Semester: Sept 2016 – Jan 2017

Course: PHY440 Mechanics, Waves and Thermal Physics

Text book: Jewett, J.W. and Serway, R.A. (2010). Physics for Scientists and Engineers with Modern Physics, 8th Edition, Brooks/Cole Cengage Learning.

Assignment 1

Question / Topic / Problem
1 / Section 1.3 Dimensional Analysis / No 12 (Softcopy) p.16; No 12 (Hardcopy) p. 16
12. (a) Assume the equation x = At 3 + Bt describes the motion
of a particular object, with x having the dimension of length and t having the dimension of time. Determine the dimensions of the constants A and B. (b) Determine the dimensions of the derivative dx/dt = 3At 2 + B.
2 / Section 1.4 Conversion of Units / No 21 (Softcopy) p.16; No 21 (Hardcopy) p. 16
21. One cubic meter (1.00 m3) of aluminum has a mass of
2.70 ´ 103 kg, and the same volume of iron has a mass of
7.86 ´ 103 kg. Find the radius of a solid aluminum sphere
that will balance a solid iron sphere of radius 2.00 cm on
an equal-arm balance.
3 / Challenge Problems / No 66 (Softcopy) p.19; No 66 (Hardcopy) p. 19
66. A woman stands at a horizontal distance x from a
mountain and measures the angle of elevation of the
mountaintop above the horizontal as q. After walking a distance d closer to the mountain on level ground, she finds
the angle to be f. Find a general equation for the height
y of the mountain in terms of d, f, and q, neglecting the
height of her eyes above the ground.
4 / Section 2.3 Analysis Model: Particle Under Constant Velocity / No 11(Softcopy) p.49; No 11 (Hardcopy) p. 49
11. A hare and a tortoise compete in a race over a straight
course 1.00 km long. The tortoise crawls at a speed of
0.200 m/s toward the finish line. The hare runs at a speed
of 8.00 m/s toward the finish line for 0.800 km and then
stops to tease the slow-moving tortoise as the tortoise eventually passes by. The hare waits for a while after the tortoise passes and then runs toward the finish line again at
8.00 m/s. Both the hare and the tortoise cross the finish
line at the exact same instant. Assume both animals, when
moving, move steadily at their respective speeds. (a) How
far is the tortoise from the finish line when the hare resumes the race? (b) For how long in time was the hare stationary?
5 / Section 2.6 Analysis Model: Particle Under Constant Acceleration / No 32(Softcopy) p.51; No 28 (Hardcopy) p. 50
32. A particle moves along the x axis. Its position is given by
the equation x = 2 + 3t - 4t 2, with x in meters and t in seconds. Determine (a) its position when it changes direction
and (b) its velocity when it returns to the position it had at
t = 0.
6 / Section 2.7 Freely Falling Objects / No 39(Softcopy) p.51; No 39 (Hardcopy) p. 51
39. Why is the following situation impossible? Emily challenges her friend David to catch a $1 bill as follows. She holds the bill vertically as shown in Figure P2.39, with the center of the bill between but not touching David’s index finger and thumb. Without warning, Emily releases the bill. David catches the bill without moving his hand downward. David’s reaction time is equal to the average human reaction time. You may replace this $1 US dollar bill with a RM1 note.

7 / Section 3.4 Components of a Vector and Unit Vectors / No 52 (Softcopy) p.71; No 50 (Hardcopy) p. 71
52. A ferry transports tourists between three islands. It sails
from the first island to the second island, 4.76 km away, in
a direction 37.0° north of east. It then sails from the second
island to the third island in a direction 69.0° west of north.
Finally it returns to the first island, sailing in a direction
28.0° east of south. Calculate the distance between
(a) the second and third islands and (b) the first and third
islands.
8 / Conceptual Questions / No 5 (Softcopy) p.95; No 7 (Hardcopy) p. 95
5. A projectile is launched at some angle to the horizontal with some initial speed vi, and air resistance is negligible.
(a) Is the projectile a freely falling body? (b) What is its acceleration in the vertical direction? (c) What is its acceleration in the horizontal direction?
9 / Section 4.3 Projectile Motion / No 18 (Softcopy) p.96; No 18 (Hardcopy) p. 96
18. A landscape architect is planning an artificial waterfall in
a city park. Water flowing at 1.70 m/s will leave the end of a
horizontal channel at the top of a vertical wall h = 2.35 m
high, and from there it will fall into a pool (Fig. P4.18).
(a) Will the space behind the waterfall be wide enough for
a pedestrian walkway? (b) To sell her plan to the city council,
the architect wants to build a model to standard scale,
which is one-twelfth actual size. How fast should the water
flow in the channel in the model?

10 / Section 4.6 Relative Velocity and Relative Acceleration / No 35 (Softcopy) p.98; No 39 (Hardcopy) p. 98
35. A police car traveling at 95.0 km/h is traveling west, chasing
a motorist traveling at 80.0 km/h. (a) What is the velocity of the motorist relative to the police car? (b) What is the velocity of the police car relative to the motorist? (c) If they are originally 250 m apart, in what time interval will the police car overtake the motorist?
11 / Challenge Problems / No 69 (Softcopy) p.102; No 69 (Hardcopy) p. 102
69. A dive-bomber has a velocity of 280 m/s at an angle q below the horizontal. When the altitude of the aircraft is 2.15 km, it releases a bomb, which subsequently hits a target on the ground. The magnitude of the displacement from the
point of release of the bomb to the target is 3.25 km. Find
the angle q.

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