. Let us consider a spherical rain drop, with diameter 4 mm, falling from 5.00 km until reaching the ground. a) Using that the air density is approximately 1.2 kg/m3 and the water density is 1.00 \times 103 kg/m3 what is work done by the air resistance? b) What is the total energy lost by the rain drop during its fall?

A 43-kg pole vaulter running at 10 m/s vaults over the bar. Her speed when she is above the bar is 1.5 m/s. Neglect air resistance, as well as any energy absorbed by the pole, and determine her altitude as she crosses the bar.

Shoveling snow can be extremely taxing because the arms have such a low efficiency in this activity. Suppose a person shoveling a footpath metabolizes food at the rate of 800 W. (a) What is her useful power output? (b) How long will it take her to lift 3000 kg of snow 1.20 m? (This could be the amount of heavy snow on 20 m of footpath.) (c) How much waste heat transfer in kilojoules will she generate in the process?

A spherical tank of diameter 4 m is half-full of water (weight density = 9800 N/m³). Setup the integral for the work done in pumping the content to a point 3 m from the top of the tank. (Hint: Put the bottom of the tank along the x-axis.) 9800 *S* (y³-7y² + 12y) dy 0 4 98007 (1³-9y² + 20y) dy 0 9800л S²(y²³-11y²+28y) dy 9800r ²(-y5+15y4-72y³ + 112y²2) dy

A swimming pool is round, full of contaminated water, and has an 11 foot radius. It is 11 feet tall and has 4 feet of water in it.How much work is required to remove all of the contaminated water by pumping it over the side? (Use the physical definition of work, and the fact that the weight of the contaminated water isσ=63.2lbs/ft3 )

A student evaluates a weight loss program by calculating the number of times she would need to climb a 10.0 m high flight of steps in order to lose one pound (0.45 kg) of fat. Metabolizing 1.00 kg of fat can release 3.77 x 10'J of chemical energy and the body can convert about 21.2% of this into mechanical energy (the rest goes into internal energy.) HINT (a) How much mechanical energy (in J) can the body produce from 0.450 kg of fat? (b) How many trips up the flight of steps are required for the 52.0 kg student to lose 0.450 kg of fat? Ignore the relatively small amount of energy required to return down the stairs. trips Need Help? Read It Watch It

A 59-kg pole vaulter running at 10 m/s vaults over the bar. Her speed when she is above the bar is 1.3 m/s. Neglect air resistance, as well as any energy absorbed by the pole, and determine her altitude as she crosses the bar.

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(a) A steel ball of mass 0.2 kg is projected vertically upwards, from the top of a building 100 m high, with an initial velocity of 40 m.s. Ignore air frietion and calculate: i. the total mechanical energy of the ball the time it was projected. ii. the total mechanical energy of the ball the time it reached the ground level (i.e at the bottom of the building) -1 iii. the total mechanical energy of the ball the time it reaches its maximum height above the ground. iv. the velocity of the ball the time it reached the ground level v. time taken by the ball to reach the ground level from the time it was projected vi. the maximum height above the ground the ball reached vii. the velocity of the ball the time it was 20 m above the ground (b) Two objects of mass 12 kg and 8 kg respectively move towards each other at velocities 10 m.s and 5 m.s respectively. If the objects unite during collision, calculate the resultant velocity. Page 5

Situation 2: A crate of mass 10.0 kg is pulled up a rough incline with an initial speed of 1.50 m/s. The pulling force is 100 N parallel to the incline, which makes an angle of 20.0° with the horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled 5,00 m. 18. Determine the increase in internal energy of the crate-incline system due to friction. 19. How much work is done by the 100-N force? 20. What is the change in kinetic energy of the crate?