A man of mass 69.5 kg stands on a scaffold supported by a vertical rope at each end. The scaffold has a mass of 22.3 kg and is 2.4 m long. Suppose the man stands to the right from the middle of the scaffold that is a distance one sixth of the length of the scaffold. What is the tension in the right rope?
You have to write equations about arbritary points, but it is very convenient.
I will do one for you, about the right end.
-69.5g*2/6*2.4-22.3g*1.2 + Tl*2.4 =0
You do the left equation.
Dont forget the sum of vertical forces..
Tl+Tr -22.3g-69.5g=0
Let T1 be the tension in the left rope and T2 be the tension in the right rope. A vertical force balance tells you that
T1 + T2 = (M1+M2)g = (69.5 + 22.3)* (9.8) N
You don't need that equation to solve for T2.
You can use the fact that the torque about the point where the left rope meets the scaffold is zero. The weight of the scaffold acts at the midpoint, which is 1.6 m from the left end. Therefore
M1*g*1.6 m = T2* 2.4 m
Solve for T2 (in Newtons)
i still have a few questions
1) wouldn't the 1.2 be 1.6 instead?
2) and how come the first equation equals zero. isn't it somewhat of a rearrangement of the second equation, so wouldn't it equal Tr?
using drwls method i got 454N and it was wrong
Whoops. I forgot the torque due to the scaffold's weight, on the left side of the equation, which is 22.3 kg*1.2 m * 9.8 m/s^2. That's why my equation gave you the wrong answer.
thanx :)
To determine the tension in the right rope, we need to consider the forces acting on the scaffold.
First, let's identify the various forces involved:
1. The weight of the man (F_m) acting downward.
2. The weight of the scaffold (F_scaffold) acting downward.
3. The tension in the left rope (F_left) acting upward.
4. The tension in the right rope (F_right) acting upward.
Since the system is in equilibrium, the sum of the forces in the vertical direction must be zero.
1. The weight of the man (F_m) can be calculated using the formula F = m * g, where m is the mass of the man and g is the acceleration due to gravity (approximately 9.8 m/s^2):
F_m = 69.5 kg * 9.8 m/s^2
2. The weight of the scaffold (F_scaffold) can be calculated in a similar manner:
F_scaffold = 22.3 kg * 9.8 m/s^2
3. The tension in the left rope (F_left) and the tension in the right rope (F_right) cancel each other out since the scaffold is in equilibrium.
Since the man is standing to the right from the middle of the scaffold, the distance from the right rope to the man is 2/6 (or 1/3) of the length of the scaffold.
To calculate F_right, we need to find the horizontal component of the weight of the scaffold. This can be done using trigonometry:
F_scaffold_horizontal = F_scaffold * cos(theta)
where theta is the angle between the weight vector and the horizontal.
Since the scaffold is in equilibrium, F_left and F_right are equal in magnitude.
Therefore, F_right = F_scaffold_horizontal + F_m.
Now, we can calculate the tension in the right rope:
F_right = F_scaffold_horizontal + F_m
Finally, plug in the values and solve for F_right.