Non-conservative Forces: Mathematical Solution

Non-conservative Forces: Mathematical Solution

For an object in the gravitational field of the Earth, the mechanical system is the object and the Earth. The force [interaction] is described by…
Potential Energy: Mathematical Solution

Potential Energy: Mathematical Solution

Example: A steelball with mass in = 0.44 kg and radius r = 1.0 cm moves along a rollercoaster. Seven photogates are placed along the…
Work-Kinetic Energy: Mathematical Example

Work-Kinetic Energy: Mathematical Example

Example: An object with mass m = 3.2 kg sits on an incline plane at an angle θ = 23°. The object slides down the…
Explain Work-Kinetic Energy

Explain Work-Kinetic Energy

We start from the kinematics equation in one dimension with time eliminated, v2 – v02 = 2aΔx. We multiply by the mass of the object…
Uniform Circular Motion: Mathematical Solution

Uniform Circular Motion: Mathematical Solution

Example 1: An object goes around a vertical circular track, as shown. Find the minimum speed of the object near the top of the loop,…
What is Uniform Circular Motion?

What is Uniform Circular Motion?

In uniform circular motion, the object travels with constant speed v along a fixed circular trajectory with radius r. The speed and radius determine the…
What is Gravitational Force?

What is Gravitational Force?

The weight W = mg is the gravitational force that the Earth exerts on an object with mass (m). In general, there is an attractive…
Motion in 2 Dimension: Mathematical Examples

Motion in 2 Dimension: Mathematical Examples

Example 1: A projectile is launched with V0 = 19.2 m/s at angle θ0 = 38.7°. a) Does the projectile `clear’ a 3.0 m- high…
Motion in 1 Dimension: Mathematical Examples

Motion in 1 Dimension: Mathematical Examples

Example 1: Emmy starts at time t = 0 and drives along a straight path: she starts at point A, drives straight to point B,…
What are Units in Mathematical Tools?

What are Units in Mathematical Tools?

Physical quantities are measured using instruments; a meter stick for length (L), a clock for time (T), and a balance scale for mass (m). Thus,…
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