Since it is known that the pouring time (T) of the sand in an hourglass depends on the height of the sand before it is poured (H), the density of the sand (ρ), the hole diameter (d) and the gravitational acceleration (g), obtain the phenomenon with the Buckingham pi theorem.

Q: Suppose that a particle follows the cycloid x = x(t) = 1 – cos(t) y = y(t) = t – sin(t). Determine…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: A particle is under the influence of the force F= (-cosh (4x4) + xy)i + (e-y + x)j. The corner…

A:

Q: A particle of mass m is moving under the force of attraction of another particle of mass m1 at a…

A: When a force F is applied to an object of mass m, the position of body changes. According to…

Q: Exercise 4. Show that if a has unit speed, i.e., |la'(t)|| = 1, then its velocity and acceleration…

A: We will prove the following result.

Q: 12) Find the force on a submerged gate shaped as a parabola 12m high and 8m across its top if the…

A: Here we will use the concept of pressure applied on the parabolic surface. Based on the given…

Q: A uniform sphere of mass m rolls from rest at A along a frictionless hemispherical surface, under…

A: Consider the given figure as

Q: A 68 kg skydiver jumps out of an airplane. We assume that the forces acting on the body are the…

A: Given, Force of gravity acting on the 68 kg skydiver, Fg=mg (downward) Force due to air resistance,…

Q: A sodium ion (Na+) moves in the xy-plane with a speed of 2.90 ✕ 103 m/s. If a constant magnetic…

A:

Q: a) The position of point moving in space is given by R(t) = 3 tan t i + cott j +2 lnt k, find the…

A:

Q: Find the unit tangent vector at the indicated point of the vector function T(π/2) = ( r(t) = e²t…

A:

Q: Without findingT and N, write the acceleration of the motion r(t)=(cost+t sint)i+(sint-tcost)j, in…

A:

Q: Assume it to be approximately an annular ring with an inner radius of R, = 0.280 m and an outer…

A: Here, R1 = 0.280 m R2 = 0.4 m m = 11Kg moment of inertia of wheel , I = 0.5 * m * (R1^2 + R2^2) I =…

Q: A cable exerts a constant upward tension of magnitude 2.14 ✕ 104 N on a 2.00 ✕ 103 kg elevator as it…

A: A cable exerts a constant upward tension of magnitude 2.14 ✕ 104 N on a 2.00 ✕ 103 kg kg elevator as…

Q: (a) Show that the change in momentum over a time interval [to, t1] is equal to the integral of F…

A:

Q: A 600-lb cable is 100 ft long and hangs vertically from the top of a tall building. (a) How much…

A: We are given a cable of 100 ft with weight 600lb. We need to find the work done by lifting the cable…

Q: Let F be the fluid force on a side of a semicircular plate of radius r meters, submerged vertically…

A: Given: Radius of the submerged plate is r. (a) The figure below represents a schematic diagram.…

Q: The automobile has a mass of 2 Mg and the center of mass at G. Determine the towing Q3 30 force F…

A:

Q: Let W be the work (against the Sun’s gravitational force) required to transport an 80-kg person from…

A:

Q: The figure shows the side view of a portable traffic signal. The upper portion of the signal with…

A: The objective of this question is to determine the necessary input force F that will just start to…

Q: Q1: Consider an electromagnetic (EM) in free space whose electric field is given by E = 60 exp [-i…

A:

Q: An infinitely long, thin, massive cylinder exerts a gravitational force of 14OUm newtons on any…

A: Given: Gravitational force = = 1400r ln 3 729 meters from the cylinder's axis and starts moving away…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.