Two window washers, Bob and Joe, are on a 3.00-m-long, 335-N scaffold supported by two cables attached to its ends. Bob weighs 755 N and stands 1.00 m from the left end,Two meters from the left end is the 500-N washing equipment. Joe is 0.500 m from the right end and weighs 850 N. Given that the scaffold is in rotational and translational equilibrium, what are the forces on each cable?
a. left cable _________ kN
b. right cable _________kN
I will be happy to check your work. Also, do remember sum of vertical forces is zero.
Fy=0= T1+t2-755-335-500-850
Sum of tor. =0= (T2*3)-755(1)-335(2)-500(2)-850(2.5)
I solved for T1=923.34
and
T2=1516.666
But it's still wrong. I'm not sure what I am doing wrong
To find the forces on each cable, we need to analyze the forces acting on the scaffold.
Let's start by calculating the total torque acting on the scaffold. Torque is defined as the product of force and the perpendicular distance from the pivot point (or the point about which the object rotates). In this case, we can consider the pivot point to be the left end of the scaffold.
For the left cable:
The vertical force exerted by Bob is 755 N.
The perpendicular distance between Bob's position and the left end of the scaffold is 1.00 m.
So, the torque exerted by Bob is (755 N) * (1.00 m) = 755 N·m.
The washing equipment on the left side exerts a force of 500 N.
The perpendicular distance between the washing equipment and the left end of the scaffold is 2.00 m.
So, the torque exerted by the washing equipment is (500 N) * (2.00 m) = 1000 N·m.
Therefore, the total torque exerted on the scaffold by the left cable is 755 N·m + 1000 N·m = 1755 N·m.
For the right cable:
The vertical force exerted by Joe is 850 N.
The perpendicular distance between Joe's position and the left end of the scaffold is 3.00 m - 0.500 m = 2.50 m.
So, the torque exerted by Joe is (850 N) * (2.50 m) = 2125 N·m.
Since the scaffold is in rotational and translational equilibrium, the total torque on the left side must be equal to the total torque on the right side. Therefore, the total torque exerted on the right cable is also 1755 N·m.
To calculate the force on each cable, we divide the total torque by the perpendicular distance from the pivot point to each cable.
For the left cable:
The perpendicular distance between the left end of the scaffold and the left cable is 0.00 m.
Force on the left cable = (Total torque on the left side) / (Perpendicular distance) = 1755 N·m / 0.00 m = undefined.
For the right cable:
The perpendicular distance between the left end of the scaffold and the right cable is 3.00 m - 0.500 m = 2.50 m.
Force on the right cable = (Total torque on the right side) / (Perpendicular distance) = 2125 N·m / 2.50 m = 850 N.
Therefore, the forces on each cable are:
a. left cable: undefined
b. right cable: 850 N