A person of mass m is standing on a scale in an elevator that is accelerating downward with an acceleration...

Question

A person of mass m is standing on a scale in an elevator that is accelerating downward with an acceleration of magnitude a
Which of the following is a correct expression for the normal force exerted on the person by the scale?
Select {responseValue}
m(g-a)
Select {responseValue}
ma
Select {responseValue}
mg
Select {responseValue}
m(g+a)

SnapAndSolve AI · Accepted Answer

To determine the correct expression for the normal force exerted on a person standing on a scale in an elevator that is accelerating downward with an acceleration \( a \), we start by analyzing the forces acting on the person.
1. **Forces Involved**:
- Gravitational force (\( F_g \)): This is the force due to gravity acting on the person, calculated as:
\[
F_g = mg
\]
- Normal force (\( F_N \)): This is the force exerted by the scale on the person, which we need to find.
2. **Net Force**:
In an accelerating system, the net force can be expressed using Newton's second law:
\[
F_{net} = ma
\]
3. **Direction of Forces**:
- The gravitational force acts downward: \( mg \).
- The normal force acts upward: \( F_N \).
4. **Application of Newton's Second Law**:
Since the elevator is accelerating downward, the net force acting on the person in the downward direction can be set up as follows:
\[
F_{net} = F_g - F_N
\]
Plugging in the values we have:
\[
ma = mg - F_N
\]
5. **Rearranging the Equation**:
To isolate the normal force \( F_N \), rearrange the equation:
\[
F_N = mg - ma
\]
This simplifies to:
\[
F_N = m(g - a)
\]
6. **Conclusion**:
Thus, the correct expression for the normal force exerted on the person by the scale is:
m(g - a)

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