What fraction of the distance do the block move?

[JD<3]

A block slides a distance d down a frictionless plane and then comes to a stop after sliding a distance s across a rough horizontal plane, as shown in the accompanying figure.

What fraction of the distance s does the block slide before its speed is reduced to one-third of the maximum speed it had at the bottom of the ramp?

a) s/3
b) 2s/3
c) s/9
d) 8s/9

Thanks for the help! :)

 

[SHISHKABOB]

could you show what attempts you have made at solving the problem?

 

[JD<3]

I thought that since it is reduced by 1/3 then it would be s/3. But I'm so confused because I know when something is reduced then you multiply to find the number.

 

[alienprophecy]

Is that all of the information that they gave you? It seems like they would have given you some other information, such as the angle between the smooth and rough surface, and especially the friction coefficient for the rough surface (usually denoted by the symbol μ).

 

[asteriatic]

The correct answer is b) 2s/3. This can be determined using the conservation of energy principle, where the initial potential energy of the block at the top of the ramp is converted into kinetic energy as it slides down. At the bottom of the ramp, the block's kinetic energy is at its maximum, and as it slides across the rough horizontal plane, this energy is gradually lost due to friction. When the block's speed is reduced to one-third of its maximum speed, it has lost two-thirds of its kinetic energy. Since the distance traveled is directly proportional to the kinetic energy, the block must have traveled two-thirds of the distance s before its speed is reduced to one-third. Therefore, the fraction of distance traveled is 2s/3.