Classical Mechanics Answers

Question #170676

Calculate the divergence of the following vector functions:

Vb = xy X +2yzY +3zx Z

Calculate the resultant vector for the following forces:

1)     N = 8.9/ Direction = 39.0˚

F_{R =}

2)     N = 15.5/ Direction = -149.1˚

F_{R =}

Estimate the number of gallons of gasoline consumed by the total of all automobile drivers in the U.S., per year. (There are about 3 x 108 people in the U.S. Assume that half of them have cars, that they drive an average of 12,000 miles per year, and that their cars get an average of 20 miles per gallon of gasoline.)

A cliff is 20 m above the ground. A boy rolls a ball off the edge with an unknown initial velocity and it strikes the ground a distance of 3 m horizontally away. Calculate (a) the ball’s initial velocity, (b) its time of flight, and (c) the magnitude and direction of its velocity when it strikes the ground

A boy walked 22 m East, then 43 m West, and then 3 m East. What is total distance travelled and displacement?

  1. Speed is 72 km/h. Convert km/h to m/s.

Ans.:

What force parallel to the inclined is required to push a 40 kg up on a 50^o inclined plane if the coefficient of friction (static) is 0.3.

The same boat (𝑣𝐵𝑊 = 1.85 𝑚/𝑠 ) now heads directly across the river whose current is still 1.2 𝑚/𝑠. 

Figure 3 shows a 200 N block that sits on a frictionless incline at an angle 30°. This

box is connected by a relatively massless string, over a frictionless pulley, and finally

connected to a second block.

(a) Identify all the forces acting on the block and draw them separately.

(b) If the system is in equilibrium, determine the:

(i) weight of the second block.

(ii) normal force exerted on the first block.