SPH3U Unit 3: Energy and Society

Comprehensive flashcards covering Work, Kinetic and Gravitational Potential Energy, Conservation of Mechanical Energy, Power, Energy Efficiency, and Thermal Energy Heat Exchange.

How is energy defined in physics, and what is its standard SI unit?

Energy is the ability to do work, representing a force applied over a distance. The SI unit for energy is the Joule ($\text{J}$), where $1\,\text{J} = 1\,\text{N} \cdot 1\,\text{m}$.

What is the primary difference between potential energy and kinetic energy?

Potential energy is energy stored in an object due to its position relative to other objects, whereas kinetic energy is the working form of energy that an object possesses because of its motion.

What formula is used to calculate the kinetic energy ($E_k$) of an object?

$E_k = \frac{1}{2}mv^2$, where $m$ is mass in kilograms ($\text{kg}$) and $v$ is velocity in meters per second ($\text{m/s}$).

Why can electrical energy be classified as both potential energy and kinetic energy?

It is potential energy when electrons are stationary in an open circuit waiting to move from the electrical panel to the outlet, and kinetic energy when a device is plugged in, closing the circuit and allowing electrons to move.

What are the seven types of electromagnetic radiation that carry radiant energy, ranked from lowest to highest energy?

From lowest to highest energy: Radio Waves, Microwaves, Infrared, Visible light, Ultraviolet, X-rays, and Gamma rays.

What three conditions must be met for mechanical work ($W$) to be done on an object?

A force must be applied, the object must undergo displacement, and a component of the applied force must be in the direction of motion ($W = F\cos(\theta)\Delta d$).

A tourist pulls luggage with a force of $55\,\text{N}$ at an angle of $55^\circ$ from the horizontal over a displacement of $125\,\text{m}\text{ [E]}$. How much work is performed?

$W = F\cos(\theta)\Delta d = (55\,\text{N})\cos(55^\circ)(125\,\text{m}) = 3.9 \times 10^3\,\text{J}$.

A warehouse worker lifts an $11.6\,\text{kg}$ box vertically $97.5\,\text{cm}$, carries it horizontally $11.2\,\text{m}$ at constant speed, and places it back onto the floor. How much work is done to lift the box, and what is the total work done overall?

Work done to lift the box is $W = mg\Delta d = (11.6\,\text{kg})(9.81\,\text{m/s}^2)(0.975\,\text{m}) = 111\,\text{J}$. Total work is $0\,\text{J}$ because carrying it horizontally applies force perpendicular to motion ($\cos(90^\circ) = 0$), and lowering it back down does negative work of equal magnitude.

A worker pushes two stacked boxes with a combined mass of $26\,\text{kg}$ across a concrete floor ($\mu_k = 0.26$) at a constant velocity for $4.5\,\text{m}$. How much work is done?

$W = F_{\text{app}}\Delta d = \mu_k mg\Delta d = (0.26)(26\,\text{kg})(9.81\,\text{m/s}^2)(4.5\,\text{m}) = 3.0 \times 10^2\,\text{J}$.

A curler applies $22.0\,\text{N}$ of force to a curling stone, accelerating it from rest to $3.10\,\text{m/s}$ in $2.10\,\text{s}$. How much work does the curler do on the stone?

Displacement is $\Delta d = \left(\frac{v_f + v_i}{2}\right)\Delta t = \left(\frac{3.10\,\text{m/s} + 0}{2}\right)(2.10\,\text{s}) = 3.26\,\text{m}$. Work done is $W = F\Delta d = (22.0\,\text{N})(3.26\,\text{m}) = 71.7\,\text{J}$.

How is total mechanical energy ($E_m$) defined mathematically?

Mechanical energy is the sum of an object's kinetic energy and its gravitational potential energy: $E_m = E_k + E_g$.

An asteroid with a mass of $7.34 \times 10^3\,\text{kg}$ travels at $3.59 \times 10^3\,\text{m/s}$. How much kinetic energy does it possess, and how many sticks of dynamite ($1.0 \times 10^6\,\text{J}$ each) possess equivalent energy?

The asteroid possesses $E_k = \frac{1}{2}(7.34 \times 10^3\,\text{kg})(3.59 \times 10^3\,\text{m/s})^2 = 4.73 \times 10^{10}\,\text{J}$. This equals $4.73 \times 10^4$ sticks of dynamite.

