What is the tension in the rope nearer the 669N worker when he stands 1 m from one end? Find the tension in the cable. Answer in units of N.
The acceleration of gravity is 9.8 m/s^2.
A window worker is standing on a scaffold supported by a vertical rope at each end. The scaffold weighs 262 N and is 3.09 m long.
The scaffold AB is of length 3.09.
Let the centre of gravity G be the mid point of AB. So, AG= 3.09/2=1.545m
Let the Man stand at X i.e 1 m from B. Then AX=2.09 and XB=1m
Now the tension in the rpoe at A be T1 Upward and the tension,T2 at B is upward . 262N the wight force of the scaffold at G is downward and 669N downward, the wetght force of the worker at X are the the forces acting.
Since the scaffold is at equilibrium,
i)The resulting sum of the forces on the scaffold is zero and
ii) the sum of the moments of the about any point is zero.
By condtion (i) T1+T2-262N-66N=0 or
By condition (ii) Taking moments of the forces about A,we get:
clockwise moment+anticlock wise moments
-(AG*262+2.09*669) +0*T1+ T2*309=0
Therefore, T2= (1.545*262+2.09*669)=583.4951N
Therefore, T1= 931-T2=347.5049N
Here the weight of worker and the scaffold are already specified in N. Therefore I assume that weight refers to force exerted due to gravity, which equals mass multiplied by acceleration of gravity.
The two ropes support the weight of scaffold plus the weight of the worker.
The weight of the scaffold will be supported equally by the two ropes. However, weight of the worker supported by each worker will be shared in inverse proportion of distance of the worker from the ropes.
Let us name the two ropes as rope A, which is nearer to the worker, and rope B. Distance of worker from rope A = 1 m
Then distance of worker from rope B
= (Length of scaffold) - (Distance of worker from rope A)
= 3.08 - 1 = 2.08 m
Then the weight of worker (669 N) supported by rope A
= 669*(2.08/3.08) = 451.79 N
And weight of worker supported by rope B = 669 - 451.79 = 217.21 N
Weight of scaffold supported by each of rope A and B =262/2 131 N
Therefore total weight supported by rope A = 451.79 + 131 = 582.79 N
And total weight supported by rope B = 217.21 + 131 = 348.21 N
Tension in rope nearer to worker = 582.79 N
and tension in other rope = 348.21 N