Inclined Planes Inclined Planes On an inclined plane

Inclined Planes

Inclined Planes » On an inclined plane the normal force is not opposite the weight » Therefore it is necessary to break one of them into its x and y components so you can find the net force N θ mg

Inclined Planes » Since the box is speeding up down the incline, the acceleration is in that direction, and therefore the net force is in that direction as well N a θ mg » It is easier to break the weight into components because the acceleration is down the incline which is perpendicular to the normal force

Inclined Planes » Now some trigonometry y N x a θ 90 - θ θ mg

Inclined Planes » Replace the force of gravity with its components. » Perpendicular to the ramp will be Fg cosƟ. » Parallel to the ramp will be Fg sinƟ. N a mg θ n i s θ θ mg mg θ s o c

Inclined Planes » Use Newton’s second law for both the parallel and perpendicular directions x y N a mg θ n i s θ θ mg mg θ s o c

Example A person pushes a 30 -kg shopping cart up a 10 degree incline with a force of 85 N. Calculate the coefficient of friction if the cart is pushed at a constant speed. Fa Fn q Ff mg q 0. 117

Find the acceleration of a 1000 kg roller coaster down an incline of 45 o if µ=. 12

Example What is the ms required to prevent a sled from slipping down a hill of slope 30 degrees? ms = 0. 577

» Example - a block of weight 180 N is pulled along a horizontal surface by a force of 80 N acting at an angle 30 with the horizontal at a constant speed. What is the normal force equal to?

Example The man pushes/pulls with a force of 200 N. The child and sled combo has a mass of 30 kg and the coefficient of kinetic friction is 0. 15. For each case: What is the frictional force opposing his efforts? What is the acceleration of the child? f=59 N, a=3. 80 m/s 2 / f=29. 1 N, a=4. 8 m/s 2