- #1

Dorothy Weglend

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I seem to be specializing in plumb bobs this week

A box car has a freely hangling plumb bob (from the ceiling). It is accelerating up an incline. which makes an angle b with the horizontal. The plumb bob makes an angle c with the perpendicular to the ceiling. Find the acceleration of the box car.

This didn't seem that tough, but my solution is so different from the books that I thought I would ask about it. I hope someone has some time to look this over. I've attached a diagram for my work.

From the box car ceiling, I have two angles. One is just b, the same as the incline, which is the angle the bob would make with the perpendicular if there is no acceleration. The other is a, which is the angle caused by the acceleration. So a+b = c, the angle of the perpendicular to the ceiling.

Fy = T cos a - mg = 0

Fx = T cos a = m

Solve these to get

a = c - b, so the final solution is:

The books answer is quite complicated:

I tried simplifying this with some trig identities to get my expression, but it doesn't seem to be possible.

Thanks, as always, for any help.

Dorothy

A box car has a freely hangling plumb bob (from the ceiling). It is accelerating up an incline. which makes an angle b with the horizontal. The plumb bob makes an angle c with the perpendicular to the ceiling. Find the acceleration of the box car.

This didn't seem that tough, but my solution is so different from the books that I thought I would ask about it. I hope someone has some time to look this over. I've attached a diagram for my work.

From the box car ceiling, I have two angles. One is just b, the same as the incline, which is the angle the bob would make with the perpendicular if there is no acceleration. The other is a, which is the angle caused by the acceleration. So a+b = c, the angle of the perpendicular to the ceiling.

Fy = T cos a - mg = 0

Fx = T cos a = m

**a**Solve these to get

**a**= g tan a.a = c - b, so the final solution is:

**a**= g tan (c - b). Simple and nice. I wish it were right, tooThe books answer is quite complicated:

**a**= g ((cos b)(tan c) - (sin b))I tried simplifying this with some trig identities to get my expression, but it doesn't seem to be possible.

Thanks, as always, for any help.

Dorothy