Seat Belt Buckle
During crash testing of an automobile, the lap and shoulder seat belts develop tensions of 300 lb. Treating the buckle B as a particle, determine the tension T in the anchor strap AB, and the angle at which it acts. (See Figure 4.17)
Approach
We are tasked with finding the magnitude and direction of the tension in the seat belt anchor strap. By treating the buckle as a particle, we can assume that all the force from the shoulder and lap belts act on the anchor strap. The weights of the straps are assumed to be negligible. The free body diagram of the buckle is drawn along with the x-y coordinate system to indicate our sign convention for the positive horizontal and vertical directions. Three forces act on the buckle: the two given 300-lb forces and the unknown force in the anchor strap. For the buckle to be in equilibrium, these three forces must balance. Although both the magnitude T and direction θ of the force in strap AB are unknown, both quantities are shown on the free body diagram for completeness. There are two unknowns, T and θ , and the two expressions in Equation (4.10)
\sum\limits_{i=1}^{N}{F_{x,i}=0}
\sum\limits_{i=1}^{N}{F_{y,i}=0} (4.10)
are available to solve the problem. (See Figure 4.18)
