SPH 4U1 Evans

Unit 2: Dynamics(Causes of Motion)

Note 1: Newton’s Law’s, Forces & Problems (Chpt 2.1-2.3)

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Reference Text Sections 2.1, 2.2., 2.3

Force: push or pull of a definite magnitude and direction.  Force is a vector quantity.  SI unit is newtons (N).

Newton: force needed to accelerate a mass of one kg at the rate of 1 metre per second squared.

Mass: Amount of matter in an object.  It is a scalar and is constant on any planet.

Weight: force of gravity on an object.  Weight is a vector and is not constant (depends on which planet and the object’s distance from the centre of the planet). Weight=

Unbalanced force: The resultant force acting on an object is the unbalanced or net force.  It is the vector sum of all the forces acting on the object.

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Newton’s First Law (Inertia): When no external unbalanced force acts on an object, its velocity (or state of rest) remains constant.

Newton’s Second Law: When an external unbalanced force acts on an object, it accelerates.

we define the Newton so that k is 1

Newton’s Third Law (action-reaction): For every action force, there is a simultaneous reaction force equal in magnitude but opposite in direction.

Steps to solve problems: Draw diagram and free body diagram. Label all forces.  Resolve into components (one component should be in direction of acceleration). Determine net forces.

Free Body Diagrams:

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Example 1:

Inga is pulling a monument with a force of 100N {E30N}.  Anna is pulling the same monument with a force of 100N [E30S].  William is pulling the same monument with a force of 10N[W].  What is the net force on the monument?

Example 2:

You hit a ball with a force of 9.9N [33 above the horizontal] for 5.0 ms.  The force of gravity on the ball is 2.6N [down].  Determine the net force on the ball as it is being struck.

Review Sample Problem 3 on page 79

Example 3:

Forces of 100N[N] and 80N[W] act simultaneously on an object of mass 10 kg.  What is the acceleration of the object?

Example 4:

A car can accelerate by 3 m/s2. What is its acceleration if it is towing another car like itself?

Example 5:

A car with a mass of 1000 kg is moving in a straight line at a constant speed of 30 m/s.  It is brought to rest in 25 s.  What constant force is acting to stop the car?

Example 6:

A force of 45N [E] acting at 37 degrees above the horizontal is applied to a  kg mass, causing it to accelerate from rest in an easterly direction.  The frictional force between the mass and the horizontal surface is 14N[W].

a)      Calculate the acceleration of the mass.

b)      Find the velocity of the mass after 5.0 s.

c)      After the 5.0 s time interval, the applied force of 45 N[E] is removed.  How far will the mass move before coming to rest?

When solving INCLINED PLANE problems, resolve your vectors parallel and perpendicular to the plane…………….

Example 7:

A girl pushes a suitcase having a mass of 35 kg up a ramp inclined at 24 degrees to the horizontal.  The applied force is 280N [up the ramp].  The magnitude of the frictional force is 120N.  Find the acceleration of the suitcase.

When solving PULLEY problems, define your positive direction for the entire system of objects (i.e. in some cases this may be clockwise and could result in +ve being up on one side of the system and down on the other side of the system)…………

Example 8:

Two masses A and B are suspended by a string on either side of a single fixed pulley.  The mass of A is 5.0 kg.  When the two masses are released, the acceleration of A is 1.4 m/s2 [down]. Find

a)      The magnitude of the tension in the string.

b)      The mass of B.

Example 9:

In the diagram shown, a force of 150N [W] is applied at 37 degrees above the horizontal to a block with a mass of 35 kg.  This block is connected to another block with a mass of 35 kg. This block is connected to another block with mass 5.0 kg by means of a string passing over a smooth peg.  The frictional force between the 35 kg block and the table is 47 N[E]. Find

a)      The acceleration of the 35 kg block

b)      The magnitude of the tension in the string.