Does a Sliding Mass on an Incline Have a Horizontal Acceleration Component?

[Natalie456]

1. For the following, the x-axis is not allowed to be set along the ramp. If a mass, starting from rest, slides along a linear, frictionless incline of length D and then falls a distance h to the ground, will it have an x-component of acceleration?

2. Relevant kinematics formulas?

3. I wasn't certain. It does travel a distance of Dcosθ in the horizontal direction. I initially figured that, because it starts at rest and travels this horizontal distance, there must be some component of acceleration in the x-direction, as well as in the y-direction, but, now, I am uncertain. A similar question with the coordinate axis set similarly also confused me.

Thanks!

 

[BvU]

The way I read the exercise is that you can choose the x-axis in any direction, except along the ramp. Thing to do is make a drawing, choose an x-axis direction and see if the actual acceleration (which way is that pointing ?) has a component along such an x-axis.

 

[TomHart]

If a mass, starting from rest, slides along a linear, frictionless incline of length D and then falls a distance h to the ground, will it have an x-component of acceleration?

Is the question asking if it will have an x-component of acceleration after it hits the ground, during the fall to the ground, or at any time during the whole process? Based on the wording, I would interpret it to be asking if it has an x component of acceleration after it hits the ground. But I'm not sure if that's what they meant. But in order to have an x-component of acceleration, there needs to be a net force acting in the x direction. And the result of that will be a change in the x component of velocity.

 

[BvU]

Perhaps I'm being a bit too suspicious (a lot of experience ?). If the exercise composer meant well, he or she may have thought of only two (the most frequently used) choices of coordinate systems: horizontal or along the incline.
Especially if you (and teacher?) are fairly new to the subject: a reasonable way to read the exercise is:

will it have a horizontal component of acceleration during this last part of the trip