Find the kinematic diagram for time vs velocity
Question: The time vs velocity diagrams of a 10-kg object for \(x\) and \(y\) directions are given as shown. Describe […]
An elliptical orbit evolving a star: Kepler’s second law
Question: A planet orbits a star in an elliptical orbit. The distance at aphelion is \(2a\) and the distance at […]
Find the gravitational field at height from the surface of a planet
Question: Find the magnitude of the gravitational acceleration near the surface of a planet of radius \(R\) at height, \(h\) […]
Solve the spring motion with the law of conservation of energy
Question: A pendulum bob is released from the height of \(h\) to hit a spring that creates the force \(F=-kx-bx^3\) […]
Find the equation for a linear line, by knowing the coordinates of two points
Question: A line goes through points (-3, 9) and (2, 4). Find the equation of the linear line. Answer: There […]
The tidal force that the Moon causes on the Earth’s ocean
Question: The gravitational force between the moon and Earth creates a tidal force. From the figure, \(a\) is the distance […]
Find the gravitational field of a hollow sphere
Question: A hollow sphere has region \(a<r<b\) filled with mass of uniform density \(\rho\). Find the magnitude of the gravitational […]
Find the half life of radio active decay
Question: Find the half life for the process of radioactive decay. Assume that \(\lambda\) is the decay constant. Answer: The […]
Kepler’s law toward a binary-star system
Question: Consider a binary star system to find the mass of the stars. The distance between them is found out […]
Inequality relationship between trigonometric functions
Question: (1) The range of \(x\) is: \(0^o \leq x \leq 180^o\). Solve \(\cos^4 x > \sin^4 x\). (2) The […]