A trailer weighing 2400 lb is attached to a 2900 lb SUV by a ball-and-socket tru

Question

A trailer weighing 2400 lb is attached to a 2900 lb SUV by a ball-and-socket truck hitch at D as shown in the image below. The 1400 lb load is currently placed in the trailer such that the center of mass of the trailer is coincident with the center of mass of the load. Where should the center of mass of the load be placed such that the trailer might be able to balance over its axle and the force in the y-direction of the trailer on the SUV might be minimized when at rest? Assume that the load must remain in the trailer and that the center of mass cannot be adjusted in the y and z direction.

Explanation / Answer

solution:

1)here given data as follows

weigh of trailer=2400 lb

weigh of load=1400 lb

distane of CG from axle of trailer is L1=2 ft

distance of load is currently placed at distance x ft on opposite side of axle

2)load should be placed in trailer such that it should cause any rotation of trailer around axle so we can write as

Moment about axle=Ma=0

2400*L1=1400*x

L1=2 ft

on putting value we get that

x1=3.4285 ft left from axle or x=6-x1=2.5714 ft and its CG point will now shift over axle

so for perfect balancing on axle load should be placed at distance of x=3.4285 ft left from axle where CG is on right side of axle at L distance.

3)here let consider beam which is loaded by weight of trailer at x=8 ft and load is placed at x=2.5714 ft and it will cause reaction to generate at axle as Rb and at joint of SUV and trailer as Rc

for zero moment at joint we get reaction at axle as

Mc=0

Rb*(17-6)-2400*(17-8)-1400*(17-2.5714)=0

Rb=3800 lb

for Mb=0

Rc*(17-6)-2400*(8-6)+1400*(6-2.5714)=0

Rc=0 lb

in this way by balancing load over axle y direction force get minimize from initial position and it fall to zero.

4)hence for balancing load should placed on left of axle at distance of x1=3.4285 ft or x=2.5714 ft,it will gives perfect balancing and reduction in reaction at joint of SUV and trailer as Rc=0 lb

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