Notes, summaries, assignments, exams, and problems for Physics

Law of Gravitation

Every object in the universe that has mass exerts a gravitational attraction on other objects with mass, regardless of the distance between them. According to this law, more massive objects exert a greater force of attraction. In parallel, the closer objects are, the greater the force, following an inverse square law.

Considering two masses whose size is small compared with the distance that separates them, we can summarize this in an equation or law that states that the force exerted by a given object with mass m1 on one with mass m2 is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.

A force is central where the position vector r is parallel to the force... Continue reading "Fundamental Physics Concepts Explained" »

44. (a) The Young’s modulus is given by

(b) Since the linear range of the curve extends to about 2.9 × 10⁸ N/m², this is approximately the yield strength for the material.

46. Since the force is (stress × area) and the displacement is (strain × length), we can write the work integral (eq. 7-32) as

  W =

  = A (differential strain)L  = AL (differential strain)

which means the work is  (wire-area) × (wire-length) × (graph-area-under-curve).  Since the area of a triangle (see the graph in the problem statement) is  (base)(height)  then we determine the work done to be

            W = (2.00 x 10^-6 m²)(0.800 m)(1.0 × 10^-3)(7.0 × 10⁷ N/m²) = 0.0560 J .

48. 46. Since the force is (stress × area) and the displacement is (strain... Continue reading "Young's Modulus and Material Strength Calculations" »

Understanding Energy Forms

• A circulating car: Kinetic energy.
• A shining light bulb: Thermal and light energy.
• A book on a library shelf: Potential energy.
• A cat chasing a mouse: Kinetic energy.

Kinetic Energy Calculation: Bullet Example

A bullet with a mass of 15 g moving at 50 m/s.

The formula for kinetic energy (Ec) is:

Ec = 1/2 * m * v2

Calculation:

Ec = 1/2 * 0.015 kg * (50 m/s)2 = 18.75 J

Potential Energy Calculation: Crane Example

The formula for gravitational potential energy (Ep) is:

Ep = m * g * h

Calculation for a 350 kg object lifted 7 m (assuming g = 10 m/s²):

Ep = 350 kg * 10 m/s2 * 7 m = 24,500 J

Energy Transformations in Action

Observe the following scenarios and identify who loses/gains energy and the types of energy involved:

• Launching an Arrow

Abbe Operation

Abbe Operation is based on the determination of the critical angle. The technique is to calibrate the device, usually with distilled water at 20ºC, by matching the shade formed by the prism surface illuminated by a brand (not recorded) in the center of the telescope. Perform the same operation with the test sample to make the correct reading of the refractive index in the eyepiece of the telescope. Since the refractive index varies with temperature, it is important to perform the measurement with the apparatus thermostatted at 20°C or at least know the temperature at which to make the determination.

Understanding Light Polarization

• Natural Light: It is a vibration in all directions perpendicular to the beam.
• Polarized Light: It