Conceptual-Questions-2
Kepler's laws of planetary motion are as follows:
(1) Kepler's first law: The orbit of each planet about the Sun is an ellipse with the Sun at one focus. (2) Kepler's second law: Each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal times. (3) Kepler's third law: The ratio of the squares of the periods of any two planets about the Sun is equal to the ratio of the cubes of their average distances from the Sun: T12 /T22=r13 / r23, where T is the period (time for one orbit) and r is the average radius of the orbit.
Which statement is correct? (a) Net force causes motion. (b) Net force causes change in motion. Explain your answer
(b) is correct. According to Newton's second law, F = mg that is, a net force causes acceleration, which is the change in motion
The conversion between radians and degrees is
1rad=57.3º, 2πrad=360º= 1 revolution
Drag forces acting on an object moving in a fluid oppose the motion. For larger objects (such as a baseball) moving at a velocity v in air, the drag force is given by FD=12CρAv2, where
C is the drag coefficient, A is the area of the object facing the fluid, and ρ is the fluid density.
There is an analogy between rotational and linear physical quantities. What rotational quantities are analogous to distance and velocity?
Distance is analogous to Angle Theta Velocity is analogous to Angular velocity w
Kepler's second law of planetary motion:
Each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal times.
Newton's universal law of gravitation: Every particle in the universe attracts every other particle with a force along a line joining them. The force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. In equation form, this is F=G(mM)/r2, where
F is the magnitude of the gravitational force. G is the gravitational constant, given by G=6.674×10-11N⋅m2/kg2
Centripetal force Fc is any force causing uniform circular motion. It is a "center-seeking" force that always points toward the center of rotation. It is perpendicular to linear velocity v and has magnitude Fc=mac, which can also be expressed as
Fc=mv2/r or Fc=mrω2
What properties do forces have that allow us to classify them as vectors?
Forces have magnitude and Direction
A rock is thrown straight up. What is the net external force acting on the rock when it is at the top of its trajectory?
Gravitational force downwards.
What is the relationship between weight and mass? Which is an intrinsic, unchanging property of a body?
Mass is the amount of materials in an object. Weight is the gravitational force on mass. The mass is the intrinsic unchanging property of a body.
When objects rest on a non-accelerating horizontal surface, the magnitude of the normal force is equal to the weight of the object:
N=mg.
(a) Give an example of different net external forces acting on the same system to produce different accelerations. (b) Give an example of the same net external force acting on systems of different masses, producing different accelerations.
Newton's Second law of Motion gives F = ma. So, (a) if F is different then acceleration a will be different. (b) If F is the same but m is different then acceleration a will be different.
A thrust is a reaction force that
Pushes a body forward in response to a backward force. Rockets, airplanes, and cars are pushed forward by a thrust reaction force.
The period and radius of a satellite's orbit about a larger body M are related by
T2= (4π2/GM)r3 or r3/T2=(G/4π2)M.
Why does an ordinary rifle recoil (kick backward) when fired? The barrel of a recoil-less rifle is open at both ends. Describe how Newton's third law applies when one is fired.
The bullet applies equal and opposite force that the rifle gives to the bullet. This is an example of Newton's third law of motion.
Kepler's first law of planetary motion:
The orbit of each planet about the Sun is an ellipse with the Sun at one focus.
Kepler's third law of planetary motion:
The ratio of the squares of the periods of any two planets about the Sun is equal to the ratio of the cubes of their average distances from the Sun: T12 /T22=r13 / r23, where T is the period (time for one orbit) and r is the average radius of the orbit.
If a constant, nonzero force is applied to an object, what can you say about the velocity and acceleration of the object?
The velocity will increase but the acceleration will remain the same
When you take off in a jet aircraft, there is a sensation of being pushed back into the seat. Explain why you move backward in the seat—is there really a force backward on you?
This is the effect of the Newton's first law of motion, the law of Inertia. There is no backward force. An object at rest tends to stay at rest. So, when the jet aircraft starts to move forward, the body at rest likes to stay at rest and does not want to move with the jet. That gives the feeling of moving backward.
