Engineering Mechanics

Problem
A train is moving at the rate of 8 mi/h along a piece of circular track of radius 2500 ft. Through what angle does it turn in 1 min?

Situation
The three-hinged arch shown below is loaded with symmetrically placed concentrated loads as shown in the figure below.
 

The loads are as follows:
$$P_1 = 90 ~ \text{kN} \qquad P_2 = 240 ~ \text{kN}$$
 

The dimensions are:
$$H = 8 ~ \text{m} \qquad S = 4 ~ \text{kN}$$
 

Calculate the following:
 

1.   The horizontal reaction at A.

2.   The total reaction at B.

3.   The vertical reaction at C.

Problem
A 150 g ball at the end of a string is revolving uniformly in a horizontal circle of radius 0.600 m. The ball makes 2 revolutions in a second. What is the centripetal acceleration?

Problem
What is the angle between zero-based vectors ${\bf V_1} = (-\sqrt{3}, ~ 1)$ and ${\bf V_2} = (2\sqrt{3}, ~ 2)$ in an x-y coordinate system?

Problem
Compute the value of b if A and B are orthogonal.
$${\bf A} = 2{\bf i} + b{\bf j} + {\bf k}$$

$${\bf B} = 4{\bf i} - 2{\bf j} - 2{\bf k}$$

Problem
A catapult is placed 100 ft from the castle wall, which is 35 feet high. The soldier wants the burning bale of hay to clear the top of the wall and land 50 feet inside the castle wall. If the initial velocity of the bale is 70 feet per second, then at what angle should the bale of hay be launched so that it travel 150 feet and pass over the castle wall. Use g = 32 ft/sec².
 

Situation
Diagonals BG, CF, CH, and DG of the truss shown can resist tension only.
 

If W = 3 kN and P = 0, find the following:
1.   the force in member CF.

2.   the force in member BF.

3.   the force in member DH.

Situation
Flexible cables BE and CD are used to brace the truss shown below.
 

1.   Determine the load W to cause a compression force of 8.9 kN to member BD.

2.   Which cable is in tension and what is the tensile reaction?

3.   If W = 20 kN, what will be the tensile reaction of member CE?