- #1
marcusesses
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Homework Statement
Say I have two objects on top of each other in an elevator (say Object 1 on the bottom and Object 2 on top), each with a given mass. The elevator is accelerating downward (meaning the elevator is moving up and slowing down). What would the normal force be on Object 1?
Homework Equations
Newtons second law!
The Attempt at a Solution
Newton's 2nd law for Object 2 is:
$$
\Sigma F_{x2} = F_{N2} - F_{g2} =- m_2 a ,
$$
since it's the object on top, it only has a normal force and gravity acting on it. Therefore,$$
F_{N2} =- m_2 a + F_{g2}
$$
For Object 1 it is:
$$
\Sigma F_{x1} = F_{N1} - F_{g1} - F_{C1} = -m_1 a
$$
This object has the normal force from the floor of the elevator pushing up, gravity of the book, *and* the additional contact force of Object 2 pushing down on it. Since $F_{N2} = - F_{C1}$ from Newton's Third Law
$$
\Sigma F_{x1} = F_{N1} - F_{g1} + m_2 a + F_{g2} = -m_1 a
$$
Solving for the normal force on Object 1 gives
$$
F_{N1} = F_{g1} + m_2 a - F_{g2} - m_1 a
$$
$$
F_{N1} = m_1 g + m_2 a - m_2 g - m_1 a
$$
$$
F_{N1} = m_1(g-A) -m_2(g-a)
$$
$$
F_{N1} = (m_1-m_2)(g-a)
$$
which is the final result. However, if the masses are equal, there's no normal force, which doesn't make sense.
The more intuitive answer comes if I assume $F_{N2} = F_{C1}$, which gives
$$
F_{N1} = (m_1+m_2)(g-a)
$$
I'm not sure how to explain why this one is right and the other is wrong though.
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