Acceleration and Inclined Planes - dummies

By Steven Holzner

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