Question

In the figure, horizontal scaffold 2, with uniform mass m2​=27 kg and length L2​=2.4 m, hangs from horizontal scaffold 1 , with uniform mass m1​=53 kg. A 15 kg box of nails lies on scaffold 2, centered at distance d=0.65 m from the left end. What is the tension T in the cable indicated? Number Units

Answer 1

The tension in the cable is 264.6 N.

Step-by-step explanation:

To find the tension T in the cable, we need to consider the forces acting on scaffold 2. The weight of scaffold 2 is mg, where m = 27 kg and g = 9.8 m/s². The tension T is the sum of the vertical components of the forces acting on scaffold 2. We can write an equation using Newton's second law: T - mg = 0. Solving for T, we get T = mg = (27 kg) * (9.8 m/s²) = 264.6 N.

Answer 2

The tension T in the cable is 354.9 Newtons as the box of nails lies on scaffold 2 which is centered at distance from the left end.

L1 is the Distance from the pivot point where the cable is attached to scaffold 1 to the point where the cable connects to scaffold 2 is 1.5 m. The pivot point is at the end of scaffold 1 where the cable is attached.

we now go ahead to calculate the torques:

Torque due to T (clockwise): T * 1.5

Torque due to m2g (counterclockwise): 27g * (1.5 + 2.4/2) = 27g * 2.7

Torque due to box of nails (counterclockwise): 15g * (1.5 + 0.65) = 15g * 2.15

Torque due to m1g (clockwise): 53g * (1.5/2) = 53g * 0.75

Στ = 0

T * 1.5 - 27g * 2.7 - 15g * 2.15 + 53g * 0.75 = 0

T = (27g * 2.7 + 15g * 2.15 - 53g * 0.75) / 1.5

T ≈ 354.9 N