# Is the Block Moving Horizontally or Perpendicularly on the Inclined Plane?

• cs2018
In summary, the block slides down the plane at a speed proportional to the magnitude of the force applied.
cs2018

## Homework Statement

[/B]
This problem is from David Morin's Introduction to Classical Mechanics, Chapter 3, Problem 7:
A block is placed on a plane inclined at angle θ. The coefficient of friction between
the block and the plane is μ = tan θ. The block is given a kick so that it initially
moves with speed V horizontally along the plane (that is, in the direction perpen-
dicular to the direction pointing straight down the plane). What is the speed of the
block after a very long time?

## Homework Equations

I've set up the equations and shown that the force (along the plane) from the effect of gravity is equal to the friction force (along the plane). The issue is understanding what it is saying about the initial motion.

## The Attempt at a Solution

What does it mean to move "horizontally along the plane"? Is this the same as moving along the plane? That's usually how these questions are set up. One complication is that the title of the question is "Sliding sideways along a plane" and this is a different title from question 6, which is "Sliding down a plane" and can easily be solved.

The part in parentheses (that is, in the direction . . .) suggests that the block is moving perpendicular to the (inclined) plane because the motion is perpendicular to the direction pointing straight down the plane. Or is this perpendicular to the level ground because the direction pointing straight down the plane is the vertical direction?

The solution is not helpful and says at the end that after a long time, the block is essentially moving down the plane. How else is it supposed to move if it doesn't move down the plane? Shouldn't the block always be moving down the plane if the acceleration down the plane is zero, as the solution states?

Hi cs2018 and welcome to PF.

This is how I interpret the picture.
Imagine the x-axis along the incline, positive is downhill. Imagine the z-axis perpendicular to the incline pointing away from the surface. The block has an initil velocity that is along the y-axis which is, of course, perpendicular to both the x and z axes. Gravity is perpendicular to the y-axis only; it forms angle θ with respect to the negative x-axis and angle 90o-θ w.r.t. the negative z-axis.

A plane has two directions. One horizontal and one is the slope direction. Note that friction will not cancel gravity exactly from the beginning.

Hi kuruman and Orodruin,

Thank you very much for the help. It seems obvious, but just didn't get it. The comment about friction not cancelling gravity right away was very helpful for getting the solution. Thank you again. :)

## 1. What is sliding sideways along a plane?

Sliding sideways along a plane is a type of motion where an object moves parallel to the surface of a plane, without changing its orientation.

## 2. What is the difference between sliding sideways and rolling?

Sliding sideways refers to motion where an object maintains contact with the surface it is sliding on, while rolling involves an object rotating on a surface without sliding.

## 3. What are some real-life examples of sliding sideways along a plane?

Some examples include a car skidding on an icy road, a hockey puck sliding on ice, or a person sliding down a water slide.

## 4. What factors affect the speed of sliding sideways along a plane?

The speed of sliding sideways along a plane is affected by the friction between the object and the surface, the angle of the plane, and the weight and shape of the object.

## 5. How is the coefficient of friction related to sliding sideways along a plane?

The coefficient of friction is a measure of the roughness of a surface and the force required to slide an object along it. It plays a crucial role in determining the speed and distance of an object sliding sideways along a plane.

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