Newton's third law of motion represents a basic symmetry in nature. It states:
Whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction to the force that the first body exerts.
The relationship between the deformation and the applied force can also be written as ΔL=(1/Y)(F/A)L0, where
Y is Young's modulus, which depends on the substance, A is the cross-sectional area, and L0 is the original length.
Acceleration, a is defined as
a change in velocity, meaning a change in its magnitude or direction, or both.
When objects rest on a surface, the surface applies a force to the object that supports the weight of the object. This supporting force acts perpendicular to and away from the surface. It is called
a normal force, N
In equation form, Newton's second law of motion is
a=F / m or F = ma
Centripetal acceleration ac is the acceleration experienced while in uniform circular motion. It always points toward the center of rotation. It is perpendicular to the linear velocity v and has the magnitude
ac=v2/r; ac=rω2
An external force is one
acting on a system from outside the system, as opposed to internal forces, which act between components within the system.
External forces are
any outside forces that act on a body.
Force is a vector having
both magnitude and direction.
The various types of forces that are categorized for use in many applications are all manifestations of the
four basic forces in nature summarized in Table 4.1
Dynamics is the study of
how forces affect the motion of objects.
A free-body diagram
is a drawing of all external forces acting on a body.
Mass
is the quantity of matter in a substance.
Inertia
is the tendency of an object to remain at rest or remain in motion. Inertia is related to an object's mass.
Rotating and accelerated frames of reference are
non-inertial.
Friction is a contact force between systems that opposes the motion or attempted motion between them. A normal force is always perpendicular to the contact surface between systems. Simple friction is proportional to the
normal force N pushing the systems together.
Friction is a force that
opposes the motion past each other of objects that are touching.
For small objects (such as a bacterium) moving in a denser medium (such as water), the drag force is given by Stokes' law, Fs=6πηrv, where
r is the radius of the object, η is the fluid viscosity, and v is the object's velocity.
Newton's first law of motion
states that a body at rest remains at rest, or, if in motion, remains in motion at a constant velocity unless acted on by a net external force. This is also known as the law of inertia.
The ratio of the change in length to length, ΔL/L0, is defined as
strain (a unitless quantity). In other words, (stress=Y×strain)
The ratio of force to area, F/A, is defined as
stress, measured in N/m2, (stress=Y×strain)
The pulling force that acts along a stretched flexible connector, such as a rope or cable, is called
tension, T.
Newton's second law of motion a = F/m or F=ma states that
the acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass.
The weight w of an object is defined as
the force of gravity acting on an object of mass m.
If the only force acting on an object is due to gravity,
the object is in free fall.
Angular velocity ω is the rate of change of an angle, ω=Δθ/Δt, where a rotation Δθ takes place in a time Δt. The units of angular velocity are radians per second (rad/s). Linear velocity v and angular velocity ω are related by
v=rω or ω=v/r
When a rope supports the weight of an object that is at rest, the tension in the rope is equal to the
weight of the object: T=mg.
Uniform circular motion is motion in a circle at constant speed. The rotation angle Δθ is defined as the ratio of the arc length to the radius of curvature: Δθ=Δs/r
where arc length Δs is distance traveled along a circular path and r is the radius of curvature of the circular path. The quantity Δθ is measured in units of radians (rad), for which 2πrad=360º= 1 revolution
Hooke's law is given by F=kΔL, where
ΔL is the amount of deformation (the change in length), F is the applied force, and k is a proportionality constant that depends on the shape and composition of the object and the direction of the force.
The kinetic friction force fk between systems moving relative to one another is given by fk=μkN where
μk is the coefficient of kinetic friction, which depends on both materials.
Friction depends on both of the materials involved. The magnitude of static friction fs between systems stationary relative to one another is given by fs≤μsN, where
μs is the coefficient of static friction, which depends on both of the materials.
