Double torque problems. Not sure if I'm on the right track.

[NasuSama]

Homework Statement

A symmetrical ladder of mass M = (mass 16.2 kg) leans against a smooth, frictionless wall so the top of the ladder is height h = 6.65 m above the floor, and the bottom of the ladder is distance d = 2.69 m from the base of the wall. Since the floor is also frictionless, a horizontal wire connects the bottom of the ladder to the wall so the ladder does not slip.

a) With no one on the ladder, find T, the magnitude of the tension in the wire.

b) b) Suppose the wire will snap when the magnitude of the tension is T = 230 N. Find x, the distance a man of mass m = 88.1 kg can climb up along the ladder before the wire snaps.

Homework Equations

→torque equation obviously

The Attempt at a Solution

a) I would say that the equation is...

0 = -mgh + Fdtan(θ)
F = mgh/(dtan(θ))

tan(θ) = h/d

Am I on the right track?

Also for part (b), I have..

b) The equation I believe is...

0 = -(m + M)gx + Fdtan(θ)

Actually, the answers are not right.

 

[Delphi51]

0 = -mgh + Fdtan(θ)

Is this a "sum of torques about a point = 0" statement? If so, what point are you doing? The force of gravity acts on the center of the ladder, which isn't a distance h away from anywhere . . .
What is force F? Perhaps you should begin with a diagram showing all the forces acting on the ladder. The wall will push horizontally on the ladder, the floor vertically.

 

[NasuSama]

Oops. I'm wrong. It's actually based on the method I followed..

https://www.physicsforums.com/showthread.php?t=592563

Nvm. Looks like I got 'em right with the right method [not the method I used here].

However, I'm stuck with the second part. I will get help from you when I'm done finding the tension of the wire.

The answer is T = 32.2 N. This is the equation I use.

L * sin(x) * F_wall - L/2 * cos(x) * N = 0

 

[NasuSama]

For the second part of the problem, I believe the expression is...

7.17 * sin(θ) * F_wire - x * cos(θ) * 1023 = 0 where...

θ = angle of the ladder
1023 = normal force
7.17 = length of the ladder

Then, I solve for x and then, take the difference between the center of the ladder initially and the value of x.

Seems like I'm stuck for this problem!

 

[Delphi51]

Odd, I get 32.14 N. Still having trouble identifying symbols - is "N" the weight mg?
Torques about the bottom of the ladder, right?

 

[NasuSama]

Odd, I get 32.14 N. Still having trouble identifying symbols - is "N" the weight mg?
Torques about the bottom of the ladder, right?

Actually, I'm told to round the values to the three significant figures [This is the part of my Webassign assignments. A lot of people have these works online!]

Yes, it is N and actually I have the right answer. Thanks for your help though. I actually figured out the second problem. Here is the answer to the second part..

7.17sin(68) * 230 = (16.2 * 9.81 * 7.17/2 + 88.1 * 9.81 * x)cos(68) [Sorry if I keep rounding each term in terms of 3 sig fig]

Then, I solve for x to get around 4.06.

 

[Delphi51]

I agree with your final answer. I don't follow your work because I used symbols until the very end so all numbers went into the calculator at once - no rounding off at all until the final answer.

By the way, to guarantee 3 digit accuracy in the answer, you need to keep 4 digits in intermediate steps for multiplying, even more when subtracting is involved. For example, if you have
10(1.2345*100 - 1.22*100)
=10(123 - 122) keeping 3 digit accuracy in intermediate step!
=10
Run the first line through your calculator without rounding and you get 14.5

 

[NasuSama]

I agree with your final answer. I don't follow your work because I used symbols until the very end so all numbers went into the calculator at once - no rounding off at all until the final answer.

By the way, to guarantee 3 digit accuracy in the answer, you need to keep 4 digits in intermediate steps for multiplying, even more when subtracting is involved. For example, if you have
10(1.2345*100 - 1.22*100)
=10(123 - 122) keeping 3 digit accuracy in intermediate step!
=10
Run the first line through your calculator without rounding and you get 14.5

Oh, I actually didn't show you by just solving for a variable of the equation. I usually do that when I use the formula.

Yes, it's better to answer question this way. I would take your method if I'm working out the problems scientifically.