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In order to raise a mass of 100kg a man of mass 60kg fastens a rope to it and passes the rope over a smooth pulley. He climbs the rope with an acceleration 5g/4 relative to rope. The tension in the rope is?
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In order to raise a mass of 100kg a man of mass 60kg fastens a rope to...
Understanding the System
To analyze the situation, let’s understand the forces acting on both the man and the mass being lifted.
Forces Acting on the Man
- The man has a mass of 60 kg and is climbing with an acceleration of 5g/4 relative to the rope.
- The gravitational force acting on him is: F_gravity_man = 60kg * g.
- The net force acting on him while climbing is: F_net_man = T - F_gravity_man, where T is the tension in the rope.
Forces Acting on the Mass
- The mass to be lifted is 100 kg, which experiences a gravitational force of: F_gravity_mass = 100kg * g.
- The net force acting on the mass can be expressed as: F_net_mass = F_gravity_mass - T.
Setting Up Equations
1. For the man climbing the rope, the effective acceleration is (5g/4) + g = (9g/4) due to the upward acceleration.
- Thus, F_net_man = 60kg * (9g/4).
2. For the mass being lifted, if it accelerates upwards, it must overcome its weight plus the tension.
- F_net_mass = 100kg * a, where a is the acceleration of the mass.
Finding Tension in the Rope
Combining these equations, we can solve for T to find the tension in the rope.
- From the man’s equation: T = 60kg * (9g/4) + 60kg * g.
- From the mass’s equation: T = 100kg * a + F_gravity_mass.
Final Calculation
After solving the equations and substituting values, you will arrive at the tension T in the rope.
This analysis provides a systematic approach to determine the tension in the rope when the man climbs with a specific acceleration.
To analyze the situation, let’s understand the forces acting on both the man and the mass being lifted.
Forces Acting on the Man
- The man has a mass of 60 kg and is climbing with an acceleration of 5g/4 relative to the rope.
- The gravitational force acting on him is: F_gravity_man = 60kg * g.
- The net force acting on him while climbing is: F_net_man = T - F_gravity_man, where T is the tension in the rope.
Forces Acting on the Mass
- The mass to be lifted is 100 kg, which experiences a gravitational force of: F_gravity_mass = 100kg * g.
- The net force acting on the mass can be expressed as: F_net_mass = F_gravity_mass - T.
Setting Up Equations
1. For the man climbing the rope, the effective acceleration is (5g/4) + g = (9g/4) due to the upward acceleration.
- Thus, F_net_man = 60kg * (9g/4).
2. For the mass being lifted, if it accelerates upwards, it must overcome its weight plus the tension.
- F_net_mass = 100kg * a, where a is the acceleration of the mass.
Finding Tension in the Rope
Combining these equations, we can solve for T to find the tension in the rope.
- From the man’s equation: T = 60kg * (9g/4) + 60kg * g.
- From the mass’s equation: T = 100kg * a + F_gravity_mass.
Final Calculation
After solving the equations and substituting values, you will arrive at the tension T in the rope.
This analysis provides a systematic approach to determine the tension in the rope when the man climbs with a specific acceleration.
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In order to raise a mass of 100kg a man of mass 60kg fastens a rope to it and passes the rope over a smooth pulley. He climbs the rope with an acceleration 5g/4 relative to rope. The tension in the rope is?
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In order to raise a mass of 100kg a man of mass 60kg fastens a rope to it and passes the rope over a smooth pulley. He climbs the rope with an acceleration 5g/4 relative to rope. The tension in the rope is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In order to raise a mass of 100kg a man of mass 60kg fastens a rope to it and passes the rope over a smooth pulley. He climbs the rope with an acceleration 5g/4 relative to rope. The tension in the rope is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In order to raise a mass of 100kg a man of mass 60kg fastens a rope to it and passes the rope over a smooth pulley. He climbs the rope with an acceleration 5g/4 relative to rope. The tension in the rope is?.
In order to raise a mass of 100kg a man of mass 60kg fastens a rope to it and passes the rope over a smooth pulley. He climbs the rope with an acceleration 5g/4 relative to rope. The tension in the rope is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In order to raise a mass of 100kg a man of mass 60kg fastens a rope to it and passes the rope over a smooth pulley. He climbs the rope with an acceleration 5g/4 relative to rope. The tension in the rope is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In order to raise a mass of 100kg a man of mass 60kg fastens a rope to it and passes the rope over a smooth pulley. He climbs the rope with an acceleration 5g/4 relative to rope. The tension in the rope is?.
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