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A body of mass 40kg stands on aweighing machine in an accelerated lift the reading on the scale of the weighing machine is 300. Find the magnitude and direction?
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A body of mass 40kg stands on aweighing machine in an accelerated lift...
M=40kg
F=300N
suppose that g=9.8m/s^2
Now, when the lift goes down, 2 types of accelerations are applied,
1. gravitational acceleration
2.acceleration of life
By thinking about the FBD of the lift,
if the lift moves down, the sum of acceleration = g-a
and if it moves up, it is g+a
[why? Becuase when the life moves, an illusory acceleration is applied on it, which is 'a' here]
That means,
1. if the lift is moving upwards,
F=m(g+a)
300=40(10+a)
a= -2/5 m/s^2
2. if lift is going down,
F=m(g-a)
300=40(10-a)
a= +2/5 m/s^2
Now the directions:
1.if the lift moves downwards, the magnitude of acceleration is +2/5 m/s^2
2.if the lift moves downwards, the magnitude of acceleration is -2/5 m/s^2
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A body of mass 40kg stands on aweighing machine in an accelerated lift...
Problem Statement:
A body of mass 40kg stands on a weighing machine in an accelerated lift. The reading on the scale of the weighing machine is 300. Find the magnitude and direction.
Solution:
Step 1: Analyzing the Situation
- In this scenario, the body is standing on a weighing machine in an accelerated lift.
- The weighing machine measures the normal force exerted by the body on the machine.
- The reading on the scale of the weighing machine is 300, which is the normal force experienced by the body.
Step 2: Understanding the Forces Acting on the Body
- In this case, there are two main forces acting on the body:
1. Gravitational force (mg): This force is always directed downwards and has a magnitude equal to the product of mass (m) and acceleration due to gravity (g).
2. Normal force (N): This force is exerted by the weighing machine and is equal in magnitude but opposite in direction to the gravitational force.
Step 3: Applying Newton's Second Law
- According to Newton's second law of motion, the net force acting on an object is equal to the product of its mass and acceleration.
- In this case, the net force is the difference between the gravitational force and the normal force.
- Therefore, the net force is given by the equation: Net force = mg - N.
Step 4: Solving the Equation
- We know that the mass of the body is 40kg and the acceleration due to gravity is approximately 9.8 m/s^2.
- The normal force is given as 300 (reading on the scale of the weighing machine).
- Substituting these values into the equation, we get: Net force = (40 * 9.8) - 300.
Step 5: Calculating the Net Force
- Evaluating the equation, we find: Net force = 392 - 300 = 92 Newtons.
Step 6: Interpreting the Result
- The net force acting on the body is 92 Newtons.
- The direction of the net force depends on the relative magnitudes of the gravitational force and the normal force.
- Since the normal force is smaller than the gravitational force, the net force is directed downwards.
Conclusion:
- The magnitude of the net force acting on the body is 92 Newtons, and its direction is downwards.
A body of mass 40kg stands on a weighing machine in an accelerated lift. The reading on the scale of the weighing machine is 300. Find the magnitude and direction.
Solution:
Step 1: Analyzing the Situation
- In this scenario, the body is standing on a weighing machine in an accelerated lift.
- The weighing machine measures the normal force exerted by the body on the machine.
- The reading on the scale of the weighing machine is 300, which is the normal force experienced by the body.
Step 2: Understanding the Forces Acting on the Body
- In this case, there are two main forces acting on the body:
1. Gravitational force (mg): This force is always directed downwards and has a magnitude equal to the product of mass (m) and acceleration due to gravity (g).
2. Normal force (N): This force is exerted by the weighing machine and is equal in magnitude but opposite in direction to the gravitational force.
Step 3: Applying Newton's Second Law
- According to Newton's second law of motion, the net force acting on an object is equal to the product of its mass and acceleration.
- In this case, the net force is the difference between the gravitational force and the normal force.
- Therefore, the net force is given by the equation: Net force = mg - N.
Step 4: Solving the Equation
- We know that the mass of the body is 40kg and the acceleration due to gravity is approximately 9.8 m/s^2.
- The normal force is given as 300 (reading on the scale of the weighing machine).
- Substituting these values into the equation, we get: Net force = (40 * 9.8) - 300.
Step 5: Calculating the Net Force
- Evaluating the equation, we find: Net force = 392 - 300 = 92 Newtons.
Step 6: Interpreting the Result
- The net force acting on the body is 92 Newtons.
- The direction of the net force depends on the relative magnitudes of the gravitational force and the normal force.
- Since the normal force is smaller than the gravitational force, the net force is directed downwards.
Conclusion:
- The magnitude of the net force acting on the body is 92 Newtons, and its direction is downwards.
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A body of mass 40kg stands on aweighing machine in an accelerated lift the reading on the scale of the weighing machine is 300. Find the magnitude and direction?
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A body of mass 40kg stands on aweighing machine in an accelerated lift the reading on the scale of the weighing machine is 300. Find the magnitude and direction? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A body of mass 40kg stands on aweighing machine in an accelerated lift the reading on the scale of the weighing machine is 300. Find the magnitude and direction? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body of mass 40kg stands on aweighing machine in an accelerated lift the reading on the scale of the weighing machine is 300. Find the magnitude and direction?.
A body of mass 40kg stands on aweighing machine in an accelerated lift the reading on the scale of the weighing machine is 300. Find the magnitude and direction? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A body of mass 40kg stands on aweighing machine in an accelerated lift the reading on the scale of the weighing machine is 300. Find the magnitude and direction? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body of mass 40kg stands on aweighing machine in an accelerated lift the reading on the scale of the weighing machine is 300. Find the magnitude and direction?.
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