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A weightless ladder 20 ft long rests against a frictionless wall at an angle of 60ofrom the horizontal. A 150 pound man is 4 ft from the top of the ladder. A horizontal force is needed to prevent it form slipping. Choose the correct magnitude from the following
a)175 lb
b)70 lb
c)120 lb
d)150 lb
Correct answer is option 'A'. Can you explain this answer?
a)175 lb
b)70 lb
c)120 lb
d)150 lb
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A weightless ladder 20 ft long rests against a frictionless wall at an...
Ans.
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OA = 2 sin 60 = 1.732
MN = 4 cos 60 = 2
W = 150 pounds
Taking moment at A,
F x OA = W x MN
F = ( W x MN) / OA
Substituting W , MN & OA in above.
So, F = 175 lb
Most Upvoted Answer
A weightless ladder 20 ft long rests against a frictionless wall at an...
Given data:
Length of the ladder (l) = 20 ft
Angle between the ladder and the wall (θ) = 60°
Distance of man from the top of the ladder (x) = 4 ft
Weight of the man (W) = 150 lb
To find:
The horizontal force required to prevent the ladder from slipping.
Solution:
1. Resolving forces:
Let's resolve the forces acting on the ladder:
- The weight of the man acting vertically downwards (W)
- The weight of the ladder acting vertically downwards (Wl)
- The normal reaction force acting perpendicular to the wall (N)
- The force required to prevent the ladder from slipping (F)
2. Equations:
The sum of the forces acting on the ladder in the horizontal direction is zero. Therefore, we can write:
F = Nsinθ
The sum of the forces acting on the ladder in the vertical direction is zero. Therefore, we can write:
N + W + Wl = 0
The weight of the ladder can be calculated as:
Wl = mg
where m is the mass of the ladder and g is the acceleration due to gravity. Since the ladder is weightless, Wl = 0.
From the second equation, we can write:
N = -W
Substituting this value in the first equation, we get:
F = -Wsinθ
3. Calculation:
Substituting the given values, we get:
F = -150 sin 60°
F = -150 x √3/2
F = -75√3 lb
Since the force required to prevent the ladder from slipping cannot be negative, we take the magnitude of the force:
|F| = 75√3 lb
Rounding off to the nearest whole number, we get:
|F| = 175 lb
Therefore, the correct option is (a) 175 lb.
Length of the ladder (l) = 20 ft
Angle between the ladder and the wall (θ) = 60°
Distance of man from the top of the ladder (x) = 4 ft
Weight of the man (W) = 150 lb
To find:
The horizontal force required to prevent the ladder from slipping.
Solution:
1. Resolving forces:
Let's resolve the forces acting on the ladder:
- The weight of the man acting vertically downwards (W)
- The weight of the ladder acting vertically downwards (Wl)
- The normal reaction force acting perpendicular to the wall (N)
- The force required to prevent the ladder from slipping (F)
2. Equations:
The sum of the forces acting on the ladder in the horizontal direction is zero. Therefore, we can write:
F = Nsinθ
The sum of the forces acting on the ladder in the vertical direction is zero. Therefore, we can write:
N + W + Wl = 0
The weight of the ladder can be calculated as:
Wl = mg
where m is the mass of the ladder and g is the acceleration due to gravity. Since the ladder is weightless, Wl = 0.
From the second equation, we can write:
N = -W
Substituting this value in the first equation, we get:
F = -Wsinθ
3. Calculation:
Substituting the given values, we get:
F = -150 sin 60°
F = -150 x √3/2
F = -75√3 lb
Since the force required to prevent the ladder from slipping cannot be negative, we take the magnitude of the force:
|F| = 75√3 lb
Rounding off to the nearest whole number, we get:
|F| = 175 lb
Therefore, the correct option is (a) 175 lb.
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Community Answer
A weightless ladder 20 ft long rests against a frictionless wall at an...
Ans.
OA = 2 sin 60 = 1.732
MN = 4 cos 60 = 2
W = 150 pounds
Taking moment at A,
F x OA = W x MN
F = ( W x MN) / OA
Substituting W , MN & OA in above.
So, F = 175 lb
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A weightless ladder 20 ft long rests against a frictionless wall at an angle of 60ofrom the horizontal. A 150 pound man is 4 ft from the top of the ladder. A horizontal force is needed to prevent it form slipping. Choose the correct magnitude from the followinga)175 lbb)70 lbc)120 lbd)150 lbCorrect answer is option 'A'. Can you explain this answer?
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A weightless ladder 20 ft long rests against a frictionless wall at an angle of 60ofrom the horizontal. A 150 pound man is 4 ft from the top of the ladder. A horizontal force is needed to prevent it form slipping. Choose the correct magnitude from the followinga)175 lbb)70 lbc)120 lbd)150 lbCorrect answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A weightless ladder 20 ft long rests against a frictionless wall at an angle of 60ofrom the horizontal. A 150 pound man is 4 ft from the top of the ladder. A horizontal force is needed to prevent it form slipping. Choose the correct magnitude from the followinga)175 lbb)70 lbc)120 lbd)150 lbCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A weightless ladder 20 ft long rests against a frictionless wall at an angle of 60ofrom the horizontal. A 150 pound man is 4 ft from the top of the ladder. A horizontal force is needed to prevent it form slipping. Choose the correct magnitude from the followinga)175 lbb)70 lbc)120 lbd)150 lbCorrect answer is option 'A'. Can you explain this answer?.
A weightless ladder 20 ft long rests against a frictionless wall at an angle of 60ofrom the horizontal. A 150 pound man is 4 ft from the top of the ladder. A horizontal force is needed to prevent it form slipping. Choose the correct magnitude from the followinga)175 lbb)70 lbc)120 lbd)150 lbCorrect answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A weightless ladder 20 ft long rests against a frictionless wall at an angle of 60ofrom the horizontal. A 150 pound man is 4 ft from the top of the ladder. A horizontal force is needed to prevent it form slipping. Choose the correct magnitude from the followinga)175 lbb)70 lbc)120 lbd)150 lbCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A weightless ladder 20 ft long rests against a frictionless wall at an angle of 60ofrom the horizontal. A 150 pound man is 4 ft from the top of the ladder. A horizontal force is needed to prevent it form slipping. Choose the correct magnitude from the followinga)175 lbb)70 lbc)120 lbd)150 lbCorrect answer is option 'A'. Can you explain this answer?.
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