# 20 physics math equations

To get credit all answers must have work shown

- A baseball of mass 1.23 kg is thrown at a speed of 65.8 mi/h. What is its kinetic energy?
- How much potential energy due to gravity would a person have if they were standing on top of a building that is 45.4 m high? Assume that they have a mass of 94.2 kg.
- Suppose a person pushes a box over a distance of 3.1 m with a constant force of 440.8 N. How much work do they do over this distance?
- Using conservation of energy, how fast would a rollercoaster be traveling at a point half way above the ground where it started from, assuming that is started at rest and 88.3 m above the ground?
- What is the power done by gravity to make a ball of mass 0.6 kg roll from 8.9 m above the ground to the bottom along a curved path if it takes 5.45 s to do so?
- How much momentum does a car of mass 1,940 kg have if it travels at a constant speed of 21.4 m/s?
- A car of mass 1,388 kg traveling at 18.67 m/s collides and sticks to a car with a mass of 1,488 kg. What is the resulting velocity of the two cars right after the collision, assuming that there’s no friction present?
- How much pressure does a box whose sides are 1.17 m long each exert on the ground due to gravity?Assume that the box has a mass of 47.5 kg. HINT: Look at the definition of pressure – what force is doing the “pushing?” What’s the area?
- The Earth’s atmosphere at sea level and under normal conditions has a pressure of 1.01×10
^{5}Pa, which is due to the weight of the air above the ground pushing down on it. How much force due to this pressure is exerted on the roof of a building whose dimensions are 15.7 m long and 13.6 m wide? - Tire gauges for air pressure, as well as most other gauges used in an industrial environment take into account the pressure due to the atmosphere of the Earth. That’s why your car gauge reads 0 before you put it on your tire to check your pressure. This is called gauge pressure.
- A Celsius thermometer reads an outdoor temperature of 16.33
^{o}C. What is this temperature in Fahrenheit? (do not put units into your final answer) - How many degrees Celsius is 92.9
^{o}F? (do not put in units) - 1,776
^{o}C is what in absolute? - An iron rod with an initial length of 12.26 m has its temperature raised from 9
^{o}C to 40.49^{o}C. If iron has a coefficient of thermal expansion of 12×10^{-6}1/^{o}C, what is the change in length of the rod? - Suppose that an ideal gas in a sealed metal container (so it has a fixed volume) has its temperature increased by a factor of 4.68x. By what factor would the pressure of the gas increase or decrease in the container?
- If I add 10,637 J of energy to an ideal gas inside a balloon, causing the internal energy to increase by 6,069 J, how much work is done on the environment by the gas as the balloon expands?
- How much energy is required to raise the temperature of 6.72 kg of water from 29.95
^{o}C to 51.31^{o}C? The specific heat of water in this state is 4186 J/kg-^{o}C. - Suppose that you had water in a pot on a stovetop. Neglecting the material that the pot is made out of, and neglecting heat energy lost use to other processes, how long would it take for a 1000 W stovetop to raise 2.87 kg of water from 94
^{o}C to 9^{o}C? The specific heat of water in this state is 4186 J/kg-^{o}C. HINT: Find the amount of heat first, then look at the equation for power. - An air conditioner uses 11,771 J of energy to run, but only 5,382 J of energy is used to heat or cool the air of a home. What is its energy efficiency?
- An electric generator at a power plant produces energy by passing superheated steam from a high temperature container (reservoir), through a pipe connected to a series of fans, and then into a low temperature reservoir. As the steam passes across the blades of the fans some of the heat energy of the steam is transformed into mechanical energy, which turns the fans which in turn are connected to a generator, which in turn converts the mechanical energy into electrical energy.

The real pressure within a tire or other object containing pressurized stuff would be a combination of what the gauge reads as well at the atmospheric pressure. If a gauge on a tire reads 24.05 psi, what is the real pressure in the tire in pascals? The atmospheric pressure is 1.01×105 Pa.

If the high temperature steam has a temperature of 436.7 K and the low temperature reservoir has a temperature of 106.7 K, what is the Carnot efficiency of this process?