Question

2 4.2 m A 55 kg person stands on a uniform 17 kg, 6.0 m long ladder resting against a frictionless wall EXAMPLE NOTES IMAGES DISCUSS UNITS STATS HELP Part Description Answer Chk History What is the magnitude of the force of the wall on ladder? (include units with answer) 6.67 pts. 100% 2% try penalty Hints: 2, # tries: 0 Show Details Format Check What is the magnitude of the normal force of the ground on ladder? (include units with answer) 6.67 pts. 100% 12% try penalty Hints: 1,0 # tries: 0 Show Details Format Check What is the minimum coefficient of friction so the ladder does not slip? 6.67 pts. 100% 2% try penalty Hints: 0,0 # tries: 0 Show Details What is the minimum coefficient of friction so the ladder does not slip for any location of the person on the ladder? 6.67 pts. 100% 2% try penalty Hints: 2, # tries: 0 Show Details

Answer 1

given

masses are 55 kg and 17 kg

6 m long ladder

and 4.2 m , angle 75^o

a )

the magnitude of the force of the wall on ladder is

17 x 3 x cos75 + 55 x 4.2 x cos75 = R_w x 6 x sin75

R_w = 17 x 3 x cos75 + 55 x 4.2 x cos75 / 6 x sin75

R_w = 12.593 kg

b )

the magnitude of the normal force of the ground on ladder is R_H = 17 + 55 = 72 kg

c )

the minimum coefficient friction is

$\mu$ x 72 $\geq$ 12.593

$\mu$$\geq$ 12.593 / 72

$\mu$$\geq$ 0.1749

or

$\mu$$\geq$ 0.175

d )

the minimum coefficient friction is

17 x 3 x cos75 + 55 x 6 x cos 75 = R_w x 6 x sin75

R_w = 17 x 3 x cos75 + 55 x 6 x cos 75 / 6 x sin75

R_w = 17.015 kg

$\mu$ = R_w / 72

= 17.015 / 72

$\mu$ = 0.2363