer in terms of “g’s,” where 1.0 g = 9.80 m/s2. 2

dtot

=

3100 km + 2800 km

Answer: The initial velocity of the car is the average speed of the car before it accelerates.

v =

d Δt

=

110 m 5.0 s

= 22 m s = v0

The final speed is v = 0, and the time to stop is 4.0 s. Use Eq. 2-11a to find the acceleration.

v = v0 + at → a=
37.

v − v0 t

=

0 − 22 m s 4.0 s

= −5.5 m s 2 = −5.5 m s 2 ⎜

(

1g ) ⎛ 9.80 m s



2

⎞ ⎟ = −0.56 g 's ⎠

A ballplayer catches a ball 3.0 s after throwing it vertically upward. With what speed did he throw it, and what height did it reach? Choose upward to be the positive direction, and take y0 = 0 to be the height from which the ball was thrown. The acceleration is...
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