1. PHYSICS 231 Lecture 29: Problems
Remco Zegers
Walk-in hour: Thursday 11:30-13:30 am
Helproom
PHY 231

2. Figure skating
A male figure-skater rotates around a vertical axis (1 rev/s)
while holding his partner at 1.5 m. He then pulls her towards
him (1 m distance). A) How fast will he rotate now? Assume
no net torque is exerted on the skaters. B) If the woman is
55 kg, how much work has the man done while pulling?
PHY 231

3. Ball on a upward slope
A ball (r=0.1 m) is rolled up a slope. Its linear velocity
at the base is 10 m/s. How high will it go? (assume the ball
does not slip and given Iball=2/5*Mr2.
PHY 231

4. Ball game Top view 1 rev/s In a children’s game at a fair,
buckets are placed at 1m from the
center around which they all rotate
(Itotal=50kg/m2, 1rev/s). The children
try to throw balls in the buckets.
After 50 balls have gone in the
buckets, the wheel has slowed down
to 0.5 rev/s. How heavy is one ball?
PHY 231

5. Bulk modulus A rubber ball, with bulk modulus B, volume V at 1 atm.
increases its volume by 1 cm3 when put in a vacuum
chamber (P=0). If a ball of the same material but 5
times larger in volume at 1 atm is put under a pressure of
3 atm, how much will its volume shrink?
B=-P/(V/V)
PHY 231

6. Buoyant forces When submerged in water an object weighs 1.6N. At the
same time, the water level in the water container (with
A=0.01 m2) rises 0.01 m. What is the specific gravity (sg) of the object? (water=1.0x103 kg/m3)
A=0.01 m2
PHY 231

7. Keep it coming. A plastic bag contains a glucose
solution. The part of the bag that
is not filled is under vacuum. If the
pressure in a blood vein is 1.33x104 Pa,
how high must one hang the bag to
make sure the solution (specific gravity
1.02) enters the body?
(w=1.0x103kg/m3)
PHY 231

8. Titanic: After the Titanic sunk, 10 people
manage to seek refuge on a 2x4m wooden raft. It is still 1.0 cm above water. A heavy debate follows when another person (60 kg) wants to board as well. Fortunately, a PHY231 student is among the 10. Can she convince the others that itis safe to pull the person on board without the whole raft sinking? (w=1.0x103 kg/m3)
PHY 231

9. Bernoulli A=5cm2 =1.0x103 kg/m3 2m A=2cm2, P=1 atm
Water flows over a height of 2m through an oddly shaped pipe.
A) If the fluid velocity is 1 m/s at the bottom, what is it at the top? B) What is the water pressure at the top?
PHY 231

10. Centipede
A centipede (100 legs) decides to cross a lake. The contact
length between each of his legs and the water is 1mm. If its
mass is 2g and water=0.073 N/m succeed? Assume that the
angle =450. Fs Fg 
1 leg
PHY 231

11. Ch. 10 Metal hoop A metal (thermal expansion coefficient
=17x10-6 1/0C) hoop of radius 0.10 m is heated from
200C to 1000C. By how much does its radius change?
0.1m
PHY 231

12. 10: Diving Bell
A cylindrical diving bell (diameter 3m and 4m tall, with an open bottom is submerged to a depth of 220m in the sea. The surface temperature is 250C and at 220m, T=50C. The density of sea water is 1025 kg/m3. How high does the sea water rise in the bell when it is submerged?
PHY 231

13. 10: Moles Two moles of Nitrogen gas (N2) are enclosed in a cylinder
with a moveable piston. A) If the temperature is 298 K and the pressure is 1.01x106 Pa, what is the volume (R=8.31 J/molK)?
b) What is the average kinetic energy of the molecules?
kB=1.38x10-23 J/K
PHY 231

14. Ch 11: 3*103 J of heat is transferred to a 1cm3 cube of gold at T=20oC
Will all the gold have melted afterwards?
Lf=6.44x104 J/kg Tmelt=1063oC cspecific=129 J/kg0C
=19.3x103 kg/m3.
PHY 231

15. 11: Heat transfer
A hot block and a cold block are thermally connected.
Three different methods to transfer heat are proposed
as shown. Which one is the most
efficient way (fastest) to transfer
heat fro hot to cold and what are
the relative rates of transfer?
A: cross section surface
of black wire,L:its length
Area: A Length L 1
0.1A
0.2L 2 3
4A 5L
PHY 231

16. Thermal equilibrium
20g of a solid at 700C is placed in 100g of a fluid at 20oC.
After waiting a while the temperature of the whole system
is 30oC and stays that way. The specific heat of the solid is:
Equal to that of the fluid
Less than that of the fluid
Larger than that of the fluid
Unknown; different phases cannot be compared
Unknown; different materials cannot be compared
PHY 231