Question

34 n -34 n
a 58 kg person pushes a 50 kg file cabinet to the left with -34 n of force.
which object accelerates more quickly?
50 kg 58 kg
not enough information. the file cabinet
the person accelerations are equal.

Explanation:

Step1: Recall Newton's Second Law

Newton's second law is \( F = ma \), which can be rearranged to \( a=\frac{F}{m} \), where \( F \) is force, \( m \) is mass, and \( a \) is acceleration.

Step2: Analyze Forces on Each Object

By Newton's third law, the force the person exerts on the cabinet (\( F_{cabinet}=- 34\space N \)) is equal in magnitude and opposite in direction to the force the cabinet exerts on the person (\( F_{person} = 34\space N \)). So, the magnitude of the net force on each object (assuming no other significant forces, like friction, are mentioned) is \( |F| = 34\space N \).

Step3: Calculate Acceleration for Each Object

• For the file cabinet (mass \( m_{cabinet}=50\space kg \)):

Using \( a=\frac{F}{m} \), the acceleration \( a_{cabinet}=\frac{34}{50}=0.68\space m/s^{2} \).

• For the person (mass \( m_{person}=58\space kg \)):

Using \( a=\frac{F}{m} \), the acceleration \( a_{person}=\frac{34}{58}\approx0.586\space m/s^{2} \).

Since \( a_{cabinet}>a_{person} \), the file cabinet accelerates more quickly.

Answer:

The file cabinet