Chapter 4 Examples

1. Newton's First Law	2. Newton's Second Law	3. Free-Body Diagrams	4. Friction	5. Friction and Inclines	6. Pulleys
Additional Example Problems with Solutions

Force Vectors

Example 1: Newton’s First Law

You place an open container of Starbuck’s coffee in front of you on the dash of a car and then accelerate. What force causes the coffee to come toward you and spill?

You place an open container of Keva Juice as above except that you slam on brakes. What force causes the container to travel towards the windshield?

Example 2: Newton’s Second Law

What force is required to stop a 1000 kg vehicle that is travelling on a straight road at 100 km per hour within a distance of 50 meters?

Diagram

We can use Newton’s second law, åF = ma, to calculate a. We assume that the car is moving to the right and place the coordinate axis at the car with positive to the right.

Knowns

v₀ = 100 km/h = 28 m/s, v = 0, x – x₀= 50 m

Unknowns – what are we trying to find?

Equation(s) to Use

We can use åF = ma to find the force if we know a. So we will find a

Assuming constant acceleration, we can use the following equation: v² = v²₀ + 2a(x – x₀) and solve for a

a = (v² – v²₀)/2(x – x₀)

Calculations

a = (0 – 28²)/2(50) = -7.8 m/s²

Note the negative sign – according to our above convention, it is opposite the direction of motion

Note: 1 N = 1kg m/s²

Said another way, a newton is the amount of force required to give an acceleration of 1m/s2 to a mass of 1 kg

å F = ma F = (1000 kg)( -7.8 m/s²) = -7800 N

The negative sign means that the force must be applied in a direction opposite to that in which the vehicle is moving

Example 3: Free-Body Diagrams

Free-body diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon an object in a given situation. A free-body diagram is a special example of the vector diagrams which were discussed earlier. These diagrams will be used throughout our study of physics.

The size of the arrow in a free-body diagram is reflects the magnitude of the force. The direction of the arrow shows the direction which the force is acting. Each force arrow in the diagram is labeled to indicate the exact type of force. It is generally customary in a free-body diagram to represent the object by a box and to draw the force arrow from the center of the box outward in the direction which the force is acting. An example of a free-body diagram is shown below.

The free-body diagram on the right depicts four forces acting upon the object. Objects do not necessarily always have four forces acting upon them. There will be cases in which the number of forces depicted by a free-body diagram will be one, two, or three. There is no hard and fast rule about the number of forces which must be drawn in a free-body diagram.

The only rule for drawing free-body diagrams is to depict all the forces which exist for that object in the given situation. If given a description of a physical situation, begin by using your understanding of the force types to identify which forces are present. Then determine the direction in which each force is acting. Finally, draw a box and add arrows for each existing force in the appropriate direction; label each force arrow according to its type.

Test your understanding by drawing free body diagrams for each of the following. Answers

¢ A book is at rest on a table top. Diagram the forces acting on the book.

¢ An egg is free-falling from a nest in a tree. Neglect air resistance. Diagram the forces acting on the egg as it is falling.

¢ A flying squirrel is gliding (no wing flaps) from a tree to the ground at constant velocity. Consider air resistance.

Diagram the forces acting on the squirrel.

¢ A rightward force is applied to a book in order to move it across a desk with a rightward acceleration.

Consider frictional forces. Neglect air resistance. Diagram the forces acting upon the book.

Example 4: Friction

A 20.0 kg box is pulled along a horizontal surface by a force F_p of 45.0 N applied at an angle of 35.0 degrees. Assume a coefficient of kinetic friction of 0.32. Calculate the acceleration.

Draw the Free-Body Diagram Solution

Answers