When water flows through river rapids or over a waterfall, it experiences a decrease in height and thus a decrease in gravitational potential energy. Some of this energy goes into producing noise and eroding rock, but much of the energy goes into heating the water. A river flows over a waterfall of height h = 46 m. Assume all the available gravitational energy is converted into internal energy of the water. There is no change in the kinetic energy, because the flow speed of the river is the same above and below the waterfall. Enter an expression for the change in temperature of the water, in terms of the height of the waterfall, h, the specific heat of water, c, and the acceleration due to gravity, g.  Calculate the change in temperature, in degrees Celsius, of the river water in this problem. The specific heat of water is 4.19×103 J/(kg⋅°C).

A simple pendulum is suspended from the ceiling by means of a string and this time, the pendulum is 2.40 m long and has a mass of 3.23 kg. You give it a push away from vertical so that it starts swinging with a speed of 2.93 m/s. Due to friction at the pivot point, 1.00 Joule of the pendulum s initial kinetic energy is lost as heat during the upward swing. What maximum angle will it reach, with respect to the vertical, before falling back down?     39.5 degrees     33.8 degrees     35.1 degrees     43.9 degrees

When you put on the brakes on your bicycle, friction heats the steel rims of your wheels. Could this heating be a problem? Suppose a 65 kg cyclist with a 15 kg bike is descending Trail Ridge Road in Rocky Mountain National Park, going down a 7.0% grade and thus losing 7.0 m in height for every 100 m oftravel along the road. If the cyclist keeps a constant speed of 6.0 m/s, and we assume that all of the “lost” energy ends up as thermal energy in the two steel rims, each of mass 0.80 kg, by how much does the temperature of each rim rise in 1.0 minute?

A weightlifter curls a 26 kg bar, raising it each time a distance of 0.65 m . How many times must he repeat this exercise to burn off the energy in one slice of pizza?  Assume 25% efficiency. Energy content of one slice of pizza is 1260  kJ

A 150-g particle on the inside of a smooth hemispherical bowl of radius R 35.0 cm (see the figure below) is released from point A at rest. Its speed at B is 1,10 m/s. (a) What is its kinetic esergy at B? T h (b) How much mechanical energy is lost as a result of friction as the particle goes from A to B2 (c) Is it possible to determine u from these results in a simple manner? O Yes O No Explain. ..

When you skid to a stop on your bike, you can significantly heat the small patch of tire that rubs against the road surface. Suppose a person skids to a stop by hitting the brake on his back tire, which supports half the 80 kg combined mass of the bike and rider, leaving a skid mark that is 40 cm long. Assume a coefficient of kinetic friction of 0.80. How much thermal energy is deposited in the tire and the road surface?

A typical coal-fired power plant burns 340 metric tons of coal every hour to generate 2.5 × 106 MJ of energy. One metric ton has a mass of 1000 kg and a metric ton of coal has a volume of 1.5 m^3. The heat of combustion is 28 MJ/kg. What is the power plant’s efficiency?

a rock with mass0.15kg is placeedin a sling shot and the elastic band of the sling shot is stretched by 70 cm from its relaxed position to store elastic potential energy in it. the spring constant of the elastic band is 28,5 N . the elastic band is then released to launched the rock. what is the speed of the rock when it leaves the sling shot if  a) no heat is produced when the Celtic band is released? b: 2.8 J of heat energy are produced when the elastic band is released?

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

Let W = (2.70 ✕ 105 J) ln(Vf /Vi). Solve for the unknown quantity in each of the following cases:   (a) the final volume Vf is three times the initial volume Vi  W= ______Joules (b) the initial volume is 1.00 m3 and the work W is 3.25 ✕ 105 J Vf =  ______ m3