Two stacked objects sliding down inclined plane.

In summary, the conversation discusses a 60kg boy riding down an icy hill on a bathroom scale and determining the static friction force between the scale and the boy. It is mentioned that there is no friction between the scale and the hill, and the forces acting on the boy are gravity, normal force, and the force of inertia. The conclusion is that the force of static friction is 0.
  • #1
michaelwiggin
3
0

Homework Statement


"A 60kg boy rides down an icy hill of 19º slope while standing on a 2.6kg flat-bottomed bathroom scale. Assume there is no frictional force between the bottom of the scale and the hill. The static friction force the scale exerts on the boy is ____.


Homework Equations


... F = ma
Ff=[tex]\mu[/tex]Fn
Not sure what else... really its the theory of it that's getting me.


The Attempt at a Solution


Well, my understanding is that if there was no friction between the boy and the top of the scale, then while the scale was sliding down the hill, the boy would be sliding downward not only with respect to the hill (as a result of the acceleration of the scale) but also with respect to the scale. But because it asks for the static friction of the scale on the boy, this must mean he's not moving, and thus when determining the friction we can use the usual Ff=mgsin[tex]\theta[/tex] equation.


Thus 60kg(9.8m/s2)(sin19) = 191.4

Any mistakes that you all notice?

Thanks!
-Michael
 
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  • #2
Both the boy and the scale slide downhill together. What is the acceleration of the boy? What are the forces acting on the boy?

ehild
 
  • #3
>>Well, my understanding is that if there was no friction between the boy and the top of the scale
no, there is no frictional force between the scale and the ice hill

>>this must mean he's not moving
yes, relative the the scale he is not moving
 
  • #4
The scale is not an inertial frame of reference as it is accelerating with respect to the stationary ground. If you stick to the scale as frame of reference, there is a force of inertia -ma acting on each body of mass m where a is the acceleration of the scale along the slope. You have gravity, the force of inertia, normal force and static friction acting on the boy. The sum of these forces must give zero.

ehild
 
  • #5
You're correct ehild, my initial thinking was completely foolish. Somehow I believed that if frictionless plates (any objects I suppose) were stacked atop each other upon an inclined plane, than *each* accelerated with respect to the surface that they were placed on. That's absurd, of course, because if 100 plates were stacked then the top one would be accelerating at a rate of 981 m/s^2.*facepalm*The force of static friction is 0. Thanks fellas.
-Michael
 

FAQ: Two stacked objects sliding down inclined plane.

1. What is the relationship between the angle of the inclined plane and the acceleration of the stacked objects?

The acceleration of the stacked objects depends on the angle of the inclined plane. The steeper the angle, the greater the acceleration will be.

2. How does the mass of the stacked objects affect their motion down the inclined plane?

The mass of the stacked objects does not affect their motion down the inclined plane. According to Newton's Second Law of Motion, the acceleration of an object is directly proportional to the net force acting on it, and inversely proportional to its mass.

3. Is the friction between the stacked objects and the inclined plane a factor in their motion?

Yes, the friction between the stacked objects and the inclined plane can affect their motion. Friction is a force that opposes motion, and it can decrease the acceleration of the stacked objects as they slide down the inclined plane.

4. How does the length of the inclined plane impact the final velocity of the stacked objects?

The length of the inclined plane does not directly affect the final velocity of the stacked objects. However, a longer inclined plane would allow the objects to accelerate for a longer period of time, resulting in a higher final velocity.

5. What factors can affect the accuracy of calculations for the motion of stacked objects down an inclined plane?

The accuracy of calculations for the motion of stacked objects down an inclined plane can be affected by factors such as air resistance, the presence of external forces, and the smoothness of the inclined plane's surface.

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