Question 2.CE.9: A book on the table A book sits on a tabletop. Identify the ......
A book on the table
A book sits on a tabletop. Identify the forces exerted on the book by other objects. Then, for each of these forces, identify the force that the book exerts on another object. Explain why the book is not accelerating.
Sketch and translate Draw a sketch of the situation and choose the book as the system.
Simplify and diagram Assume that the tabletop is perfectly horizontal and model the book as a pointlike object. A force diagram for the book is shown at right. Earth exerts a downward gravitational force on the book \vec{F}_{\mathrm{E} \text { on } \mathrm{B}} \text {, } and the table exerts an upward normal (contact) force on the book \vec{N}_{\text {Ton B }} . Newton’s second law explains why the book is not accelerating; the forces exerted on it by other objects are balanced and add to zero. The subscripts on each force identify the two objectsinvolved in the interaction. The Newton’s third law pair force will have its subscripts reversed. For example, Earth exerts a downward gravitational force on the book ( \vec{F}_{\mathrm{E} \text { on } \mathrm{B}} \text {, } ) . According to Newton’s third law, the book must exert an equal-magnitude upward gravitational force on Earth \left(\vec{F}_{\mathrm{B} \text { on } \mathrm{E}}= \vec{F}_{\mathrm{E} \text { on } \mathrm{B}}\right) , as shown at right. The table exerts an upward contact force on the book \left(\vec{N}_{\mathrm{T} \text { on B }}\right) , so the book must exert an equal-magnitude downward contact force on the table \left(\vec{N}_{\mathrm{B} \text { on }\mathrm{T}}=-\vec{N}_{\text {Ton } \mathrm{B}}\right) .
Try it yourself: A horse pulls on a sled that is stuck in snow and not moving. Your friend Chris says this happen because the horse exerts on the sled the same magnitude force that the sled exerts on the horse. Since the sum of the forces is zero, there is no acceleration. What is wrong with Chris’ reasoning?
Answer: Chris added the forces exerted on two different objects and did not consider all forces exerted on the sled. If you choose the sled as the system object, then the horse pulls forward on the sled, and the snow exerts a backward, resistive force. If these two horizontal forces happen to be of the same magnitude, they add to zero, and the sled does not accelerate horizontally. If, on the other hand, we choose the horse as the system, the ground exerts a forward force on the horse’s hooves (since the horse is exerting a force backward on the ground), and the sled pulls back on the horse. If those forces have the same magnitude, the net horizontal force is again zero, and the horse does not accelerate.
