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Acceleration and Inclined Planes

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Updated:  
2016-03-26 10:47:03
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When you have a block of ice (read: frictionless) moving down a ramp, it’s being acted on by forces, which means that it’s accelerated. How fast is it being accelerated? When you know that F = ma, you can solve for the acceleration.

After you solve for the force along the ramp, you can get the acceleration (a = F/m) along the ramp. Your block of ice is going to accelerate down the ramp.

Sample question

  1. Suppose you have a block of ice on a ramp at 40 degrees, and it slides down. What is its acceleration?

    The correct answer is 6.3 m/s2.

    1. What’s important here is the force along the ramp:

      image0.png
    2. The acceleration of the ice is

      image1.png

      In other words, the acceleration is the component of g acting along the ramp. Note that this result is independent of mass.

    3. Plug in the numbers:

      image2.png

    Notice that you did not need to know the mass of the ice in this problem because the mass cancels out of the equation.

Practice questions

  1. Suppose that a block of ice is on a ramp with an angle of 60 degrees. What is its acceleration?

  2. You’re unloading a couch on a cart from a moving van. The couch gets away from you on the 27 degrees ramp. Neglecting friction, what is its acceleration?

  3. 3.You have a block of ice with a mass of 10.0 kg on a ramp with an angle of 23 degrees when it slips away from you. What is its acceleration down the ramp?

  4. You’re sliding down a toboggan run at 35 degrees. What is your acceleration?

Following are answers to the practice questions:

  1. 8.5 m/s2

    1. The force along the ramp is

      image3.png
    2. The acceleration of the ice is

      image4.png
    3. Plugging in the numbers gives you

      image5.png
  2. 4.4 m/s2

    1. The force along the ramp is

      image6.png
    2. The acceleration of the cart is

      image7.png
    3. Plugging in the numbers gives you g(sin theta) = 4.4 m/s2.

      image8.png
  3. 3.8 m/s2

    1. The force along the ramp is

      image9.png
    2. The acceleration of the ice is

      image10.png
    3. Plugging in the numbers gives you

      image11.png
  4. 5.6 m/s2

    1. The force along the ramp is

      image12.png
    2. Your acceleration is

      image13.png
    3. Plugging in the numbers gives you

      image14.png

About This Article

This article is from the book: 

About the book author:

Dr. Steven Holzner has written more than 40 books about physics and programming. He was a contributing editor at PC Magazine and was on the faculty at both MIT and Cornell. He has authored Dummies titles including Physics For Dummies and Physics Essentials For Dummies. Dr. Holzner received his PhD at Cornell.