Questions and answers for final exam (longer version)
Two persons with masses of 60 kg and 70 kg are sitting on a balanced seesaw. If the lighter person is sitting 2 m from the center, where is the heavier person sitting?
1.71m. (60 kg x 2 m)/70 kg =1.71 rounded
A child with a mass of 45 kg is riding on a merry-go-round. If the child has a speed of 2.5 m/sand is located 1.6 m from the center of the merry-go-round, what is the child's angular momentum?
180 kg m2/s. ( (45 kg) x (2.5 m/s) x (1.6 m)= 180 kg m2/s)
What is the acceleration always associated with an object in free fall?
9.8 m/s^2. This is the acceleration due to gravity, commonly called g. (On the exam, any falling object is assumed to be in free fall (no air resistance) unless told otherwise.)
What kind of work, positive or negative, can a person do by pushing on a box?
A person can do either positive or negative work by pushing on a box. If the person pushes the box in the same direction that it moves, accelerating it, then positive work is done. If the person pushes in the opposite direction of the moving box, decelerating it, then negative work is done.
What is the agreed-upon direction of rotational velocity?
Along the axis of rotation in the direction your thumb would point if the fingers of your right hand curl along the motion of the spinning object.
A second Newton's Law for rotational motion states that a net torque is equal to the product:
An angular acceleration and rotational inertia
Describe Newton's first law of motion
An object at rest will remain at rest unless acted upon by a force, and an object in motion will remain in motion unless acted upon by a greater or equal force.
Define: the kinetic energy of an object
An object's kinetic energy is the energy resulting from its motion.
A person with a mass of 70 kg stands on the unsupported end of a plank that extends 3 m beyond the pivot end. What torque does he exert on the plank?
D)2100 Nm. 70 x 3 x 10= 2100
A young man applies a force of 120 N to a merry-go-round perpendicular to its radius. The radius is 2.5 m. What is the value of the net torque on the merry-go-round?
D. 300 N· m 120 N x 2.5m= 300 N*m
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 .2kg on Earth?
F = mg = .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. W=mg
What is the centripetal force F experienced by a body travelling in a circle of radius r at a constant speed v?
F = mv^2/r. This comes from F = ma, Where: a is the centripetal acceleration. Where: v = velocity in m/s a = acceleration in m/s^2 m = mass in kg r = radius of circle in m
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 gravitational force?
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 relationship between force, mass, and acceleration in Newton's second law of motion?
Fnet = ma. net force and acceleration are both vectors & must be pointing in the same direction.
What kind of work (positive, negative, or both) can frictional forces do?
Frictional forces can only do negative work. By definition, frictional forces are always in the opposite direction of an object's motion. Hence, they can only slow the object down & only do negative work.
Give the velocity of a 1kg block after falling for 2 seconds from rest.
From: vf = vi + at. vf = 0 + (9.8)(2) = 2(9.8) = 19.6 m/s
What is its gravitational potential energy of an object of mass m that is a height h above the surface of the Earth?
GPE = mgh. This is identical to the work needed to raise the object that height & is also equal to the kinetic energy the object will gain if it is allowed to fall freely to the ground.
Which is the correct expression for rotational kinetic energy?
Half of the rotational inertia times the square of the rotational speed.
Which of these is Newton's first law as applied to rotation?
In the absence of an external interaction, the angular velocity of an object remains constant.
Kinetic energy is defined as:
KE = ½mv 2. where m is the object's mass and v is its speed. The units of kinetic energy are Joules, just like all other forms of energy.
If objects 1 and 2 are the same mass, but object 2 is moving at twice the speed of object 1, how do their kinetic energies compare?
KE2 = 4*KE1. Kinetic energy is defined as ½mv2, so it is directly proportional to the square of the velocity. If the objects' masses are the same, kinetic energy will increase with the square of the velocity.
Equation for angular momentum.
L=Iw or L=Mv * r. I is Rotational Inertia and W is angular velocity
What two characteristics are necessary to define a vector?
