Dynamics.docx

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b) The tension force is the same on either side of the pulley.

Example 2: Contact Forces on a Set of Combined Masses

Calculate

a) the acceleration, .b) the contact force which the

mass acts on the mass, .c) the contact force which the

mass acts on the mass, .


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Solution

a) The acceleration is right.

b) The net force accelerating the mass is the force of the mass pushing against it.

Alternatively, consider the fraction of the total

mass which the

mass takes up. This will equal

the fraction of the applied force it experiences.

c) The net force accelerating the mass is the difference of the applied force and the force of the

mass pushing against it.

or

Note how Newtons Third Law applies: .

Example 3: Forces at an Angle

Calculate the acceleration of the following object:

Solution

Start by drawing a free-body diagram.


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(

)

Example 4: Pulleys and Objects on Slopes

Given that the mass of the

man is

and he

would like to descend with

an acceleration of ,calculate the mass of the

box, ,a) assuming .

b) if .Solution

a) We can represent the situation as a linear system:

b) Here are two ways to solve this problem:


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Method 1: Use a process similar to a), but add the force of friction to (since they are acting in thesame direction), and subtract this sum from to obtain .

( ) ()

[ ]

Method 2: Use a system of equations.

Solve (1) and (2) simultaneously

to find and :

( )


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Example 5: Multiple Forces on an Object

A box is pulled by two cables with forces and over a frictionless surface. The box moves to theright with an acceleration of due east. Calculate and .

Solution

Method 1: Resolve the forces into their components and solve a system of equations.

|| ||

Method 2: Draw a vector diagram (below) and solve using the Sine Law.

( )

1


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Example 6: A mass on a string is attached to the centre mirror of a car. As the car

accelerates forward, the mass swings backwards with an angle . Given that the mass is

and

is

, determine the acceleration,

.

Solution

The mass experiences two forces: the tension force of the string pulling on it, and the force of gravity .Together, these two forces add up to give the resultant force, .Method 1: Use trigonometric ratios.

Method 2: Compare the horizontal and vertical components separately, then solve a system of equations.

||

() () Note: there is often more than one way to solve a problem. Read over the different methods above, and

see which one you prefer.

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Dynamics.docx