Competency #1
Answer and Explanation
First, we analyze the forces acting in the vertical and horizontal directions:
- The book has mass, so there is a force of gravity between the book and the earth (unless indicated otherwise, it is usually safe to assume a given scenario is taking place on earth). The book is touching the table, so the table must be providing a support force upward. Since the book is not accelerating upward or downward, the support force must be equal in magnitude to the force of gravity.
- The table surface was not declared to be frictionless, so we must include friction in our analysis. Friction always acts to oppose the motion and since the motion is to the left, friction must be acting to the right.
With the above analysis of the forces acting, we can now draw the force diagram:
Next, we determine the net force in the vertical and horizontal directions:
- Vertical- There are 2 forces acting and they are equal in size and opposite in direction (Note: these do not constitute a 3 rd law pair, since they are both acting on the same object). However, by being equal and opposite, these 2 forces do lead to a net vertical force of zero in this case.
- Horizontal- There is only 1 force acting in the horizontal direction. Therefore, the net force must be in the same direction and the same size of this lone force.
The net force for the book at this time can be represented as a double arrow to the right, the same length as the friction arrow. Click here to show arrow on the diagram.
Finally, we need to determine the acceleration of the book. We should do this separately for the vertical and horizontal directions:
- Vertical- We know from our understanding of the scenario that the book's vertical velocity is zero and stays at zero for the entire time. If the vertical velocity is not changing, this means the vertical acceleration is zero.
- Horizontal- We know the net horizontal force is to the right. By Newton's 2nd Law:
- we know that the acceleration must be in the same direction as the net force.
Even though the book is moving to the left, its acceleration is to the right. This is another way of saying it is slowing down.
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