Q: At Niagara Falls, 3000 m³ of water falls a distance of 50 meters every second. If the density of water is $$1000 \ \mathrm{kg/m^3$}$$, what is the power produced by the falling water? (Use $$g = 9.81 \ \mathrm{m/s^2$})$$

$$1.47 \times 10^8$ \ \mathrm{W}$$

Q: Electricity is often measured in kilowatt-hours. What is the SI equivalent of 1 kWh?

$$3.6 \times 10^6$ \ \mathrm{J}$$

Question 1

Which of the following best describes the energy transformation performed by the sun as a machine?

Accepted Answer

Nuclear energy into radiative energy (heat/photons)

Question 2

Living organisms can act as machines by transforming energy. Which of the following is NOT a typical energy transformation performed by living organisms?

Accepted Answer

Mechanical energy to nuclear energy

Question 3

The SI unit of power is the watt. Which of the following is the correct definition of power in terms of energy and time?

Accepted Answer

$$P = \frac{\Delta E}{\Delta t}$$

Question 4

At Niagara Falls, 3000 m³ of water falls a distance of 50 meters every second. If the density of water is $$1000 \ \mathrm{kg/m^3$}$$, what is the power produced by the falling water? (Use $$g = 9.81 \ \mathrm{m/s^2$})$$

Accepted Answer

$$1.47 	imes 10^8$ \ \mathrm{W}$$

Question 5

Electricity is often measured in kilowatt-hours. What is the SI equivalent of 1 kWh?

Accepted Answer

$$3.6 	imes 10^6$ \ \mathrm{J}$$

Question 6

In rotational motion, what is the rotational analog of Newton's Second Law $$F = ma$$?

Accepted Answer

$$\sum 	au = I \alpha$$

Question 7

What is the rotational analog of force $$F in $$rotational dynamics?

Accepted Answer

$$	au = F R \sin 	heta$$

Question 8

A small mass $$m is $$revolving around an axis at a radius $$R. If $$you apply a tangential force $$F_{tan}$$, what is the tangential component of Newton's Second Law?

Accepted Answer

$$F_x = m a_x$$

Question 9

Given a mass $$m$$ revolving at a constant speed $$v in a $$circle of radius $$R$$, what is the kinetic energy of the mass?

Accepted Answer

$$K = \frac{1}{2} m v^2$

Question 10

What is the equivalent expression for kinetic energy in terms of rotational equations for a mass $$m at $$radius $$R$$ rotating with angular velocity $$\omega$$?

Accepted Answer

$$K = \frac{1}{2} I \$$omega^2$$

Question 11

If $$I = m R^2$ for a point mass revolving at radius R$, what is the relationship between torque $$	au$$, force F$, and radius R$?

Accepted Answer

$$	au = F R \sin 	heta$$

Question 12

A machine converts 100 Joules of energy in 5 seconds. What is its power output?

Accepted Answer

$$20 \ \mathrm{W}$$

Question 13

Which of the following is the correct SI unit for power?

Accepted Answer

$$\mathrm{kg \ m^2$ / s^3$}$$

Question 14

If a force $$F is $$applied tangentially to a mass $$m at $$radius $$R$$, what is the resulting angular acceleration $$\alpha$$?

Accepted Answer

$$\alpha = \frac{F R}{I}$$

Question 15

A rotating disk has a moment of inertia $$I$$ and angular velocity $$\omega. $$What is its rotational kinetic energy?

Accepted Answer

$$K = \frac{1}{2} I \$$omega^2$$

Question 16

Which of the following best describes the process of photosynthesis in terms of energy transformation?

Accepted Answer

Radiative energy to chemical energy

Question 17

A machine is characterized by its power. If it transforms $$\Delta E$$ energy in $$\Delta t$$ time, which equation correctly expresses its power?

Accepted Answer

$$P = \frac{\Delta E}{\Delta t}$$

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