Question

A plank 2.65 m long is supported by a cable, and a small ledge. The cable attaches 79.7 cm from the ledge, and makes an angle of 40.3 with the plank. It can hold 2648 N. How close (in meters) to the end of the plank can a 76.4 kg person walk before the cable breaks? Ignore the mass of the plank itself.

Answer 1

0.51 m

Step-by-step explanation:

Given :

Plank length = 2.65 m

Distance from the ledge from which the cable is attached = 79.7 cm = 0.797 m

Angle = 40.3 degree

Mass of the man, m = 76.4 kg

Now the net torque acting on the plank is zero.

Therefore, maximum torque applied by cable is

= 2648 x 0.797 x cos (40.3)

= 1609.5 N-m

We know that the man should apply the same torque,

Therefore, x
`*`76.4
`*` g = 1609.5

x =2.14 m

Therefore, length to the end of the plank is = 2.65-2.14

=0.51 m