1.7.1 The Concept of Force - Weebly

SPH 4U Unit #1 Dynamics Topic #7: Forces and Free Body Diagrams (Teacher)

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1.7.1 The Concept of Force

Defined as: any influence which tends to change the motion of an object.

1.7.1a The Fundamental Forces

The four fundamental forces, arranged in increasing order of strength, are:

1. The Force due to Gravity

The weakest of the four fundamental forces, yet it is the dominant force in the universefor shaping the large scale structure of galaxies, stars, etc. It is an example of aninverse square law force. The force is always attractive and acts along the line joiningthe centers of mass of the two masses. The forces on the two masses are equal in sizebut opposite in direction, obeying Newton's third law. Viewed as an exchange force, themassless exchange particle is called the graviton.

2. The Weak Nuclear Force

An extremely short range exchange force (10 m. approx. the size of a proton) that–18

involves the exchange of the W and Z intermediate vector bosons. It is involved inmany decays of nuclear particles and is essential to the formation of deuterium which isused by the sun during fusion. Its most familiar effect is beta decay (of neutrons inatomic nuclei) and the associated radioactivity. The word "weak" derives from the factthat the field strength is some 10 times less than that of the strong force.13

3. The Electromagnetic Force

This force holds atoms and molecules together. It manifests itself through the forcesbetween charges (Coulomb's Law) and the magnetic force, both of which aresummarized in the Lorentz force law ( ). The electromagnetic force is anexchange force involving the exchange of photons . It has infinite range and it obeysthe inverse square law, like the force due to gravity.

4. The Strong Nuclear Force

This force holds the nucleus together against the enormous forces of repulsion of theprotons. However, it is not an inverse square force like the electromagnetic force and ithas a very short range. It has been modelled as an exchange force in which theexchange particles are pions and other heavier particles.


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1.7.1b The Units of Force

The SI unit for force is the Newton, which is defined by 1 Newton = 1 kg m/s as you2

may recall from Newton's second law.

1.7.1c Common Forces

In our everyday lives, we usually experience forces like the ones listed below:

the force due to gravity (directed downward)tension (along the rope)friction (opposes the motion)normal (perpendicular to the surface)

Eg.#1 Label these forces on the diagram above.

1.7.2 Drawing Free Body Diagrams

When analyzing situations involving forces, it is much easier to determine the net effectof all of the forces if we draw a simpler diagram called a free body diagram. A free-bodydiagram is a simplified sketch of a situation where:

i) the object is replaced by a pointii) all the surrounding objects are stripped away iii) all of the forces acting on the body are indicated by force vectors drawn to scale that originate at the point drawn in (i) above

Eg.#2 Draw a free-body diagram of a bicyclist that is traveling on a road inclined at 30degrees that experiences the following forces:

• the force due to gravity: 780 N [down]• the normal force: 680 N [perpendicular to the plane of the road surface]• the friction force: 390 N [up the incline]

Elevation view Free-body diagram


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Eg.#3 Draw an FBD for each of the following:

a) A hot dog sits on a table. b) A length of railway track is beingraised at a constant speed by a cableconnected to a crane.

c) A pencil has just begun falling d) A stove is being pulled up a ramp into from a desk to the floor (assume that a delivery truck by a cable parallel to theair resistance is negligible). ramp. The ramp is at an angle of 18/

above the horizontal.

Eg.#4 Draw an FBD of a ball that is dropped from a tall building assuming there is aforce of friction caused by air resistance.

a) shortly after it leaves b) two seconds later c) when it reaches terminal speedyour hand,


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Eg.#5 The tourist at right is pulling a heavy suitcase at aconstant velocity to the right with a force applied to the

handle at an angle above the horizontal. A smallforce of friction resists the motion.

a) Draw an FBD of the suitcase, labeling b) Draw an FBD of the suitcase, labelingthe components of the appropriate forces. the components of the appropriate Choose the direction of motion to be the forces. Choose the +x direction as the +x direction. direction in which the handle is pointing.

c) Which choice of +x is more convenient? Explain your answer

Choosing the direction in which the handle is pointing means that only one force needsto be resolved into two components, making the analysis easier.

d) How do you know which reference frame to choose? Explain your answer.

Choose the reference frame that includes the acceleration. This will make Newton’ssecond law much easier to apply as the net force will not have to be broken intocomponents.


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1.7.3 Finding the Net Force

1.7.3a Finding the Net Force Using the Sine and Cosine Law

Eg.#6 While competing, a long jumper whose weight is 538 N. experiences a force of6380 N [68.3° back from the vertical] at the instant she lands.

a) Draw a free body diagram to scale

b) Find the net force on the jumper.


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1.7.3b Finding the Net Force Using Vector Components

Eg.#7 A boat pulling two water skiers is shown below:

If the water applies a force of 450 N.[forward] on the boat and the water skiers eachapply a force of 225 N. back on the boat in the directions shown above,

a) draw a free body diagram of the boat to scale

b) find the net force on the boat.

Because of the symmetry of the situation,


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Worksheet 1.7

1. You push your ruler westward across the desk at a constant speed by applying aforce at an angle of 25 degrees above the horizontal.

a) Name all of the forces acting on the ruler b) Draw a freebody diagram of the ruler

Normal, friction, applied force and weight

2. Draw a freebody diagram for each of the following objects:

a) A cup hanging from a hook b) A curling rock sliding freely in astraight line on a rink

c) A person standing in an elevator that d) A crate being dragged across theis accelerating downward floor, with a significant amount of

friction, by a person pulling on a rope atan angle of 23 degrees above the horizontal


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3. The force of gravity on a textbook is 18N.[down]

a) What is the net force on the book if b) Neglecting air resistance, what is the it is held stationary in your hand? net force acting on the book if you

suddenly remove your hand?

4. At one particular instant in its flight, a ball experiences a force due to gravity of

and an air resistance of . Calculate

the net force on the ball.


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5. Given the following force vectors:

a) Draw a free body diagram to scale.

b) Find the net force using the method of components.


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c) Draw to scale.

d) Find using the sine and cosine laws.


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6. Given and determine the third force

that must be added to the sum to produce a net force of zero.

The required force is:


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7. A crate is being dragged across the horizontal icy sidewalk by two people pulling

horizontally on cords as shown below. The net horizontal force is . The

tension in cord 1 is 27N[E]. If friction is negligible, determine the tension in cord 2.

1.7.1 The Concept of Force - Weebly

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