A .308 Winchester fires an $11.66\,\text{g}$ bullet at $817.8\,\text{m/s}$, while a .300 Winchester Magnum fires the same bullet at $893.1\,\text{m/s}$ through a $0.559\,\text{m}$ barrel. What percentage greater recoil force does the .300 Winchester Magnum produce?

The .308 generates a recoil force of $6.97 \times 10^3\,\text{N}$ ($E_k = 3.89 \times 10^3\,\text{J}$), while the .300 Magnum generates $8.32 \times 10^3\,\text{N}$ ($E_k = 4.65 \times 10^3\,\text{J}$). The shooter experiences $19.3\%$ greater recoil force from the .300 Winchester Magnum.

Based on the diagram, a $2250\,\text{kg}$ roller coaster car starts from rest at Point A ($30\,\text{m}$). Assuming mechanical energy is conserved, what is its maximum speed at ground level?

At Point A, total mechanical energy is $E_g = mgh = (2250\,\text{kg})(9.81\,\text{m/s}^2)(30\,\text{m}) = 662175\,\text{J}$. At the ground, all potential energy becomes kinetic energy: $v = \sqrt{2gh} = \sqrt{2(9.81\,\text{m/s}^2)(30\,\text{m})} = 24.3\,\text{m/s}$.

What does the Law of Conservation of Energy state regarding energy changes in an isolated system and its surroundings?

Energy cannot be created or destroyed; it can only change from one form to another ($\Delta E = 0$). Within any physical system, $\Delta E_{\text{system}} = -\Delta E_{\text{surroundings}}$.

Two high jumpers, one weighing $70\,\text{kg}$ and the other $68\,\text{kg}$, leave the ground with an initial vertical velocity of $4.8\,\text{m/s}$. Which jumper reaches a greater height?

Both jumpers reach the exact same height of $1.17\,\text{m}$. Setting $\frac{1}{2}mv^2 = mgh$ cancels out mass, giving $h = \frac{v^2}{2g} = \frac{(4.8\,\text{m/s})^2}{2(9.81\,\text{m/s}^2)} = 1.17\,\text{m}$.

A $4.15\,\text{kg}$ IKEA Tarno folding chair is dropped from a balcony $92.4\,\text{m}$ above the street. What maximum speed does it reach right before impact?

Using conservation of energy, $v = \sqrt{2gh} = \sqrt{2(9.81\,\text{m/s}^2)(92.4\,\text{m})} = 42.6\,\text{m/s}$.

A hiker standing on a $3.7\,\text{m}$ cliff throws a rock upward at $12\,\text{m/s}$. What is the rock's maximum height above the release point, and what is its maximum speed upon hitting the ground?

The rock reaches a maximum height of $h = \frac{v^2}{2g} = \frac{(12\,\text{m/s})^2}{2(9.81\,\text{m/s}^2)} = 7.3\,\text{m}$ above the release point. Dropping from a total height of $3.7\,\text{m} + 7.3\,\text{m} = 11.0\,\text{m}$, its impact speed is $v = \sqrt{2g(h_{\text{total}})} = 15\,\text{m/s}$.

How is power ($P$) defined in physics, and what units are used to measure it?

Power is a scalar quantity describing the rate at which energy transfer or work occurs: $P = \frac{\Delta E}{\Delta t} = \frac{W}{\Delta t}$. It is measured in Joules per second ($\text{J/s}$), commonly called Watts ($1\,\text{W} = 1\,\text{J/s}$).

A powerlifter raises an $88.5\,\text{kg}$ barbell a vertical distance of $2.10\,\text{m}$ in $0.94\,\text{s}$. How much power did the lifter exert?

$P = \frac{mgh}{\Delta t} = \frac{(88.5\,\text{kg})(9.81\,\text{m/s}^2)(2.10\,\text{m})}{0.94\,\text{s}} = 1.9 \times 10^3\,\text{W}$.

A $60\,\text{W}$ desk light bulb consumes $1.84 \times 10^6\,\text{J}$ of energy before being turned off. How long was the bulb left on?

$\Delta t = \frac{\Delta E}{P} = \frac{1.84 \times 10^6\,\text{J}}{60\,\text{W}} \approx 30667\,\text{s}$, which equals $8.5\,\text{h}$.

