Question

in this problem, we will consider the following situation as depicted in the diagram (figure 1). a block of mass m slides at a speed v along a horizontal, smooth table. it next slides down a smooth ramp, descending a height h, and then slides along a horizontal rough floor, stopping eventually. assume that the block slides slowly enough so that it does not lose contact with the supporting surfaces (table, ramp, or floor). you will analyze the motion of the block at different moments using the law of conservation of energy.

part a
which word in the statement of this problem allows you to assume that the table is frictionless?
options: straight, smooth, horizontal

Explanation:

To determine which word implies the table is frictionless, we analyze each option:

• "straight" describes the table's shape, not friction.
• "smooth" in physics contexts (like for the ramp here, and by extension the table if the problem's setup implies similar for the table) means no friction (since frictionless surfaces are often described as smooth, as smooth surfaces have negligible friction).
• "horizontal" describes the table's orientation, not friction.

So the word "smooth" (even though it's initially about the ramp, the problem's setup for the table's motion being such that it slides at a speed \( v \) without losing contact and using energy conservation implies the table is also frictionless, and "smooth" is the key term related to frictionless surfaces in physics problems).

Answer:

smooth (the option with "smooth" as the text, so the correct choice is the one with "smooth" among the options, e.g., if the options are as given: the second option, so we present it as per the multiple - choice format: \(\boldsymbol{\text{smooth}}\) (the option with "smooth" text, e.g., if the options are labeled, say, the second option like: \(\boldsymbol{\text{smooth}}\) (assuming the options are: 1. straight, 2. smooth, 3. horizontal, then the answer is the second option: 2. smooth))