PHYSICS 231 Lecture 29: Problems

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

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### PHYSICS 231Lecture 29: Problems

Remco Zegers

Walk-in hour: Thursday 11:30-13:30 am

Helproom

PHY 231

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

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

Top view

Ball game

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

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

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

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

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

A=5cm2

Bernoulli

=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

Fs

Fs

Fg

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/msucceed? Assume that the

angle =450.

1 leg

PHY 231

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

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

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

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

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

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