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.