Physics and Chemistry Basics: A Comprehensive Guide
Physics
Dynamics
Momentum and Impulse
A body of mass 14 kg with a velocity of 3 m/s applies a constant force in the same direction as the velocity for 1 second. If the body’s final velocity is 9 m/s, calculate the initial and final momentum (P0, P) and the applied force.
A) Momentum Calculation:
P0 = m * v = 14 kg * 3 m/s = 42 kg m/s
P = m * v = 14 kg * 9 m/s = 126 kg m/s
B) Impulse Calculation:
I = P – P0 = 126 kg m/s – 42 kg m/s = 84 kg m/s
I = F * t
F = I / t = 84 kg m/s / 1 s = 84 N
Newton’s Third Law
Newton’s Third Law states: For every action, there is an equal and opposite reaction.
Collisions on Ice
Two friends stand at rest on an ice rink. One friend with a mass of 50 kg pushes the second friend, who has a mass of 60 kg, with a force of 60 N. Calculate the acceleration reached by each.
Friend 1:
F = m * a
60 N = 60 kg * a
a = 60 N / 60 kg = 1 m/s²
Friend 2:
F = m * a
-60 N = 50 kg * a
a = -60 N / 50 kg = -1.2 m/s²
Tennis Ball Impact
A tennis player hits a 125 g (0.125 kg) tennis ball with their racket. The ball reaches a speed of 12 m/s and returns in the opposite direction at 20 m/s. If the force applied by the player is 400 N, calculate the time of contact between the racket and ball.
Ft = mv – mv0
400 N * t = (-20 m/s * 0.125 kg) – (12 m/s * 0.125 kg)
400 N * t = -2.5 kg m/s – 1.5 kg m/s
400 N * t = -4 kg m/s
t = -4 kg m/s / 400 N = 0.01 s
Forces and Friction
Horizontal and Inclined Planes
- Horizontal Plane
- Inclined Plane
- Linked Masses
- Dynamics of Rotation
Friction
Friction forces oppose motion and are produced between the ground and a body. The force of friction depends on the nature of the surfaces and is calculated using the coefficient of friction (static or dynamic).
Example: Cabinet on a Horizontal Surface
A force is applied horizontally to an 80 kg cabinet at rest on a horizontal surface. Determine if it will move or remain at rest. Calculate the force of friction in these cases:
A) F = 250 N
B) F = 325 N
Coefficient of friction (μ) = 0.25
Fr = μ * N = μ * m * g = 0.25 * 80 kg * 9.8 m/s² = 196 N
Case A: F = 250N > Fr = 196 N (The cabinet moves)
Net Force = 250 N – 196 N = 54 N
a = F / m = 54 N / 80 kg = 0.675 m/s²
Circular Motion
Centripetal force (Fc) is the force that keeps an object moving in a circular path. It is calculated as:
Fc = m * v² / R
Chemistry
Moles and Mass
1 mol = 6.02 x 10²³ particles (atoms, molecules, etc.)
Chemical Reactions
Sodium Chloride Formation
Calculate the mass of chlorine that reacts with 4.02 g of Na, knowing that 10.2 g of sodium chloride is obtained at the end of the reaction.
Mass of Cl = 10.2 g (NaCl) – 4.02 g (Na) = 6.18 g (Cl)
Iron Sulfide Formation
Experimentally, it is found that 5.58 g of iron reacts with 3.21 g of sulfur to form iron sulfide. Calculate the mass of iron required to react with 1.23 g of sulfur.
(5.58 g Fe / 3.21 g S) = (x g Fe / 1.23 g S)
x = (5.58 g Fe * 1.23 g S) / 3.21 g S ≈ 2.14 g Fe
Gas Laws
Boyle’s Law
If the temperature of a gas remains constant, the product of the pressure and volume of the gas also remains constant.
Charles’s Law
If the pressure of a gas remains constant, the volume of the gas is directly proportional to its temperature.
Gay-Lussac’s Law
If the volume of a gas remains constant, the pressure of the gas is directly proportional to its temperature.
Dalton’s Law of Partial Pressures
In a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases.