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sabrinarasull1pe6s61
30.07.2021 •
Physics
To get up on the roof, a person (mass 70.0kg) places a 6.00-m aluminum ladder (mass 10.0 kg) against the house on a concrete pad with the base of the ladder 2.00 m from the house. The ladder rests against a plastic rain gutter, which we can assume to be frictionless. The center of mass of the ladder is 2 m from the bottom. The person is standing 3 meters from the bottom. What are the magnitudes of the forces on the ladder at the top and bottom
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Ответ:
The magnitude of the forces acting at the top are;
The magnitude of the forces acting at the bottom are;
The known parameters in the question are;
The mass of the person, m₁ = 70.0 kg
The length of the ladder, l = 6.00 m
The mass of the ladder, m₂ = 10.0 kg
The distance of the base of the ladder from the house, d = 2.00 m
The point on the roof the ladder rests = A frictionless plastic rain gutter
The location of the center of mass of the ladder, C.M. = 2 m from the bottom of the ladder
The location of the point the person is standing = 3 meters from the bottom
g = The acceleration due to gravity ≈ 9.81 m/s²
The required parameters are;
The magnitudes of the forces on the ladder at the top and bottom
The strategy to be used;
Find the angle of inclination of the ladder, θ
At equilibrium, the sum of the moments about a point is zero
The angle of inclination of the ladder, θ = arccos(2/6) ≈ 70.53 °C
Taking moment about the point of contact of the ladder with the ground, B gives;
Therefore;
Where;
Therefore, we have;
Therefore, we get;
2 × (2/6) × 10.0 × 9.81 + 3.0 × (2/6) × 70 × 9.81 =
× √(6² - 2²)
The reaction force on the wall,
≈ 132.95 N
We note that the magnitude of the reaction force at the roof,
= The magnitude of the frictional force of bottom of the ladder on the floor,
but opposite in direction
Therefore;
Similarly, at equilibrium, we have;
∑Fₓ =
= 0
The vertical component of the forces acting on the ladder are, (taking forces acting upward as positive;
∴ The upward force acting at the bottom,
= 784.8 N
Therefore;
The magnitudes of the forces at the ladder top and bottom are;
At the top;
At the bottom;
Learn more about equilibrium of forces here;
Ответ:
0.1m/s²
Explanation:
acceleration =(final velocity - initial velocity)÷time taken
acc=(2-0)÷20
av. acc=0.1m/s²