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`Aman of mass 50 kg is standingon one end of a stationary wooden plank resting on a frictionless surface. The massof the plank is 100 kg its lengthis 75 m and the coefficient offriction between the man andthe plank is 0.2. Find the leastpossible time (in sec) in whichthe man can reach the other end starting from rest?
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`Aman of mass 50 kg is standingon one end of a stationary wooden plank...
**Solution:**
Given:
- Mass of the man, m = 50 kg
- Mass of the plank, M = 100 kg
- Length of the plank, L = 75 m
- Coefficient of friction between the man and the plank, μ = 0.2
We need to find the least possible time in which the man can reach the other end starting from rest.
**Step 1: Analysis of forces**
There are three forces acting on the man-plank system:
1. Weight of the man, mg
2. Normal force, N
3. Frictional force, f
Since the system is at rest initially, the frictional force will be static friction.
**Step 2: Calculation of normal force**
The normal force acting on the man can be calculated using the equation:
N = mg
Substituting the values, we get:
N = 50 kg * 9.8 m/s^2 = 490 N
**Step 3: Calculation of frictional force**
The frictional force can be calculated using the equation:
f = μN
Substituting the values, we get:
f = 0.2 * 490 N = 98 N
**Step 4: Calculation of net force**
The net force acting on the man-plank system can be calculated using the equation:
Net force = Weight of the man + Frictional force
Net force = mg + f
Substituting the values, we get:
Net force = 50 kg * 9.8 m/s^2 + 98 N = 490 N + 98 N = 588 N
**Step 5: Calculation of acceleration**
The acceleration of the man-plank system can be calculated using Newton's second law:
Net force = mass * acceleration
Substituting the values, we get:
588 N = (50 kg + 100 kg) * acceleration
Simplifying the equation, we get:
acceleration = 588 N / 150 kg = 3.92 m/s^2
**Step 6: Calculation of time**
The time taken by the man to reach the other end of the plank can be calculated using the equation:
Distance = (1/2) * acceleration * time^2
Substituting the values, we get:
75 m = (1/2) * 3.92 m/s^2 * time^2
Simplifying the equation, we get:
time^2 = (2 * 75 m) / 3.92 m/s^2 = 38.26
Taking the square root, we get:
time = √38.26 ≈ 6.18 s
Therefore, the least possible time in which the man can reach the other end starting from rest is approximately 6.18 seconds.
Given:
- Mass of the man, m = 50 kg
- Mass of the plank, M = 100 kg
- Length of the plank, L = 75 m
- Coefficient of friction between the man and the plank, μ = 0.2
We need to find the least possible time in which the man can reach the other end starting from rest.
**Step 1: Analysis of forces**
There are three forces acting on the man-plank system:
1. Weight of the man, mg
2. Normal force, N
3. Frictional force, f
Since the system is at rest initially, the frictional force will be static friction.
**Step 2: Calculation of normal force**
The normal force acting on the man can be calculated using the equation:
N = mg
Substituting the values, we get:
N = 50 kg * 9.8 m/s^2 = 490 N
**Step 3: Calculation of frictional force**
The frictional force can be calculated using the equation:
f = μN
Substituting the values, we get:
f = 0.2 * 490 N = 98 N
**Step 4: Calculation of net force**
The net force acting on the man-plank system can be calculated using the equation:
Net force = Weight of the man + Frictional force
Net force = mg + f
Substituting the values, we get:
Net force = 50 kg * 9.8 m/s^2 + 98 N = 490 N + 98 N = 588 N
**Step 5: Calculation of acceleration**
The acceleration of the man-plank system can be calculated using Newton's second law:
Net force = mass * acceleration
Substituting the values, we get:
588 N = (50 kg + 100 kg) * acceleration
Simplifying the equation, we get:
acceleration = 588 N / 150 kg = 3.92 m/s^2
**Step 6: Calculation of time**
The time taken by the man to reach the other end of the plank can be calculated using the equation:
Distance = (1/2) * acceleration * time^2
Substituting the values, we get:
75 m = (1/2) * 3.92 m/s^2 * time^2
Simplifying the equation, we get:
time^2 = (2 * 75 m) / 3.92 m/s^2 = 38.26
Taking the square root, we get:
time = √38.26 ≈ 6.18 s
Therefore, the least possible time in which the man can reach the other end starting from rest is approximately 6.18 seconds.
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`Aman of mass 50 kg is standingon one end of a stationary wooden plank resting on a frictionless surface. The massof the plank is 100 kg its lengthis 75 m and the coefficient offriction between the man andthe plank is 0.2. Find the leastpossible time (in sec) in whichthe man can reach the other end starting from rest?
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`Aman of mass 50 kg is standingon one end of a stationary wooden plank resting on a frictionless surface. The massof the plank is 100 kg its lengthis 75 m and the coefficient offriction between the man andthe plank is 0.2. Find the leastpossible time (in sec) in whichthe man can reach the other end starting from rest? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about `Aman of mass 50 kg is standingon one end of a stationary wooden plank resting on a frictionless surface. The massof the plank is 100 kg its lengthis 75 m and the coefficient offriction between the man andthe plank is 0.2. Find the leastpossible time (in sec) in whichthe man can reach the other end starting from rest? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for `Aman of mass 50 kg is standingon one end of a stationary wooden plank resting on a frictionless surface. The massof the plank is 100 kg its lengthis 75 m and the coefficient offriction between the man andthe plank is 0.2. Find the leastpossible time (in sec) in whichthe man can reach the other end starting from rest?.
`Aman of mass 50 kg is standingon one end of a stationary wooden plank resting on a frictionless surface. The massof the plank is 100 kg its lengthis 75 m and the coefficient offriction between the man andthe plank is 0.2. Find the leastpossible time (in sec) in whichthe man can reach the other end starting from rest? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about `Aman of mass 50 kg is standingon one end of a stationary wooden plank resting on a frictionless surface. The massof the plank is 100 kg its lengthis 75 m and the coefficient offriction between the man andthe plank is 0.2. Find the leastpossible time (in sec) in whichthe man can reach the other end starting from rest? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for `Aman of mass 50 kg is standingon one end of a stationary wooden plank resting on a frictionless surface. The massof the plank is 100 kg its lengthis 75 m and the coefficient offriction between the man andthe plank is 0.2. Find the leastpossible time (in sec) in whichthe man can reach the other end starting from rest?.
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