Lesson 5: Newtons Laws Flashcards
Define and give units for:
Force
Force is the change in velocity per unit time that a given mass is experiencing. Force can also be thought of as the change in momentum per unit time.
The SI unit of force is the Newton (N),
1N = 1 kg*m/s^2
Describe Newton’s first law of motion.
aka the Law of Inertia: An object in motion will continue with constant velocity unless acted on by a net force.
Similarly, an object at rest will continue to remain at rest until acted on by a net force.
What must be true about the acceleration of an object, if all forces acting on it cancel?
What must be true about the acceleration of an object, if all forces acting on it cancel?
What is the relationship between force, mass, and acceleration in Newton’s second law of motion?
Fnet = ma
Note: net force and acceleration are both vectors, and must be pointing in the same direction.
What is the proportional change in force to make an object move with twice its original acceleration?
Twice the original force must be applied.
From Newton’s second law, F=ma. Force and acceleration are directly proportional.
How does Newton’s third law of motion describe the forces between two objects?
F1on2 = -F2on1
For every force from one object on a second, there is an equal and opposite force from the second back on the first.
What is the formula for the universal law of gravitation?
Fg = Gm1m2 / r^2
Where:
G = gravitational constant in N*m^2/kg^2
m1 and m2 = masses in kg
r = distance between masses in m
What is the proportional change in gravitational force between two objects, if the distance between them doubles?
Force is decreased to 1/4.
Since F is proportional to 1/r^2, doubling r will reduce the force by a factor of 4.
What is the proportional change in gravitational force between two objects, if the distance between them halves and each object’s mass also halves?
No change in force.
Since each mass is directly proportional to F, halving each mass will result in 1/4 the original F. But, since F is proportional to 1/r^2, halving r will result in 4x F. The net change in F is the product both factors: 4(1/4) = 1, no change.
What is the more convenient relationship for force on a mass, due to gravity on Earth?
F = mg
Where:
F = force in N
m = mass in kg
g = acceleration due to gravity (9.8 m/s^2)
What is the magnitude of the force acting downward on an apple with mass 0.2kg on Earth?
2N.
F = mg = 0.2(9.8) ≈ 2N
Note: if the apple is resting on the ground, it will also be subject to an equivalent normal force pointing upwards.
Define:
Weight
Weight is explicitly the force on an object due to gravity. W=mg
Weight if often confused with mass; an object with one weight on Earth will have a different, lesser, weight on the moon, but its mass will remain constant.
What will the proportional weight of an object be on the moon, if the moon has 1/6 Earth’s gravity?
The object will have 1/6 the weight it had on Earth.
Since W is proportional to the acceleration due to gravity, the moon’s lesser gravity will produce a proportionally lesser weight.
Define:
Normal force
When two objects are touching, there exists an opposing force between the two objects and perpendicular to the surface in contact. This is the normal force.
Often, on the AP exam, normal force is opposing the force due to gravity.
What is the normal force for a book of mass 0.5 kg sitting stationary on a table?
5N directed towards the book, from the table.
The force pulling down on the book due to gravity is
F = mg = (0.5)10 = 5N downwards towards the table. Since the book is stationary, we know that normal force is equal and opposite; hence it must also be 5N in magnitude.
What formulas give the component forces for the force due to gravity on an inclined plane?
(note that by convention the “x” axis is along the slope of the plane, and the “y” axis is perpendicular to the plane)
Fx=mg sinθ
Fy=mg cosθ
Since these are opposite from how we normally compute components, a way to remember the x component is: sine is for slope.
What calculation will give you the normal force on a box of mass m, on an inclined plane with angle θ?
Since the box is not sinking into the slope, nor launching up off of the slope, the net force acting perpendicular to the slope must be zero. Hence, Fy=-FN
What is the force of static friction, if the box does not start to slide down the plane?
There are two forces parallel to the slope of the plane; the component of gravity parallel to the plane, with magnitude mg sin(θ), and the force of static friction, pointing in the opposite direction.
These forces must be equal and opposite to prevent motion.
In the pulley system demonstrated below, m2 is twice the mass of m1 and there is no net movement. What is the relationship between the tension in the string at points 1 and 2?
The tensions are equal.
A key to all pulley questions is to remember that the tension in the string running through the system is always constant since it is all one string and we assume the mass of the string is negligible.
What is the force F in the pulley apparatus below, with respect to the mass m1, assuming that all masses are stationary and no friction exists?
There are two forces acting on m1; gravity and tension. If the box isn’t moving, they must be equal and opposite, so T = -m1g. Since tension is constant through the string, the force on m2 from tension must also be F = -T = m1g.
What is the force F in the pulley apparatus below, with respect to the mass m2, assuming that all masses are stationary and no friction exists?
F = -m2g sinθ
There are two forces acting on the box along the inclined plane: the x component of gravity and the tension in the string. If the box isn’t moving, they must be equal and opposite. Hence
F = T = -m2g sinθ.
Give the equation for terminal velocity.
Where:
VT = terminal velocity in m/s
m = mass of object in kg
g = acceleration due to gravity in m/s^2
C = drag coefficient which is unitless
ρ = density of fluid object is traveling through in kg/m^3
A = cross-sectional area in m^2
