The last static equilibrium problem.

[akan]

You have been called on to testify in a product liability lawsuit. An infant sitting in a portable seat that is supported by the edge of a table fell to the floor (see the figure). The manufacturer claims the child was too heavy for the seat, and the parents claim the seat was defective. Testing showed that the seat can withstand the weight of a child when the force at A does not exceed 96.2 N and the force at B does not exceed 229 N. The child has a mass of 10 kg. In whose favor should the judge rule?

http://img370.imageshack.us/img370/5152/rw1264ji6.jpg
http://g.imageshack.us/img370/rw1264ji6.jpg/1/

How do I solve this?

 

[tiny-tim]

Hi akan!

Show us what you've tried, and where you're stuck, and then we'll know how to help.

 

[akan]

(x) Sum(F_x) = 0 (no forces)
(y) Sum(F_y) = F_a - F_b - F_child = 0

F_child = mg = 10*9.8 = 98

pivot at B:
(2) Sum(T_z) = F_a * (.22) - F_child (.16) = 0

pivot at C (child):
(3) Sum(T_z) = F_a * (.38) - F_b (.16) = 0

(2) .22 F_a = .16 F_child
(2) F_a = (.16 / .22) F_child = (.16 / .22) (98) = 71.27

(3) (.16 / .22) F_child (.38) = F_b (.16)
(3) F_b = (.38 / .22) F_child = (.38 / .22) (98) = 169.272727

Neither of these exceeds the allowed values, so why is the correct answer "in favor of parents"?

 

[tiny-tim]

judge rules ok!

Neither of these exceeds the allowed values, so why is the correct answer "in favor of parents"?

You have been called on to testify in a product liability lawsuit. An infant sitting in a portable seat that is supported by the edge of a table fell to the floor (see the figure). The manufacturer claims the child was too heavy for the seat, and the parents claim the seat was defective. Testing showed that the seat can withstand the weight of a child when the force at A does not exceed 96.2 N and the force at B does not exceed 229 N. The child has a mass of 10 kg. In whose favor should the judge rule?

Hi akan!

I haven't checked your calculations …

but assuming they're correct, that means that the child would have been safe if the seat was well-made.

Since the child wasn't safe, that proves the seat was defective, and so the judge should rule "in favor of parents".

 

[akan]

The calculations show that the force did not exceed the specifications. Yeah, I guess that means that it's the manufacturer's fault and the seat was flawed. Thanks.