** SPH 4U1 Evans**

**
Physics Grade 12**

**
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.

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**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.

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**Review Sample Problem 3 on page 79**

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**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/s^{2}. 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/s^{2} [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.

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