Linear Impulse and Momentum Problem No. 2

The crate shown has a weight of 50 lb and is acted upon by a force having a variable magnitude P=(20t) lb, where t is in seconds. Compute the crate's velocity 2 s after P has been applied. The crate has an initial velocity V₁=3 ft/s down the plane, and the coefficient of kinetic friction between  the crate and the plane is U_k=0.3.

Figure

Linear Impulse and Momentum Problem No.1

The 100-kg crate shown is originally at rest on the smooth horizontal surface. If a force of 200 N, acting at an angle of 45°, is applied to the crater for 10-s, determine the final velocity of the crate and the normal force which the surface exerts on the crate during the time interval.

Figure

Kinetics of a Particle: Impulse and Momentum

Principle of Linear Impulse and Momentum

The equation of motion for a particle of mass m can be written as:

where a and ν are both measured from an inertial frame of reference. Rearranging the terms and integrating between the limits ν=ν₁ at t=t₁ and ν=ν₂ at t=t₂, we have:

or

Vector Analysis Problem No.2

Given the vector field F=0.4(y-2x)ax-[200/(x²+y²+z²)]az; (a) evaluate |F| at P(-4,3,5); (b) find a unit vector specifying the direction of F at P. Describe the locus of all points for which: (c) Fx=1; (d) |Fz|=2.

Vector Analysis Problem No.1

Given the two vectors r_A= -ax-3ay-4az and r_B= 2ax+2ay+2az, and point C(1,3,4), find: (a) R_AB; (b)|r_A|; (c)a_A; (d)a_AB; (e) a unit vector directed from C toward A.

Basic Electrical Theory

Electrical Circuit

Electric circuit theory and electromagnetic theory are the two fundamental theories upon which all branches of electrical engineering are built. Many branches of electrical engineering, such as power, electric machines, control, electronics, communications, and instrumentation, are based on electric circuit theory. Therefore, the basic electric circuit theory course is the most important course for an electrical engineering student, and always an excellent starting point for a beginning student in electrical engineering education. Circuit theory is also valuable to students specializing in other branches of the physical sciences because circuits are a good model for the study of energy systems in general, and because of the applied mathematics, physics, and topology involved. In electrical engineering, we are often interested in communicating or transferring energy from one point to another. To do this requires an interconnection of electrical devices. Such interconnection is referred to as an electric circuit, and each component of the circuit is known as an element.