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A 11kg monkey is climbing a massless rope attached to a 15 kg log of wood over a frictionless tree limb with what minimum acceleration must monkey climb the rope so that it can raise the log off the ground?
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Analysis:
The key to solving this problem lies in understanding the forces acting on the system. The monkey must exert a force greater than the weight of the log in order to lift it off the ground. By applying Newton's second law, we can calculate the minimum acceleration the monkey must have to achieve this.
Forces Involved:
- Weight of the monkey: \( F_{m} = m_{m} \cdot g \)
- Weight of the log: \( F_{l} = m_{l} \cdot g \)
- Tension in the rope: T
Equations of Motion:
- Net force on the system: \( F_{net} = T - F_{m} - F_{l} \)
- Acceleration of the system: \( a = \frac{F_{net}}{m_{m} + m_{l}} \)
Minimum Acceleration Calculation:
- Given: \( m_{m} = 11 \, kg, \, m_{l} = 15 \, kg \)
- Substitute the values of \( F_{m} \) and \( F_{l} \) into the net force equation
- Net force becomes: \( F_{net} = T - 11g - 15g \)
- Simplify: \( F_{net} = T - 26g \)
- Substitute into the acceleration equation
- Minimum acceleration: \( a = \frac{T - 26g}{11 + 15} \)
Minimum Acceleration Requirement:
To raise the log off the ground, the tension in the rope must be greater than the combined weight of the monkey and the log. Therefore, the minimum acceleration required for the monkey to achieve this is when the tension in the rope is just enough to lift the log off the ground.
By setting the tension equal to the combined weight of the monkey and the log, we can calculate the minimum acceleration needed for the monkey to achieve this.
The key to solving this problem lies in understanding the forces acting on the system. The monkey must exert a force greater than the weight of the log in order to lift it off the ground. By applying Newton's second law, we can calculate the minimum acceleration the monkey must have to achieve this.
Forces Involved:
- Weight of the monkey: \( F_{m} = m_{m} \cdot g \)
- Weight of the log: \( F_{l} = m_{l} \cdot g \)
- Tension in the rope: T
Equations of Motion:
- Net force on the system: \( F_{net} = T - F_{m} - F_{l} \)
- Acceleration of the system: \( a = \frac{F_{net}}{m_{m} + m_{l}} \)
Minimum Acceleration Calculation:
- Given: \( m_{m} = 11 \, kg, \, m_{l} = 15 \, kg \)
- Substitute the values of \( F_{m} \) and \( F_{l} \) into the net force equation
- Net force becomes: \( F_{net} = T - 11g - 15g \)
- Simplify: \( F_{net} = T - 26g \)
- Substitute into the acceleration equation
- Minimum acceleration: \( a = \frac{T - 26g}{11 + 15} \)
Minimum Acceleration Requirement:
To raise the log off the ground, the tension in the rope must be greater than the combined weight of the monkey and the log. Therefore, the minimum acceleration required for the monkey to achieve this is when the tension in the rope is just enough to lift the log off the ground.
By setting the tension equal to the combined weight of the monkey and the log, we can calculate the minimum acceleration needed for the monkey to achieve this.
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A 11kg monkey is climbing a massless rope attached to a 15 kg log of wood over a frictionless tree limb with what minimum acceleration must monkey climb the rope so that it can raise the log off the ground?
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A 11kg monkey is climbing a massless rope attached to a 15 kg log of wood over a frictionless tree limb with what minimum acceleration must monkey climb the rope so that it can raise the log off the ground? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A 11kg monkey is climbing a massless rope attached to a 15 kg log of wood over a frictionless tree limb with what minimum acceleration must monkey climb the rope so that it can raise the log off the ground? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 11kg monkey is climbing a massless rope attached to a 15 kg log of wood over a frictionless tree limb with what minimum acceleration must monkey climb the rope so that it can raise the log off the ground?.
A 11kg monkey is climbing a massless rope attached to a 15 kg log of wood over a frictionless tree limb with what minimum acceleration must monkey climb the rope so that it can raise the log off the ground? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A 11kg monkey is climbing a massless rope attached to a 15 kg log of wood over a frictionless tree limb with what minimum acceleration must monkey climb the rope so that it can raise the log off the ground? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 11kg monkey is climbing a massless rope attached to a 15 kg log of wood over a frictionless tree limb with what minimum acceleration must monkey climb the rope so that it can raise the log off the ground?.
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