SPH4U1: Forces LESSON 3 – Applying Newton’s Laws: Incline Plane and 2 Body Systems
APPLYING NEWTON’S LAWS: The following is a list of steps that should be followed
when solving complicated dynamics problems.
Step #1: Read the problem carefully.
Step #2: Draw a FBD for each object and label all forces.
Step #3: Set up x & y axis. Their direction is up to you to set.
Step #4: Decide which direction (both x & y directions) is to be positive. Note: it is easier
to pick the direction of motion as positive.
Step #5: Set up sub titles: horizontal (x) and vertical (y) components for each object.
Step #6: Break up any force into components if necessary.
Step #7: Write a 2nd law equation for each object in both the x & y directions
(∑ F = Fnet = ma)
Step #8: Solve the equations algebraically; may need to combine some of the equations.
INCLINE PLANE PROBLEMS: Incline Plane problems are most easily solved using coordinate rotation. The positive axes should be parallel and perpendicular to the incline
itself. When breaking up the gravitational force into components, be sure to use the
angle (θ), between the force and the incline.
SPH4U1: Forces LESSON 3 – Applying Newton’s Laws: Incline Plane and 2 Body Systems
EX1: Evil Kinevil is driving his motorcycle up a ramp that is inclined at 30° to the
horizontal before jumping over a row of cars. If there’s a constant frictional force of
1000N on the ramp, determine the force that the engine must apply to accelerate the
1
motorcycle up the ramp at g . (Assume Evil and his bike have a combined mass of
3
250kg).
EX 2: A skateboarder slides down a frictionless ramp inclined at an angle of 30° to the
horizontal. He then slides across a frictionless horizontal floor and begins to slide up a
second incline at an angle of 25° to the horizontal. The skateboarder starts at a distance
of 10m from the bottom of the first incline. How far up the second incline will he go if
the coefficient of kinetic friction on the second incline is 0.10?
SPH4U1: Forces LESSON 3 – Applying Newton’s Laws: Incline Plane and 2 Body Systems
STRING – and – PULLEY Problems: In order to solve a 2 body system problem (or any
multiple body system problem), you need to draw a FBD for each object being
considered. You must then determine the direction of motion of each object, and write
an algebraic description of Newton’s second law for each object. ASSUMPTIONS: Pulleys
are massless and frictionless. Strings are infinitely strong, massless and never stretch.
EX 3: Two 5.0 kg masses are connected as shown. Determine the
acceleration of the system and the tension in the rope if the
table top is frictionless.
EX 4: You attach a loonie (m=6.99g) and a dime (m=2.09g) to the ends of a thread
(don’t question how it was attached….maybe some massless tape to go along with the
massless thread). You place the thread around a smooth pulley. You release your hands
and watch as the loonie drops and the dime rises.
a) Determine the acceleration of the coins.
b) Determine the tension in the thread.
SPH4U1: Forces LESSON 3 – Applying Newton’s Laws: Incline Plane and 2 Body Systems
EX 5: Jane Bond is suspended in the unfortunate situation shown below. If Jane has a
mass of 75 kg and her car has a mass of 1500 kg, and the coefficient of friction between
the ramp and the car is 0.15, determine
a) the direction of Jane’s motion.
b) Jane’s acceleration.
c) the tension in the rope.
HMWK: Pg. 92 #5,7
Pg. 95 #5-7,10