Magnitude and direction. Magnitude is the quantity, size, or amount and is a scalar value since it lacks direction. Direction of a vector: Direction provides spacial orientation, angle, or path.
The momentum, p, of an object is its mass times its current velocity.
Momentum can also be thought of as the inertia of an object, or the mass times change in distance per unit time.
Which of the following statements is true about any collision between two objects with no net applied force acting?
Momentum is always conserved and kinetic energy is sometimes conserved.
SI unit for torque
N x m
SI unit of impulse
N x s
What is the power flowing through a wire, if 1,000 J of energy flow through in 0.1 s.
P = 10,000 W = 10 kW Power is energy divided by time; 1000 J / 0.1 s = 10,000 W. Note that kW is a commonly-used unit on the Phy. exam.
Define power, as used in physics.
Power is a measure of the rate of energy flow. Power is defined as energy divided by time: P = E/t. The units of power are Watts, where 1 W = 1 J/s.
What is the relationship between normal force and friction for a static object?
Static friction (or rolling friction) is a force that opposes any two surfaces in contact from sliding over each other. fs ≤ μsFN Where: fs = force of static friction in N μs = coefficient of static friction FN = normal force in N
What is the maximum height of a ball thrown directly upwards from the ground with a velocity of 10 m/s?
The ball's maximum height is 5m. The kinematic equation is vf^2= v0^2 + 2aΔx Setting v0 to 10m/s, vf to 0m/s, and a to -10m/s^2. yields: 0 = 100 + 2(-10)Δx Δx = 5m
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.
An object is moving with 100 J of kinetic energy, and a frictional force acts on it, doing 50 J of work. What is the object's final kinetic energy?
The object's final KE is 50 J. According to the work-energy theorem, the net work done on the object results in a change in its kinetic energy. Since the frictional force is the only force affecting motion, the work done equals the change in kinetic energy. Frictional forces can only do negative work, so the final kinetic energy is lowered.
An object with mass m falls through a distance h. What is its final kinetic energy? (assume no dissipative forces).
The object's final KE is mgh
Define: the principle of conservation of energy.
The principle of conservation of energy states that, in the absence of dissipative forces, a system's total mechanical energy is constant. Dissipative forces such as friction or air resistance will decrease a system's total mechanical energy.
How does the acceleration experienced by a child on a merry-go-round change if the speed of the merry-go-round doubles?
The velocity increases by a factor of 4. Since acceleration is proportional to the velocity squared, if the velocity doubles, the acceleration increases by the square of that amount, or 4x.
How could an object's perceived (or instantaneous) weight seemingly change?
The weight is the force pushing back on an object against gravity. This is a specific type of normal force. A person might experience a decreased instantaneous weight if the ground falls away beneath them, such as if an elevator accelerates downwards.
Define: the work-energy theorem
The work-energy theorem states that the net work done on an object by all the forces acting on it equals the change in the object's kinetic energy. Wnet = ΔKE
which of the following is true about frictional forces
They can decrease kinetic energy.
what variables are with for volume
V
what are the variables associated with velocity
V. also a vector. though rarely used, s may be used for speed (magnitude only, scalar).
What is the work done by a force F which acts on an object as it moves through a distance d?
W = F x d. only the component of force parallel to the motion contributes to the work; any forces perpendicular to motion do not work.
What is the work done by gravity as an object of mass m moves from the ground to a height h?
W = mgh
What are the units of work, as defined in physics?
Work has units of Joules (J). N x m, or kg x m^2 /s^2, which is identical to the units of Joules
What is the formula for the centripetal acceleration acting on a body following a circular path with a constant speed v?
a = v^2/r
What are the variables for acceleration
a. also a vector
Stable equilibrium is:
an equilibrium state where any small rotation results in a torque that acts to produce rotation back in the opposite direction.
Translational (linear) speed is displacement divided by time, and rotational speed is:
angular displacement divided by time.
What does inelastic collision results in
at least one object being deformed, heated, broken, or otherwise changed. Also, friction causes heat, or compression causes potential energy or work on an object. At least one object will be deformed, heated, broken, or otherwise changed.
