Kinetic Energy, Heat Transfer, and Algebraic Equations

Kinetic Energy and Potential Energy

Kinetic Energy (KE) Calculation:

A body with a mass of 50kg has a velocity of 20 m/s.

KE = (1/2) * M * V²

KE = (1/2) * 50kg * (20 m/s)²

KE = (1/2) * 50 * 400

KE = 10000 Joules

Total Energy Calculation:

A body with a mass of 5kg is at a height of 10m and moving at a speed of 20 m/s. Calculate its total energy.

Mass (M) = 5kg

Height (H) = 10m

Velocity (V) = 20 m/s

Potential Energy (PE) = M * g * H = 5kg * 9.8 m/s² * 10m = 490 Joules

Kinetic Energy (KE) = (1/2) * M * V² = (1/2) * 5kg * (20 m/s)² = 1000 Joules

Total Energy = KE + PE = 1000 Joules + 490 Joules = 1490 Joules

Heat Transfer and Temperature Conversion

Kelvin to Celsius Conversion:

How to convert 300 Kelvin to Celsius, as applicable to converting 100 Celsius to Kelvin.

K = °C + 273.15

To convert Celsius to Kelvin: K = 273.15 + °C

Example: 100°C = 273.15 + 100 = 373.15 K

To convert Kelvin to Celsius: °C = K - 273.15

Example: 300 K = 300 - 273.15 = 26.85°C

Heat Conduction and Convection:

Heat conduction is the process of heat transfer through a material by direct contact. Convection is the process of heat transfer through a fluid (liquid or gas) by the movement of the fluid itself. For example, hot air rises during the daytime due to convection.

Heat Calculation:

Calculate the amount of heat required to raise the temperature of a 5g body with a specific heat of 0.23 cal/g·K from 10°C to 15°C.

Q = M * c * ΔT

Q = 5g * 0.23 cal/g·K * (15°C - 10°C)

Q = 5 * 0.23 * 5

Q = 5.75 calories

Joule to Calorie Conversion:

1 Joule = 0.24 calories

Convert 200 calories to Joules:

X Joules = 200 calories

X = 200 / 0.24 = 833.33 Joules

Electronvolt to Joule Conversion:

1 eV = 1.6 x 10^-19 Joules

Convert 50 Joules to electronvolts:

X eV = 50 Joules

X = 50 / (1.6 x 10^-19) = 3.125 x 10²⁰ eV

Algebraic Equations

Solving Linear Equations:

Is X = 2 a solution of the equation 3X + 4 - X = 7X + 1?

3X + 4 - X = 7X + 1

3X - X - 7X = 1 - 4

-5X = -3

X = -3 / -5 = 0.6

Therefore, X = 2 is not the answer.

Equation Equality:

Indicate if 3[X + 2] - 4 = 2[X + 1] + X is an equation equality.

3[X + 2] - 4 = 2[X + 1] + X

3X + 6 - 4 = 2X + 2 + X

3X + 2 = 3X + 2

3X - 2X - X = 2 - 6 + 4

0 = 0

This is an equality.

Word Problems

Age Problem:

A father is 36 years old and his son is 10 years old. In how many years will the father's age be double the son's age?

Father's age: 36 + X

Son's age: 10 + X

36 + X = 2(10 + X)

36 + X = 20 + 2X

X = 36 - 20

X = 16 years

Velocity Problem:

A car has a velocity V. A bus's velocity is half that of the car plus 10 km/h, and a motorcycle's velocity is triple that of the bus. If the car is traveling at 120 km/h, what are the velocities of the bus and motorcycle?

Car (V) = 120 km/h

Bus = V/2 + 10

Motorcycle = 3 * (V/2 + 10)

Bus = (120/2) + 10 = 60 + 10 = 70 km/h

Motorcycle = 3 * (120/2 + 10) = 3 * (60 + 10) = 3 * 70 = 210 km/h

Money Problem:

If you paid me double what I have now plus 10, it would be 60.

2x + 10 = 60

2x = 60 - 10

2x = 50

x = 50 / 2

x = 25

Apple Basket Problem:

Three baskets have a total of 575 apples. The first basket has 10 more apples than the second, and the second has 15 more than the third. How many apples are in each basket?

Let x be the number of apples in the first basket.

First basket: x

Second basket: x - 10

Third basket: x - 10 - 5 = x - 15

x + (x - 10) + (x - 15) = 575

3x - 25 = 575

3x = 600

x = 200

• First basket: 200 apples
• Second basket: 190 apples
• Third basket: 185 apples