Finding a velocity of an object moving down an inclined plane help

In summary, a block with a mass of 1.137 kg is placed on an inclined plane with a length of 2.592 m. The angle of the plane can be adjusted to change the height of the top. The lower half of the plane has a rough surface while the top half is smooth, with specific coefficients given. The minimum angle for the block to start sliding downwards is 7.688 degrees. To calculate the speed of the block halfway down the slope, you must consider the friction force acting along the slope.
  • #1
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Homework Statement



A block with a mass of 1.137 kg is placed at the top of an inclined plane. The plane is d = 2.592 m long. The angle θ the plane makes with the horizontal can be adjusted, changing the height of the top of the plane.

The lower half of the plane has a rough surface with μs = 0.417, μk = 0.375, while the top half of the plane is smooth with μs' = 0.135, μk' = 0.087. These coefficients are given between the plane and the block.

The block is placed at rest at the very top of the slope. What minimum angle should the slope be set for the block to just start sliding downwards?

I calculated the angle to be 7.688 degrees (which is been accepted as correct)

Now I need to calculate - The slope is held at this angle and the block slowly accelerates from rest down the slope. What is the speed of the block halfway down the slope?

The Attempt at a Solution



Vf^2 - Vi^2 = 2as

Vf^2 = 2 x (9.8m/s x sin(7.688) x 1.296m
= 3.398
sqrroot = 1.84m/s

But this is incorrect. Can anyone point me in the right direction or let me know what I am not understanding? Thank you in advance! :)
 
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  • #2
g x sin θ applies only for a frictionless surface.

When there is friction, you must determine the nett force acting along the slope, and use that to calculate accn.
 

1. How do you calculate the velocity of an object moving down an inclined plane?

The velocity of an object moving down an inclined plane can be calculated using the equation v = √(2ghsinθ), where v is the velocity, g is the acceleration due to gravity, h is the height of the inclined plane, and θ is the angle of inclination.

2. What information do I need to know to find the velocity of an object on an inclined plane?

In order to calculate the velocity of an object on an inclined plane, you will need to know the angle of inclination, the height of the inclined plane, and the acceleration due to gravity. These can typically be measured or given in the problem.

3. How does the angle of inclination affect the velocity of an object on an inclined plane?

The angle of inclination directly affects the velocity of an object on an inclined plane. The greater the angle, the faster the object will accelerate down the plane due to the increased force of gravity pulling it downwards.

4. Can the velocity of an object on an inclined plane be negative?

Yes, the velocity of an object on an inclined plane can be negative if the object is moving in the opposite direction of the positive direction chosen for the calculation. This could happen if the object is sliding up the incline instead of down.

5. Are there any other factors that can affect the velocity of an object on an inclined plane?

Yes, there are other factors that can affect the velocity of an object on an inclined plane. These include friction, air resistance, and the mass of the object. However, in the basic calculation for finding the velocity, these factors are not taken into account.

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