Finding Tension in Rope Connecting Refrigerator to Truck

[Naeem]

A refrigerator is approximately a uniform parallelepiped h = 7 ft tall, w = 3 ft wide, and d = 2 ft deep. It sits upright on a truck with its 3 ft dimension in the direction of travel. Assume that the refrigerator cannot slide on the truck and that its mass is 100 kg. For the first three parts of this problem, the rope shown in the picture is not there.


Suppose now that a rope connects the top of the refrigerator with the cab of the truck, which now accelerates at twice the acceleration calculated in (c). The refrigerator lifts off slightly at the front but is held in place by the horizontal rope. Find the tension in the rope.

I did as follows:

I need to find two equations and two unknowns, the help says

0 = ma ( h/2) - Th - mg ( w/2)

where w is the width of the fridge, T , tension in the rope, a - acceleration.

Tried to plug in the values, got a wrong answer, Don't know what is wrong.

For the acceleration, I plugged in the doubled value.

Pl. Help!

 

[Naeem]

Can anybody help me with the previous post.

 

[Naeem]

Ok, nobody helped me, but somehow I managed to get the correct answer.

It goes:

0 = ma (h/2) -Th -mg (w/2)
0 = 100 * 8.408 ( 3.5 /2) - T (7) - [ 100 * 9.81 ( 3/2) ] ( w - width of fridge ), also plug in double the value for acceleration from part c. which was 4.204 , now 4.204 * 2 = 8.408 m/s2.

Cranked it out and got tension to be T = 210.18 N

Thanks for looking !