Question

1. a 980 n man stands on a scale in a motionless elevator. when the elevator begins to move, the scale reads 1200 n. what is the magnitude and direction of the elevators acceleration?

Explanation:

Step1: Find the mass of the man

The weight \( W = mg \), where \( g = 9.8\ m/s^2 \). Given \( W = 980\ N \), we can find the mass \( m \) using the formula \( m=\frac{W}{g} \).
Substituting the values, we get \( m=\frac{980\ N}{9.8\ m/s^2}=100\ kg \).

Step2: Analyze the forces acting on the man

The normal force \( F_N \) (read by the scale) is \( 1200\ N \) and the weight \( mg = 980\ N \). Using Newton's second law \( \sum F = ma \), where the net force \( \sum F = F_N - mg \) (since \( F_N \) is upward and \( mg \) is downward).

Step3: Calculate the acceleration

Substitute \( F_N = 1200\ N \), \( m = 100\ kg \), and \( g = 9.8\ m/s^2 \) into the formula \( a=\frac{F_N - mg}{m} \).

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Since the normal force is greater than the weight, the net force is upward, so the acceleration is upward.

Answer:

The magnitude of the elevator's acceleration is \( 2.2\ m/s^2 \) and the direction is upward.