## heat engine operates between two finite thermal reservoirs initially at temperatures T1 and T2>T1. The reservoirs have the same total heat capacities, each equal to C. Both reservoirs gradually come to the same final temperature T3, at which time the heat engine stops working. a. Present an argument to show that T3 ≥ √(T1·T2) b. Whatmaximumworkisobtainablefromtheproc

A heat engine operates between two finite thermal reservoirs initially at temperatures T1 and T2>T1. The reservoirs have the same total heat capacities, each equal to C. Both reservoirs gradually come to the same final temperature T3, at which time the heat engine stops working.

a. Present an argument to show that T3 ≥ √(T1·T2)

b. Whatmaximumworkisobtainablefromtheprocess?

## The negative pion (π-) is an unstable particle with an average lifetime of 2.60 x 10-8 s (measured in the rest frame of the pion). (a) If the pion is made to travel at very high speed relative to a laboratory, its average lifetime is measured in the laboratory to be 4.20 x 10-7 s. Calculate the speed of the pion expressed as a fraction of c. (b) What distance, measured in the laboratory, does the pion travel during its average lifetime?

The negative pion (π) is an unstable particle with an average lifetime of 2.60 x 10-8 s (measured in the rest frame of the pion). (a) If the pion is made to travel at very high speed relative to a laboratory, its average lifetime is measured in the laboratory to be 4.20 x 10-7 s. Calculate the speed of the pion expressed as a fraction of c. (b) What distance, measured in the laboratory, does the pion travel during its average lifetime?

## Consider a situation where blood flows through a section of a horizontal artery that is partially blocked by a reservoir along the wall of the artery. A hemoglobin molecule moves from the narrow region to the wider region. What happens to the pressure acting on the molecule? Explain with fundamentals of fluid physics.

Consider a situation where blood flows through a section of a horizontal artery that is partially blocked by a reservoir along the wall of the artery. A hemoglobin molecule moves from the narrow region to the wider region. What happens to the pressure acting on the molecule? Explain with fundamentals of fluid physics.

## Five boys are pushing on a snowball, and each is pushing with a force of 10.0 N. However, each boy is pushing in a different direction. They are pushing north, northeast, east, southeast, and south. (Each boy is pushing at an angle of 45.0° relative to his neighbor.) What is the magnitude of the total force on the ball?

Five boys are pushing on a snowball, and each is pushing with a force of 10.0 N. However, each boy is pushing in a different direction. They are pushing north, northeast, east, southeast, and south. (Each boy is pushing at an angle of 45.0° relative to his neighbor.) What is the magnitude of the total force on the ball?

## Hydraulic engineers in the United States often use, as a units of volume of water, the acre-foot, defined as the volume of water that will cover 1 acre (where 1 acre = 43560 ft2) of land to a depth of 1 ft. A severe thunderstorm dumped 2.9 in. of rain in 30 min on a town of area 36 km2. What volume of water, in acre-feet, fell on the town?

Hydraulic engineers in the United States often use, as a units of volume of water, the acre-foot, defined as the volume of water that will cover 1 acre (where 1 acre = 43560 ft2) of land to a depth of 1 ft. A severe thunderstorm dumped 2.9 in. of rain in 30 min on a town of area 36 km2. What volume of water, in acre-feet, fell on the town?

## The recommended daily caloric intake is 2000 calories (8,400,000J). This is because this is the same value for how much the average body loses to heat and work in a typical day (your change in energy is zero because you take in the same amount of energy you lose).   A) If you lose a total of 8,400,000J (Qout+W=total lost), but consume 1200 calories of food (5,000,000J), what would your change in energy be? B) Assuming your change in energy is negative (hint-it should be), where does your body get the extra energy to maintain it’s temperature?

The recommended daily caloric intake is 2000 calories (8,400,000J). This is because this is the same value for how much the average body loses to heat and work in a typical day (your change in energy is zero because you take in the same amount of energy you lose).

A) If you lose a total of 8,400,000J (Qout+W=total lost), but consume 1200 calories of food (5,000,000J), what would your change in energy be?

B) Assuming your change in energy is negative (hint-it should be), where does your body get the extra energy to maintain it’s temperature?

## A car is waiting at a stoplight. The car has a mass of 1200 kg. What is the force (magnitude and direction) that the road puts on the wheels

1) A car is waiting at a stoplight. The car has a mass of 1200 kg. What is the force (magnitude and direction) that the road puts on the wheels?

*Note that problems 2, 3 and 4 ask for the force of friction only, not the normal force.*

2) The same car accelerates out of the stoplight at 1.5 m/s 2 . Draw a free-body diagram of the car and find the force of friction (magnitude and direction) that the road puts on the wheels.

3) The same car reaches a top speed of 15 m/s, then begins braking. It comes to a halt in 20 seconds. Draw a free body diagram of the car and find the force of friction (magnitude and direction) that the road makes on the wheels now.

4) The same car is now towing a 200kg trailer. It accelerates out of the stoplight a little slower, at 0.8 m/s 2 . Draw free-body diagrams of the car and the trailer as it accelerates. What is the force of friction that the road makes on the car wheels now?

## In a lab you measured the force between two charged pith balls where the pith balls were of the same size and mass. Your assumption was that the charge on the balls was the same.  Consider this change to that situation. You charge the balls so that they hang a distance “r” apart. Then you step out to get a drink of milk, and when you return, you find the distance between the pith balls is one third what it was before you got a drink. In terms of length L, the charge Q, and the original angle Theta, find the new charge on the pith balls and the new angle at which they hang.  Please show work.

In a lab you measured the force between two charged pith balls where the pith balls were of the same size and mass. Your assumption was that the charge on the balls was the same.

Consider this change to that situation. You charge the balls so that they hang a distance “r” apart. Then you step out to get a drink of milk, and when you return, you find the distance between the pith balls is one third what it was before you got a drink. In terms of length L, the charge Q, and the original angle Theta, find the new charge on the pith balls and the new angle at which they hang.