Two students are pushing on a crate that can slide only along a straight hallway…

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

Two students are pushing on a crate that can slide only along a straight hallway aligned with the positive xx-axis. Student A exerts a 50 N50\,\text{N} force directed in the +x+x direction, while Student B exerts a 30 N30\,\text{N} force directed in the −x-x direction. One of the students claims that the net "amount of force" acting on the crate is simply 50 N+30 N=80 N50\,\text{N}+30\,\text{N}=80\,\text{N} because "5050 plus 3030 equals 8080." (a) Identify whether force is a scalar or a vector quantity and justify your answer. (b) Determine the correct net force (magnitude and direction) acting on the crate. Express your answer using a positive or negative sign to indicate direction along the xx-axis. (c) Explain clearly how misclassifying force as a scalar leads to the incorrect result of 80 N80\,\text{N} in this scenario.

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