Applications of Newton’s Laws

Physics 11

Numerous Applications

• Apparent weight• Free fall• Inclined planes• Atwood’s machines• Universal Law of Gravitation

Apparent Weight• Due to your non-inertial frame of reference, you feel as though your

weight changes when, in an elevator, it starts to move.• You can observe this « weight change » on a scale inside the elevator.

Example 1• A person is standing on a scale in an elevator when it suddenly begins

to move upward at a rate of 0.75 m/s2. What will be the apparent weight of the person, as indicated on the scale?

Quick Practice

p.186 # 21, 22, 23

Free Fall• Free Fall occurs when gravity

is the only force acting on an object.• However, as an object falls

through Earth’s atmosphere, its collides with air molecules. This creates air resistance, a form of friction.• This friction cannot be found

using a coefficient of friction.

Importance of Inclined Planes

Motion on Inclined Planes• Always assign a coordinate system that best fits motion.• This may facilitate calculations.• For example, rotate the X axis so that it becomes parallel to the

inclined plane, and the Y axis perpendicular to the plane.

Free Body Diagram on an Inclined Plane• You must still draw

the FBD on inclined planes, but remember that the weight is always downward.

• This means that component forces can be found using a system of triangles.

Example 2• A mass of 1 kg is sliding down an icy inclined plane, as shown in the

diagram below. At what acceleration will the mass be sliding down the plane?

Example 3• Consider now an inclined surface with the same block of mass (1 kg),

but resting. Find the coefficient of friction between the mass and the surface.

Homework Practice

p.474 # 10, 11, 12, 13

Atwood’s Machine• Atwood’s machine consists of a pulley

and two masses.• When one mass weighs more than the

other, they start moving in opposite directions.• The two masses however share the same

rope, thus the same tension acts on both masses.• Our problems will neglect friction due to

the pulley.

Simplifying the Machine…• An easy way to better understand the

FBD of an Atwood’s machine is to draw the rope and masses system in a straight line with the corresponding forces.• For example, try drawing the machine

without the pulley, and in a straight line.

Example 4• Two masses are suspended on a

pulley, and then let go.• If mass 1 = 1 kg and mass 2 = 2 kg,a) What is the acceleration of the

masses?b) What is the tension in the rope?

Understanding Pulley Systems

Quick Practice

p.485 # 19, 20, 21

Example 5 : Modified Pulley Problem• Consider a mass of 5 kg connected to a

suspended mass of 3 kg, as shown in the diagram.

a) If the surface is frictionless, what is the acceleration of the masses and the tension in the rope?

b) If the surface and mass have a coefficient of friction of 0.4, what is then the acceleration of the masses and the tension in the rope?

Example 6• Consider the following:

m1 = 5 kgm2 = 4 kgµ = 0.25θ = 35°

• What is the acceleration of the masses?

Homework Practice

p.488 # 24, 25, 27, 28

Gravity Goes Both Ways…• From Newton’s 3rd Law, for all action there is a reaction.• This also applies to gravity!

Newton’s Law of Universal Gravitation• Two objects of mass and will exert a force of gravity of equal

magnitude toward each other.

Where is the force of gravity (N) is the mass of one object (kg) is the mass of a second object (kg) is the distance between the centres of the masses (m) is the universal gravitational constant:

Example• Two blocks of mass of 20 kg and 40 kg are separated by a distance of

2 metres, center to center.a) What is the gravitational force between the two blocks?b) What would be the acceleration due to gravity of the two

blocks?

Example• Johnny is measuring his mass on a scale on the ground. It indicates a

mass of 50 kg.a) What is the gravitational force exerted on Johnny by Earth?b) What is the gravitational force exerted on Earth by Johnny?.

Refer to Appendix B, p. 955 for constants.

Example• Using the law of Universal Gravitation, prove that Earth’s gravitational

acceleration is in fact 9.81 m/s2.

Refer to Appendix B, p. 955 for constants.

Quick Practice

p.580 # 1, 2, 3, 5