Acceleration down an inclined plane

In summary, the conversation discusses a problem involving a box sliding down an incline with a given mass and angle. The coefficient of kinetic friction, work done by friction, and change in potential energy are calculated using Newton's 2nd law and energy conservation. The acceleration is assumed to be constant due to no external forces acting on the box during the slide.
  • #1
jakerue
5
0

Homework Statement



A 25-kg box slides, from rest, down a 9.0-m-long incline that makes an angle of
15° with the horizontal. The speed of the box when it reaches the bottom of the
incline is 2.4 m/s. (a) What is the coefficient of kinetic friction between the box
and the surface of the incline? (b) How much work is done on the box by the
force of friction? (c) What is the change in the potential energy of the box?

Homework Equations



Fx = mg * sin15
Fn = mg * cos15
Ffr = uk * Fn = uk * mg * cos15
Vf2-Vo2 = 2 *a*d

The Attempt at a Solution



Having an issue with kinetic friction calculation here

Taking the force components and applying Newton's 2nd law -> ƩF = ma
Fx - Ffr = max
mg * sin 15 - uk (mg * cos 15) = m * ax

Since I want uk and the final velocity is given, I calculate accel -> Vf2 - Vo2 = 2*a*d so a = 2.4m/s / (2*9.0m) = 0.32 m/s^2
Can I put it into mg * sin 15 - uk (mg * cos 15) = m * ax and end up with uk = 0.2345 ?

I can't get over that ax isn't constant acceleration and I don't think I can use it in this case...
 
Last edited:
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  • #2
I would assume constant acceleration, since there is no external forces acting on the box and it's sliding under its own mass. Therefore, I believe your method is correct.
 
  • #3
What makes you think that the acceleration is not constant? Can you identify a force that changes during the slide?

If you're leery about the acceleration you could always check the result by using an energy conservation approach. You know the potential energy (due to gravity) at the top of the slope, and the kinetic energy at the bottom (i.e. velocity). The difference of the two will be the energy lost to friction.
 

1. What is acceleration down an inclined plane?

Acceleration down an inclined plane refers to the rate at which the velocity of an object changes as it travels down an inclined surface. It is affected by the angle of the incline, the mass of the object, and the force of gravity.

2. How is acceleration down an inclined plane calculated?

The acceleration down an inclined plane can be calculated using the formula a = gsinθ, where a is the acceleration, g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle of the incline.

3. Does the mass of the object affect acceleration down an inclined plane?

Yes, the mass of the object does affect the acceleration down an inclined plane. Objects with larger masses will experience a greater force due to gravity, resulting in a larger acceleration.

4. What happens to the acceleration down an inclined plane if the angle of the incline is increased?

If the angle of the incline is increased, the acceleration down the plane will also increase. This is because the force of gravity acting on the object becomes more perpendicular to the surface, resulting in a larger component of the force in the direction of the incline.

5. How does friction affect acceleration down an inclined plane?

Friction can act in the opposite direction of the object's motion, slowing down the rate of acceleration. However, if the force of friction is negligible, it will not have a significant effect on the acceleration down the incline.

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