A 6.5 m long ladder rests against as vertical wall reaching a height of 6.0 m. A 60 kg man stands hlf way up the ladder. A. Find the torque of the force exerted by the man on the ladder bout the upper end of the ladder. b.Assuming the weight of the ladder of be negligible as compared to the man and assuming the wall to be smooth find the force exerted by the ground on the ladder.

Answer

A, B, C, D

Explanation

`m=60kg`
Ladder length = 6.5m
Height of the wall =6m

Therefore torque due to the weight of the body
a. `tau=600xx6.5/2sintheta`
`rarr tau=600x6.52xxsqrt((1-cos^2theta))`
`rarr tau=600xx(6.5/2)xx(sqrt{1-(6/6.5)}^2)`
`rarr tau=70N-m`
b. `R_2=mg`
`=60xx9.8`
`R_1=muR_2`
`rarr 6.5R_1costheta=60g sin thetaxx(6.5/2)`
`rarr R_1=1/26tantheta`
`=1/260x(2.5/6)`
`[because tan theta =/]`
`rarr R_1=(2/5)g`
`rarr R_1=122.5N`