1. Forces On An Inclined Plane

3. FfFf FNFN FgFg 30° Think about the forces as she sleds down the hill in the laundry basket (if it is not a non-frictionless surface). Can you label them? What is the formula used to calculate F g ? = mg How many other forces are there? (Don’t make any up!) Two; the normal force (F N ) and the force of friction (F f ).

4. FgFg 30° F g ll Fg┴Fg┴ The force due to gravity can be broken up into vectors using the tip to tail method. They are F g ll and F g ┴. The formulas used to calculate the components are: = F g cos θ = F g sin θ One way to remember when to use cosine or sine is to look at the formulas on your reference table. A x = A cos θ (horizontal) and A y = A sin θ (vertical). Just use the opposite function for that direction when on an incline. F g ┴ = F g cos θ (vertical) and F g ll = F g sin θ (horizontal).

5. Other formulas you need to know: – F f = μF N (μ = coefficient of friction) – ΣF x = F net = ma = F gll – F f (ΣF x = sum of the forces in the x- direction)

6. Example: If a 60 kg person is sledding down a hill on waxed skis (yes, it’s a laundry basket, but just pretend!) at a 30 o incline at a constant velocity, calculate F net, F N, F g ll, F g ┴, F g, and F f. 30° = 588.6N The easiest thing to find first is the weight (F g ). Use the weight to find it’s vectors. = 509.73N = 294.3N F g ┴ = F g cos θ F g ll = F g sin θ F g = mg F g ┴ = (588.6N)cos(30°) F g ┴ = (588.6N)(0.866) F g ┴ = 509.73N F g ll = (588.6N)sin(30°) F g ll = (588.6N)(0.500) F g ll = 294.3N F g = (60kg)(9.81m/s 2 ) F g = 588.6N FgFg F g ll Fg┴Fg┴

7. What is the normal force equal to? (Remember, it has to be equal and opposite of another force.) It is equal to F g ┴. The normal force is pushing down with 509.73N of force while the ground is pushing up with an equal amount of force. F g ll Fg┴Fg┴ FgFg F N = 509.73N 30° To find the force of friction, plug in the normal force and the coefficient of friction that says waxed ski on snow. FfFf F f = μF N This would be ________ friction because it is SLIDING. kinetic *Since coefficients of friction don’t have units, keep the unit of a Newton.* F f = (0.05)(509.73N) F f = 25.49N = 25.49N

8. The last thing to figure out with all of the forces is the net force. Since she is going down the hill at a constant velocity, what does that mean? ***ZERO acceleration.*** Keep that in mind! ΣF x = F net = ma = F gll – F f 0 F net = F gll – F f F net = 294.3N – 25.49N F net = 268.81N 30° F g ll = 294.3N F f = 25.49N Subtract the force of friction because it is in the opposite direction of motion.