PHYS 1002 General Physics HW1
Note:
(1) Due: 19 Sep 2019 (Thu), 11:59pm
(2) You can submit the hardcopy either (i) directly to the instructor, or (ii) to the assignment
box outside SC 213. (Kind reminder: homework submitted to wrong box could result in
zero mark, because we cannot verify that you’ve submitted before the deadline.)
(3) Use 𝑔 = 9.81 m/s2 for gravitational acceleration throughout the problem set.
(4) Show the intermediate steps/maths.
1. A river has a steady speed of 𝑣s = 0.500 m/s due east, and a constant width of 𝑑 =
1.00 km. A student swims from the south bank to the north bank, and then swims
back to the south bank. In each leg of the round trip, the student swims along a straight
path. The student can swim at a speed of 𝑣 = 1.20 m/s in still water.
Scenario 1: Suppose the round trip takes the shortest possible time.
(a) How long does it take the student to make the round trip?
(b) Upon returning the south bank, how far does the student reach downstream from
the original point?
Scenario 2: Suppose the student reaches the location directly opposite to the starting
point, and then swims back to the starting point.
(c) How long does it take the student to make the round trip?
[15 marks]
2. After being released from rest at the top of an inclined plane, a small block slides
downslope with a constant acceleration for a total time 𝑡 and reaches the bottom of
the plane. In the first 3.0 s (let’s call it 𝑡1 ), the displacement is 𝑥1 . In the last 3.0 s
(let’s call it 𝑡2 ), the displacement is 𝑥2 .
It is known that 𝑥2 − 𝑥1 = 8.5 m, and 𝑥1 : 𝑥2 = 1: 2.
(a) Let 𝑎 be the acceleration along the slope, and 𝑡 = 𝑡1 + 𝑡 ′ + 𝑡2 , where 𝑡′ is the
time lapse in the “middle” part of the motion.
Express 𝑥1 in terms of 𝑎 and 𝑡1 . Also express 𝑥2 in terms of 𝑎, 𝑡1 , 𝑡2 , and 𝑡′.
(b) Find the value of 𝑡′.
(c) Find the value of 𝑎.
[20 marks]
1
3. Water drips from the nozzle of a shower onto the floor 2.45 m below. The drops fall
at regular interval of time, with the first drop striking the floor at the instant the third
drop begins to fall. Assume that air resistance is negligible.
(a) How long does it take for the water drop to fall from the nozzle to the ground?
(b) What is the height of the second drop (from the floor) when the first drop strikes
the floor?
[15 marks]
4. An inverted hollow cone, of base radius 𝑅 and height 𝑅
𝐿 = 2𝑅, can rotate about its fixed vertical axis. A point
particle of mass 𝑚 is placed in the smooth inner surface
of the cone. The particle is free to move on the surface.
𝐿 = 2𝑅
Yet the particle is at rest with respect to the cone surface,
and it undergoes a horizontal uniform circular motion. 𝑅
The circular path of the particle is half way between the
apex and the base.
(a) Draw the free-body diagram for the particle.
(b) Find the time taken for the particle to complete a circle?
[15 marks]
5. A block of mass 𝑚1 and a ball with mass 𝑚2 are
connected via a light inelastic string through a smooth
pulley. The block is on a fixed rough slope with
coefficient of friction 𝜇 and inclination angle 𝜃. The 𝑚2
two objects are released from rest when the string is
taut. The block starts to move up the slope, and the 𝜃
ball moves downward.
(a) Draw the free-body diagrams for the two objects.
(b) Set up three equations (two for the block and one for the ball) by applying
Newton’s laws of motion.
(c) Express the acceleration of the block in terms of the provided parameters and 𝑔.
(d) Given 𝑚1 = 1.2 kg, 𝑚2 = 2.4 kg, 𝜇 = 0.15, and 𝜃 = 25°. What is the tension
in the string?
[35 marks]
