Find the power required for a $2000-\mathrm{kg}$ car to climb a $100-\mathrm{m}$-long uphill road with a slope of $30^{\circ}$ (from horizontal) in $10 \mathrm{~s}(a)$ at a constant velocity, $(b)$ from rest toa final velocity of $30 \mathrm{~m} / \mathrm{s}$, and (c) from $35 \mathrm{~m} / \mathrm{s}$ to a final velocity of $5 \mathrm{~m} / \mathrm{s}$. Disregard friction, air drag, and rolling resistance.

Determine the work required to deflect a linear spring with a spring constant of 70 kN/m by 20 cm from its rest position.

Consider a river flowing toward a lake at an average velocity of 3 m/s at a rate of 500 m^3/s at a location 90 m above the lake surface. Determine the total mechanical energy of the river water per unit mass and the power generation potential of the entire river at that location.

The engine of a 1500-kg automobile has a power rating of 75 kW. Determine the time required to accelerate this car from rest to a speed of 100 km / h at full power on a level road. Is your answer realistic?

A classroom that normally contains 40 people is to be air-conditioned with window air-conditioning units of 5-kW cooling capacity. A person at rest may be assumed to dissipate heat at a rate of about 360 kJ/h. There are 10 lightbulbs in the room, each with a rating of 100 W. The rate of heat transfer to the classroom through the walls and the windows is estimated to be 15,000 kJ/h. If the room air is to be maintained at a constant temperature of $21^\circ C,$ determine the number of window air-conditioning units required.

Consider a river flowing toward a lake at an average velocity of $3 \mathrm{~m} / \mathrm{s}$ at a rate of $500 \mathrm{~m}^{3} / \mathrm{s}$ at a location $90 \mathrm{~m}$ above the lake surface. Find the total mechanical energy of the river water per unit mass and the power generation potential of the entire river at that location.

How are heat, internal energy, and thermal energy related to each other?

A river flowing steadily at a rate of $240 \mathrm{~m}^{3} / \mathrm{s}$ is considered for hydroelectric power generation. It is Findd that a dam can be built to collect water and release it from an elevation difference of $50 \mathrm{~m}$ to generate power. Find how much power can be generated from this river water after the dam is filled.

A river flowing steadily at a rate of $175 m^3/s$ is considered for hydroelectric power generation. It is determined that a dam can be built to collect water and release it from an elevation difference of 80 m to generate power. Determine how much power can be generated from this river water after the dam is filled.

A river flowing steadily at a rate of $175 \mathrm{m}^{3} / \mathrm{s}$ is considered for hydroelectric power generation. It is determined that a dam can be built to collect water and release it from an elevation difference of 80 m to generate power. Determine how much power can be generated from this river water after the dam is filled.

A vertical piston-cylinder device contains a gas at a pressure of 100 kPa. The piston has a mass of 10 kg and a diameter of 14 cm. Pressure of the gas is to be increased by placing some weights on the piston. Determine the local atmospheric pressure and the mass of the weights that will double the pressure of the gas in the cylinder. Answer: 93.6 kPa, 157 kg

At a certain location, wind is blowing steadily at 10 m/s. Determine the mechanical energy of air per unit mass and the power generation potential of a wind turbine with 60-m-diameter blades at that location. Take the air density to be 1.25 kg/m^3.

A spherical soap bubble with a surface-tension of 0.005 lbf/ft is expanded from a diameter of 0.5 in to 3.0 in. How much work, in Btu, is required to expand this bubble?

A model aircraft internal-combustion engine produces 10 W of power. How much power is this in (a) lbf.ft/s and (b) hp?