1. A 12kg rock approaches the foot of a hill with a speed of 18m/s. This hill sl

Question

1. A 12kg rock approaches the foot of a hill with a speed of 18m/s. This hill slopes upward at a constant angle of 40 degrees above the horizontal. The coefficient of kinetic friction between the hill and the rock is .15. use energy conservation to find the maximum height above the foot of the hill reached by the rock.

2. A 5g bullet is shot through a 1kg wood block (i.e., the bullet does not remain embedded in the block) suspended on a string 2m long. After the impact, the block swings up, rising a distance of .08m. What is the speed of the block immediately after the impact? Find the speed of the bullet as it emerges from the block if its initial speed is 450m/s.

3. A 4g bullet, traveling horizontally with a velocity of magnitude 400m/s is fired into a wooden block with mass .800kg, initially at rest on a level surface. The bullet passes through the block and emerges with its speed reduced to 190m/s. What is the speed of the block immediately after the impact? The block slides a distance of 45cm along the surface from its initial position. What is the coefficient of kinetic friction between the block and surface?

4. A diesel engine performs 2200 J of mechanical work and discards 4300 J of heat each cycle. How much heat must be supplied to the engine in each cycle? What is the thermal efficiency of the engine? If the air temperature (i.e., the temperature of the cold reservoir) is 10 degrees C, what would be the temperature (in degrees Celsius) of the hot reservoir have to be for an ideal engine to have the same efficiency as their diesel engine?

5. A glass mug has a mass of 125 g when empty and it is initially at a temperature of 20 degrees C. Then 200 g of coffee at 70 degrees C are poured into the mug. Assuming that all the heat removed from the coffee is absorbed by the mug, find the common final temperature. Assume that coffee has the same specific heat as water (4190 J/kg degrees C) and that the mug has a specific heat of 840 J/kg degrees C.

Explanation / Answer

1)

Here , let the maximum height is h

distance travelled , d = h/sin(45)

Now, using consrvation of energy

0.5 * mv^2 = m*g*h + u*m*g*cos(45) * h/sin(45)

0.5 * 18^2 = 9.8 * h + 0.15 * 9.8 * h

h = 14.01 m

the maximum height above the foot of the hill reached by the rock is 14.01 m

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