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A 96 kg man is standing in an elevator. The man experiences a net force when the elevator moves at an acceleration of 4.0 m/s2 upward and downward. Find both net forces

User Sam Debruyn
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1 Answer

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20 votes

Answer:

The net upward force the man experiences is approximately 1,324.8 N

The net downward force the man experienced is approximately 556.8 N

Step-by-step explanation:

The given mass of the man, m = 96 kg

The acceleration of the elevator, a = 4.0 m/s²

According to Newton's third law of motion which states that action ad reaction are equal and opposite, when the elevator moves upwards, we have;

The net force the man experiences, F = Gravitational force, m·g + The force of the elevator pushing upwards, m·a

∴ ↑F = m·g + m·a

Where;

F = The net force the man experiences

m = The mass of the man = 96 kg

g = The acceleration due to gravity ≈ 9.8 m/s²

a = The acceleration of the elevator = 4 m/s²

∴ ↑F = 96 kg × 9.8 m/s² + 96 kg × 4 m/s² ≈ 1,324.8 N

The net upward force the man experiences ≈ 1,324.8 N

When the elevator moves downwards, we have;

The net force the man experiences, F = Gravitational force, m·g + The loss of the gravitational force as the floor moves further downwards, -(m·a)

∴ F = m·g + -(m·a) = m·g - m·a

F = m·g - m·a

∴ ↓F = 96 kg × 9.8 m/s² - 96 k × 4 m/s² ≈ 556.8 N

The net downward force the man experienced ≈ 556.8 N

User Artefacto
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