Answer to Question #164271 in Mechanics | Relativity for Yamana

Question

A loading car, as given in figure, is at rest on a track forming an angle of 25° with the vertical.

The gross weight of the car and its load is 5000 lb, and it is applied at a point 30 in. from the 

track, halfway between the two axles. The car is held by a cable attached 24 in. from the track. 

Determine the tension in the cable and the reaction at each pair of wheels

Answer 1

Step 1: Free-Body Diagram

1. For convenience, we choose:

• x-axis parallel to the track

• y-axis perpendicular to the track

2. The reaction at each wheel is perpendicular to the track.

3. The tension force T in the cable is parallel to the track.

4. The 5500 lb weight can be resolved into components:

$Wx = +5500 cos 25^○ = +4980 lb \\Wy = −5500 sin 25^○ = −2320 lb$

Step 2: Equilibrium Equations

.

Taking the moments about A to eliminate T and R1 :

$Ç ∑MA = 0 :$  

$−( 2320 lb )(25 in.) − ( 4980 lb)( 6 in.) + R2 ( 50 in.) = 0$

$R2 = +1758 lb , R2 = 1758 lb .$

Taking the moments about B to eliminate T and R2 :

$+ Ç ∑MB = 0$  

$(2320 lb )( 25 in.) − ( 4980 lb )( 6 in.) − R1 ( 50 in.) = 0$

$R1 = +562 lb , R1 = 562 lb$

The value of T is found by:

$+ \ ∑Fx = 0 : \\+4980 lb −T = 0$

$T = +4980 lb , T = 4980 lb Ç$

Verifying:

$∑Fy = 0 : \\+562 lb + 1758 lb − 2320 lb = 0$