A small child of mass 10.2kg climbs a ladder that is in contact with two frictio

Question

A small child of mass 10.2kg climbs a ladder that is in contact with two frictionless surfaces as shown in the above diagram. The ladder has an approximately uniform mass of 12.3kg with a length of 2.97m and makes a 59.8o angle with respect to the horizon. The bottom of the ladder is attached to the wall with a string that can support a maximum tension of 79.8N before it breaks. (a) What is the tension in the string when the child is halfway up the ladder? (b) What is the maximum distance that the child can climb up the ladder before the string breaks?

Explanation / Answer

a)

Tension = (10.2+12.3)*9.8*2.97*cos(59.8 degrees)/(2*2.97*sin(59.8 degrees)) = 64.2 N

b)

For , max distance he can climb,

(12.3*9.8*2.97*cos(59.8 degrees)/2+10.2*9.8*x*cos(59.8 degrees))/(2.97*sin(59.8 degrees)) = 79.8 N

So, x = 2.28 m <-----------answer

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