Calculating Acceleration of a Block Going Down a 37 Degree Ramp Without Friction

[guss]

I had a problem where there is a block going down a slope with an angle of inclination of 37 degrees, and we did not need to account for friction.

The question was what is the acceleration of the skier.

I know how you figure out the answer, which is 5.89 m/s^2. I know you have to set the hypotenuse to 9.8 then figure out the opposite side, and that's easy enough.

But, why do you set the hypotenuse to 9.8? It doesn't make sense to me, and if this was the trend, then a ball rolling down a ramp with an angle of inclination of .1 degrees would have an acceleration of 9.8 m/s^2.

Anyone care to explain? Thanks.

 

[Doc Al]

But, why do you set the hypotenuse to 9.8? It doesn't make sense to me, and if this was the trend, then a ball rolling down a ramp with an angle of inclination of .1 degrees would have an acceleration of 9.8 m/s^2.

The angle is measured with respect to the horizontal. So g*sinθ would be about 0.0017*g. It would roll very slowly down the incline, which is practically horizontal.

In general, you want the component of the acceleration down the incline. So the full acceleration would be g acting downward (and thus the hypotenuse of a right triangle) and the component parallel to the ramp would g*sinθ.

 

[guss]

In general, you want the component of the acceleration down the incline. So the full acceleration would be g acting downward (and thus the hypotenuse of a right triangle) and the component parallel to the ramp would g*sinθ.

I still don't quite understand, sorry. What is the reason you want the component of the acceleration down the incline?

 

[berkeman]

I still don't quite understand, sorry. What is the reason you want the component of the acceleration down the incline?

Because that's the direction the skier is moving, right?

 

[guss]

Because that's the direction the skier is moving, right?

Well, in this case the component of the acceleration (down the incline) is gravity. But that doesn't make sense to me because gravity should be vertical.

 

[berkeman]

Well, in this case the component of the acceleration (down the incline) is gravity. But that doesn't make sense to me because gravity should be vertical.

The acceleration down the incline would only be g if the incline were vertical. And it would be zero if the incline were horizontal. At all angles between vertical and horizontal, you need to use trig to calculate the component of g that is in the direction down the incline.

 

[guss]

The acceleration down the incline would only be g if the incline were vertical. And it would be zero if the incline were horizontal. At all angles between vertical and horizontal, you need to use trig to calculate the component of g that is in the direction down the incline.

Oh, I see now. The way you put it made me realize how it works, now it seems obvious. Thanks all.