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A man weighing 90kg is starting climbing a 5 cm long ladder wich is weighing 20 kg and is placed at 60 to the ground and is resting with vertical wall. The co efficient friction between the ladder and ground is 0.3 and that between the ladder and the wall is 0.22 how far the man can climb so that ladder does not slip?
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A man weighing 90kg is starting climbing a 5 cm long ladder wich is we...
Analysis
To determine how far the man can climb without the ladder slipping, we need to consider the forces acting on the ladder. There are two main forces to consider: the gravitational force acting on the man and the ladder, and the frictional forces acting at the base and against the wall.
Forces acting on the ladder
- Gravitational force on the man: 90kg * 9.8m/s^2 = 882N
- Gravitational force on the ladder: 20kg * 9.8m/s^2 = 196N
- Normal force from the ground: 196N
- Normal force from the wall: 0N (vertical wall)
Frictional forces
- Frictional force between ladder and ground: 0.3 * 196N = 58.8N
- Frictional force between ladder and wall: 0.22 * 196N = 43.12N
Equilibrium condition
For the ladder not to slip, the net force acting on it must be zero. This means that the sum of the horizontal forces and the sum of the vertical forces must be zero.
Vertical forces
The vertical forces are balanced, so the ladder will not move up or down.
Horizontal forces
The horizontal forces are the frictional forces acting at the base and against the wall. As the ladder is at rest, the frictional forces must be equal and opposite. Therefore, we have:
Frictional force at base = Frictional force against wall
0.3 * 196N = 0.22 * 196N
58.8N = 43.12N
The ladder will start to slip when the man climbs to a point where the frictional force at the base becomes less than the maximum possible frictional force. This occurs when the man climbs such that the frictional force at the base reaches its maximum value of 58.8N.
Calculating maximum distance
To calculate how far the man can climb before the ladder slips, we need to determine the distance at which the frictional force at the base reaches 58.8N. This can be done using the torque equation:
Frictional force * distance = Gravitational force * distance
58.8N * x = 882N * 0.05m
x = 0.05m * (882N / 58.8N) = 0.75m
Therefore, the man can climb 0.75 meters up the ladder before it starts to slip.
To determine how far the man can climb without the ladder slipping, we need to consider the forces acting on the ladder. There are two main forces to consider: the gravitational force acting on the man and the ladder, and the frictional forces acting at the base and against the wall.
Forces acting on the ladder
- Gravitational force on the man: 90kg * 9.8m/s^2 = 882N
- Gravitational force on the ladder: 20kg * 9.8m/s^2 = 196N
- Normal force from the ground: 196N
- Normal force from the wall: 0N (vertical wall)
Frictional forces
- Frictional force between ladder and ground: 0.3 * 196N = 58.8N
- Frictional force between ladder and wall: 0.22 * 196N = 43.12N
Equilibrium condition
For the ladder not to slip, the net force acting on it must be zero. This means that the sum of the horizontal forces and the sum of the vertical forces must be zero.
Vertical forces
The vertical forces are balanced, so the ladder will not move up or down.
Horizontal forces
The horizontal forces are the frictional forces acting at the base and against the wall. As the ladder is at rest, the frictional forces must be equal and opposite. Therefore, we have:
Frictional force at base = Frictional force against wall
0.3 * 196N = 0.22 * 196N
58.8N = 43.12N
The ladder will start to slip when the man climbs to a point where the frictional force at the base becomes less than the maximum possible frictional force. This occurs when the man climbs such that the frictional force at the base reaches its maximum value of 58.8N.
Calculating maximum distance
To calculate how far the man can climb before the ladder slips, we need to determine the distance at which the frictional force at the base reaches 58.8N. This can be done using the torque equation:
Frictional force * distance = Gravitational force * distance
58.8N * x = 882N * 0.05m
x = 0.05m * (882N / 58.8N) = 0.75m
Therefore, the man can climb 0.75 meters up the ladder before it starts to slip.
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A man weighing 90kg is starting climbing a 5 cm long ladder wich is weighing 20 kg and is placed at 60 to the ground and is resting with vertical wall. The co efficient friction between the ladder and ground is 0.3 and that between the ladder and the wall is 0.22 how far the man can climb so that ladder does not slip?
Question Description
A man weighing 90kg is starting climbing a 5 cm long ladder wich is weighing 20 kg and is placed at 60 to the ground and is resting with vertical wall. The co efficient friction between the ladder and ground is 0.3 and that between the ladder and the wall is 0.22 how far the man can climb so that ladder does not slip? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A man weighing 90kg is starting climbing a 5 cm long ladder wich is weighing 20 kg and is placed at 60 to the ground and is resting with vertical wall. The co efficient friction between the ladder and ground is 0.3 and that between the ladder and the wall is 0.22 how far the man can climb so that ladder does not slip? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man weighing 90kg is starting climbing a 5 cm long ladder wich is weighing 20 kg and is placed at 60 to the ground and is resting with vertical wall. The co efficient friction between the ladder and ground is 0.3 and that between the ladder and the wall is 0.22 how far the man can climb so that ladder does not slip?.
A man weighing 90kg is starting climbing a 5 cm long ladder wich is weighing 20 kg and is placed at 60 to the ground and is resting with vertical wall. The co efficient friction between the ladder and ground is 0.3 and that between the ladder and the wall is 0.22 how far the man can climb so that ladder does not slip? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A man weighing 90kg is starting climbing a 5 cm long ladder wich is weighing 20 kg and is placed at 60 to the ground and is resting with vertical wall. The co efficient friction between the ladder and ground is 0.3 and that between the ladder and the wall is 0.22 how far the man can climb so that ladder does not slip? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man weighing 90kg is starting climbing a 5 cm long ladder wich is weighing 20 kg and is placed at 60 to the ground and is resting with vertical wall. The co efficient friction between the ladder and ground is 0.3 and that between the ladder and the wall is 0.22 how far the man can climb so that ladder does not slip?.
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