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cupoosta [38]
3 years ago
12

A uniform ladder of length l rests against a smooth, vertical wall. If the coefficient of static friction is 0.50, and the ladde

r makes a 53⁰ angle with respect to the horizontal, how far along the length of the ladder can a 56.0-kg person climb before the ladder begins to slip? The ladder is 7.5 m in length and has a mass of 21 kg.
Physics
1 answer:
Ronch [10]3 years ago
3 0

Answer:

X = 5.44 m

Explanation:

First we can calculate the normal force acting from the floor to the ladder.

W₁+W₂ = N  

W1 is the weigh of the ladder

W2 is the weigh of the  person

So we have:

m1g+m2g=N  

N=755.37 N

The friction force is:

F_{force}=\mu N=0.5\cdot 755.37=377.68 N

Now let's define the conservation of torque about the foot of the ladder:

\tau_{ledder}+\tau_{person=\tau_{reaction}}

m_{1}\cdot g\cdot X \cdot cos(53)+m_{2}\cdot g\cdot 3.75 \cdot cos(53)=F_{force}7.5sin(53)

Solving this equation for X, we have:

X = \frac{377.68\cdot 7.5\cdot sin(53)-21\cdot 9.81\cdot 3.75 \cdot cos(53)}{56\cdot 9.81\cdot cos(53)}

Finally, X = 5.44 m

Hope it helps!

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