Question

cassandra and her friend are moving two boxes. each box has the same mass. cassandra moved the first box by herself. cassandra and her friend moved the second box together. which box required more force to move? why?

Explanation:

Step1: Recall Newton's second law

Force \(F = ma\) (where \(m\) is mass and \(a\) is acceleration). Assuming the acceleration of both boxes is the same (e.g., starting from rest and moving with some non - zero acceleration), and since the mass \(m\) of each box is the same.

Step2: Analyze the force in each case

For the first box, the force \(F_1\) is applied by Cassandra alone. For the second box, the total force \(F_2\) is the sum of Cassandra's force and her friend's force. But if we consider the force required to move the box (overcoming static friction to start moving or maintaining motion), if we assume the acceleration is the same for both boxes (a common situation in a simple comparison where we just consider the force to move the box, not the distribution of the applied force among people), the force required to move an object is related to its mass and the acceleration it undergoes. Using \(F = ma\), since \(m\) (mass of the box) and \(a\) (acceleration of the box, assume same for both boxes) are the same for both boxes.

Answer:

The first box required more force. Because when moving the first box alone, Cassandra had to provide all the force to overcome the inertia (related to \(F = ma\)) of the box. When moving the second box together, the total force applied by Cassandra and her friend is the force that moves the box. But if we assume the acceleration of the box is the same in both cases (a reasonable assumption for a basic force - mass - acceleration comparison), the force required to move an object (based on \(F=ma\)) depends on the object's mass and acceleration. Since the mass of the two boxes is the same and assuming the acceleration (e.g., starting to move) is the same, the force required to move the box (the minimum force to overcome static friction and start motion or to maintain a certain motion) is the same for both boxes. Wait, no - correction: If we consider the force that each person exerts. Let's assume we want to move the box with a certain acceleration \(a\). The force \(F\) needed to move the box is \(F = ma\) (from \(F = ma\), Newton's second law). The mass \(m\) of the box is the same. If we assume the acceleration \(a\) (e.g., starting from rest and moving with some acceleration) is the same for both boxes. The force required to move the box (the net force on the box) is \(F = ma\). So the force required to move the box (the net force acting on the box) is the same for both boxes. But if we consider the force exerted by Cassandra. For the first box, \(F_{Cassandra1}=F = ma\). For the second box, \(F_{Cassandra2}+F_{friend}=ma\), so \(F_{Cassandra2}