How is the maximum height of an object in projectile motion found?
by finding the point where the vertical component of velocity, vy, equals zero. Then input this value into the equation with distance, to solve. The object moves upwards until it reaches this point, and then starts moving downwards.
what variables are associated with length or distance?
d and x are used for distance, h for height, z for depth, and r for radius.
Inelastic collision
involves some mechanical (kinetic) energy of the system being converted to internal energy, as the objects collide and separate. Momentum will remain conserved.
Totally inelastic collision
involves some mechanical (kinetic) energy of the system being converted to internal energy, as the objects stick and remain connected. Momentum will remain conserved.
The kinetic energy of an object
is directly proportional to the square of its speed.
Torque
is the ability of a force to create a change in the angular orientation of an object, by rotation about a fulcrum point. Torque can also be thought of as the component of work perpendicular to a lever arm.
impulse
is the change in momentum of an object, due to a net force applied over some amount in time.
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
Define Instantaneous velocity (vo).
is the direction and magnitude of the rate of change for distance per unit time. vo = Δx / t
Define: acceleration
is the rate at which velocity changes per unit of time. a = Δv / t
Define the total mechanical energy of a physical system.
is the sum of the kinetic and potential energies of ALL the objects that make up the system. Etotal = KEtotal + PEtotal
Define: Average velocity (Vave)
is the total distance and direction traveled from an initial position, divided by the total time. Vave = Δx total /Δttotal. or: Vave = (vf + vi)/2
SI unit of momentum
kg x m/s
The unit of momentum in SI is:
kg x m/s
The unit of Kinetic energy in SI is:
kg x m^2/s^2
If the elevator had accelerated downwards, the person would feel?
less weight. going downwards would make the person experience weightlessness
What is the momentum of an object if it has:
m = 2kg, v = 15 m/s? m = 4kg, v = 20 m/s? m = 10kg, v = 0 m/s? 30 kg*m/s 80 kg*m/s 0 kg*m/s
What is the equation relating momentum before and after a totally inelastic collision, for two masses traveling at some velocities?
m1v1 + m2v2 = (m1+m2 )vf. This is simply derived from the usual conservation of momentum, keeping in mind that after a totally inelastic collision the objects combine into a single mass.
What is Weight 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 SI unit for length or distance?
meters (m).
What SI unit is velocity?
meters/second (m/s).
What SI unit is acceleration?
meters/second^2 (m/s^2).
What SI unit is volume?
meters^3 (m^3 ).
rotational equilibrium
occurs when the net torque on an object is zero. If the sum of all torques acting on an object cancel to zero then the object will not undergo rotational acceleration
According to the work-energy theorem, the is net work done
on the object results in a change in its kinetic energy.
Which of the following is an appropriate unit for describing rotational acceleration?
rev/s^2.
Which of these is NOT a vector quantity?
rotational kinetic energy
What SI unit for time?
seconds (s).
What the variables for time?
t & T
The angular momentum of a particle moving in a circle around a point is equal to:
the mass times the speed of the particle times the radius of its orbit.
Rotational acceleration measures:
the rate at which rotational speed changes.
Since gravity is the only force acting on the object, the change in kinetic energy simply equals
the work done. Work = F * d, or, in this case, mg * h. You might also recognize this as the gravitational potential energy of the object before it fell.
What formulas can be used to find final velocity, if given initial velocity?
vf = vi + at vf 2 = vi2 + 2aΔx Where: vf = final velocity in m/s. vi = initial velocity in m/s. a = acceleration in m/s^2. Δx = displacement in m. t = time in s
elastic collision
which the mechanical (kinetic) energy and momentum of the system are both conserved. Elastic collisions require objects to bounce off each other perfectly, rigidly, without any deformation.
How will a person's instantaneous weight change if the elevator they are standing in begins to accelerate upwards?
while accelerating upwards will be greater than at rest, as the acceleration upwards adds to the normal force that the person experienced while at rest.