How is percent efficiency defined, and what is the efficiency of a $60\,\text{W}$ incandescent bulb that loses $54\,\text{J}$ to thermal energy and $0.8\,\text{J}$ to sound energy each second?

$\%\,\text{Efficiency} = \frac{E_{\text{useful out}}}{E_{\text{in}}} \times 100\%$. The useful light energy output is $60\,\text{J} - 54\,\text{J} - 0.8\,\text{J} = 5.2\,\text{J}$, resulting in an efficiency of $\frac{5.2\,\text{J}}{60\,\text{J}} \times 100\% = 8.7\%$.

A $78\,\text{kg}$ skateboarder rolls down a $6.2\,\text{m}$ ramp and reaches a speed of $5.1\,\text{m/s}$ at the bottom. What is the skateboarder's efficiency?

Input gravitational potential energy is $E_g = mgh = (78\,\text{kg})(9.81\,\text{m/s}^2)(6.2\,\text{m}) = 4744\,\text{J}$. Output kinetic energy is $E_k = \frac{1}{2}(78\,\text{kg})(5.1\,\text{m/s})^2 = 1014\,\text{J}$. The efficiency is $\frac{1014\,\text{J}}{4744\,\text{J}} \times 100\% = 21\%$.

What distinguishes temperature, thermal energy, and heat?

Temperature measures the average kinetic energy of the particles in a substance. Thermal energy is the sum of all kinetic and potential energies possessed by those particles. Heat is the transfer, release, or absorption of thermal energy between substances.

What physical phenomena serve as the reference points for the Celsius, Fahrenheit, and Kelvin temperature scales?

Celsius is based on the freezing ($0^\circ\text{C}$) and boiling ($100^\circ\text{C}$) points of water; Fahrenheit is based on an equal ice:salt mixture ($0^\circ\text{F}$); and Kelvin is based on the total thermal energy possessed by a substance, where $0\,\text{K}$ represents zero particle motion.

What are the three mechanisms of heat exchange, and how do they function?

Conduction is direct energy transfer via colliding particles in physical contact. Convection is energy transfer via the circulating movement of fluid particles (liquids or gases) caused by density differences. Radiation is energy transfer via electromagnetic waves without requiring a medium.

What is specific heat capacity ($c$), and why does beach sand heat up and cool down much faster than ocean water?

Specific heat capacity is the quantity of heat needed to change the temperature of a specific mass by a set amount ($Q = mc\Delta T$). Beach sand has a low specific heat capacity ($c = 800\,\text{J}/(\text{kg}\cdot^\circ\text{C})$), requiring roughly one-fifth the energy of water ($c = 4186\,\text{J}/(\text{kg}\cdot^\circ\text{C})$) to change temperature.

A circuit breaker trips when $3.0\,\text{kg}$ of copper wire ($c = 0.385\,\text{J}/(\text{g}\cdot^\circ\text{C})$) heats from $20^\circ\text{C}$ to $60^\circ\text{C}$. How much excess electrical energy was absorbed by the wire?

$Q = mc\Delta T = (3000\,\text{g})(0.385\,\text{J}/(\text{g}\cdot^\circ\text{C}))(60^\circ\text{C} - 20^\circ\text{C}) = 46200\,\text{J} = 4.62\,\text{kJ}$.

A $4.0\,\text{kg}$ metal bar heated to $100^\circ\text{C}$ is placed into a $100\,\text{g}$ aluminum calorimeter ($c = 920\,\text{J}/(\text{kg}\cdot^\circ\text{C})$) with $500\,\text{g}$ of water ($c = 4186\,\text{J}/(\text{kg}\cdot^\circ\text{C})$) at $20^\circ\text{C}$. If the final equilibrium temperature is $35^\circ\text{C}$, is the bar made of pure gold ($c = 129\,\text{J}/(\text{kg}\cdot^\circ\text{C})$)?

Yes. Heat gained by the water and container is $Q_{\text{gained}} = (0.5\,\text{kg})(4186)(15^\circ\text{C}) + (0.1\,\text{kg})(920)(15^\circ\text{C}) = 32775\,\text{J}$. Setting $Q_{\text{lost}} = -Q_{\text{gained}}$ yields $(4.0\,\text{kg})c(65^\circ\text{C}) = 32775\,\text{J}$, which gives $c \approx 126\,\text{J}/(\text{kg}\cdot^\circ\text{C})$, confirming it is authentic gold or very close to pure.