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A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 N, when the lift is stationary. If the lift moves downward with an acceleration of 5 ms-2, the reading of the spring balance will be
[AIEEE 2003]
- a)24 N
- b)74 N
- c)15 N
- d)49 N
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A spring balance is attached to the ceiling of a lift. A man hangs his...
In stationary position, spring balance reading => mg = 49
Most Upvoted Answer
A spring balance is attached to the ceiling of a lift. A man hangs his...
Explanation:
When the lift is stationary, the reading of the spring balance is 49 N. This means that the bag exerts a force of 49 N downwards due to gravity.
Force in stationary lift:
- In a stationary lift, the net force acting on the bag is the force due to gravity, which is equal to its weight.
- Since weight is a force, it can be calculated using the equation:
weight = mass * acceleration due to gravity.
- The acceleration due to gravity is approximately 9.8 m/s².
- However, the problem does not provide the mass of the bag, so we cannot calculate the weight directly.
Force in moving lift:
- When the lift moves downward with an acceleration of 5 m/s², an additional force acts on the bag due to the acceleration.
- This additional force is equal to the product of the mass of the bag and the acceleration of the lift.
- The direction of this force is upward, opposing the force due to gravity.
Net force in moving lift:
- The net force acting on the bag in the moving lift is the vector sum of the force due to gravity and the force due to the acceleration of the lift.
- Since these forces act in opposite directions, the net force can be calculated by subtracting the force due to acceleration from the force due to gravity.
Calculating the net force:
- Since the problem does not provide the mass of the bag, we need to find the mass using the force reading of the spring balance when the lift is stationary.
- The force reading of the spring balance is equal to the weight of the bag, which can be calculated using the equation:
weight = mass * acceleration due to gravity.
- Rearranging the equation gives us:
mass = weight / acceleration due to gravity.
- Substituting the given force reading of 49 N and the acceleration due to gravity of 9.8 m/s² into the equation, we can calculate the mass of the bag:
mass = 49 N / 9.8 m/s² = 5 kg.
- Now that we have the mass of the bag, we can calculate the force due to acceleration using the equation:
force due to acceleration = mass * acceleration of the lift.
- Substituting the mass of 5 kg and the acceleration of 5 m/s² into the equation, we can calculate the force due to acceleration:
force due to acceleration = 5 kg * 5 m/s² = 25 N.
- Finally, we can calculate the net force by subtracting the force due to acceleration from the force due to gravity:
net force = force due to gravity - force due to acceleration = 49 N - 25 N = 24 N.
Therefore, the reading of the spring balance when the lift moves downward with an acceleration of 5 m/s² is 24 N.
When the lift is stationary, the reading of the spring balance is 49 N. This means that the bag exerts a force of 49 N downwards due to gravity.
Force in stationary lift:
- In a stationary lift, the net force acting on the bag is the force due to gravity, which is equal to its weight.
- Since weight is a force, it can be calculated using the equation:
weight = mass * acceleration due to gravity.
- The acceleration due to gravity is approximately 9.8 m/s².
- However, the problem does not provide the mass of the bag, so we cannot calculate the weight directly.
Force in moving lift:
- When the lift moves downward with an acceleration of 5 m/s², an additional force acts on the bag due to the acceleration.
- This additional force is equal to the product of the mass of the bag and the acceleration of the lift.
- The direction of this force is upward, opposing the force due to gravity.
Net force in moving lift:
- The net force acting on the bag in the moving lift is the vector sum of the force due to gravity and the force due to the acceleration of the lift.
- Since these forces act in opposite directions, the net force can be calculated by subtracting the force due to acceleration from the force due to gravity.
Calculating the net force:
- Since the problem does not provide the mass of the bag, we need to find the mass using the force reading of the spring balance when the lift is stationary.
- The force reading of the spring balance is equal to the weight of the bag, which can be calculated using the equation:
weight = mass * acceleration due to gravity.
- Rearranging the equation gives us:
mass = weight / acceleration due to gravity.
- Substituting the given force reading of 49 N and the acceleration due to gravity of 9.8 m/s² into the equation, we can calculate the mass of the bag:
mass = 49 N / 9.8 m/s² = 5 kg.
- Now that we have the mass of the bag, we can calculate the force due to acceleration using the equation:
force due to acceleration = mass * acceleration of the lift.
- Substituting the mass of 5 kg and the acceleration of 5 m/s² into the equation, we can calculate the force due to acceleration:
force due to acceleration = 5 kg * 5 m/s² = 25 N.
- Finally, we can calculate the net force by subtracting the force due to acceleration from the force due to gravity:
net force = force due to gravity - force due to acceleration = 49 N - 25 N = 24 N.
Therefore, the reading of the spring balance when the lift moves downward with an acceleration of 5 m/s² is 24 N.
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A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 N, when the lift is stationary. If the lift moves downward with an acceleration of 5 ms-2, the reading of the spring balance will be [AIEEE 2003]a)24 Nb)74 Nc)15 Nd)49 NCorrect answer is option 'A'. Can you explain this answer?
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