Acceleration and Inclined Planes
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

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/s^{2}.

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

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

Plug in the numbers:
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

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

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.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?

You’re sliding down a toboggan run at 35 degrees. What is your acceleration?
Following are answers to the practice questions:

8.5 m/s^{2}

The force along the ramp is

The acceleration of the ice is

Plugging in the numbers gives you


4.4 m/s^{2}

The force along the ramp is

The acceleration of the cart is

Plugging in the numbers gives you g(sin theta) = 4.4 m/s^{2}.


3.8 m/s^{2}

The force along the ramp is

The acceleration of the ice is

Plugging in the numbers gives you


5.6 m/s^{2}

The force along the ramp is

Your acceleration is

Plugging in the numbers gives you
