PHY111 Final Exam
What is the equation for finding the maximum speed that a rocket could reach, given the engine thrust has already been found?
1. J = Ft (for engine thrust) 2. Ft = m(delta)v (for maximum speed rocket can reach)
What is the equation for third harmonic (second overtone)?
f3 = 5v / 4L
A cube is suspended from a spring scale. The scale reads the weight of the cube at 15.0 N. The cube is then submerged in water (density = 1000 kg/m^3) while still attached to the scale, which now reads 10.0 N. What is the volume of the cube?
pgV + T + mg = 0 (1000)(9.8)(V) + 10 N + -15 N = 0 V = 5.1 x 10^-4
How do you find the final velocity of a given particle after finding the horizontal and vertical components?
You add the horizontal & vertical components together. To find the direction, take the tangent^-1 of the horziontal and vertical components divided. Ex: Tan(theta) = horiz/vert
Who children push on opposite sides of a door. The first child pushes with a force of 30 N perpendicular to the door at a position 0.4 m from the hinges of the door. With what force should the second child push to maintain static equilibrium is the second child pushes at an angle 60 degrees relative to the door at a position 0.6 m from the hinges?
rF + -rFsintheta = 0
While pulling a nail out of a board, a student applies a downward 25 N force on a crowbar at a position 0.2 m horizontal from the pivot point. The nail is located 0.03 m measured horizontal from the pivot point. What is the force of the crowbar on the nail?
rF - rF = 0 (.2)(25) - (.03)(F) = 0
How do you convert rotations to radians?
rotations(2pi) = rads
What net torque is required to make a solid, 50 kg disk (I = 1/2mr^2) with a radius of 0.7 m experience an angular acceleration of 30 rad/s/s?
t = Ia *first, find I
What is the formula for torque?
t = fFsin(theta)
A wood board with a length of 2.5 is allowed to pivot at its midpoint. A 60 kg student sits 0.8 m from one end of the board. What is the torque of the student on the board?
t = mgL * because it says MIDPOINT, you have to halve the L and subtract 0.8 from the MIDPOINT. t = mg(1.25 - 0.8)
A 60 kg student stands on the end of a 1.5 m diving board. What is the student's torque on the diving board?
t = mgr
How do you find the magnitude of force caused by torque?
t = rFsintheta
What are the conditions for equilibrium?
tau = 0
Give an example of an object that experiences centripetal acceleration but not angular or translational acceleration.
A ferris wheel experiences centripetal acceleration but not angular or translational acceleration.
Give an example of an object that experiences centripetal, translational, and angular acceleration.
A motorcycle turning a corner experiences centripetal, translational, and angular acceleration.
In order for an object to experience a change in velocity, the object must experience:
A net force & an acceleration
Loudness is determined by a sound wave's:
Amplitude
What will result in a larger period for a pendulum?
An increase in the length of the rope of the pendulum
What change will result in a larger frequency for an oscillating spring-mass system?
An increase in the spring constant
Net impulse is equal to:
An object's change in momentum
Velocity is a measurement of which of:
An object's speed and direction of motion
A wheel, initially at rest, experiences a constant non-zero net torque. While the constant net torque is applied, the wheel also experiences a constant:
Angular velocity
A student has two blocks each with a different mass by the same volume. Block 1 has double the density of block 2. Both blocks are suspended from a force sensor and completely submerged in water. Which of the following is a correct statement?
The reading on sensor 1 will be larger than the reading on sensor 2.
A student has two blocks each with the same mass but different volumes. Block 1 has double the density of block 2. Both blocks are suspended from a force sensor completely submerged in water. Which of the following is a correct statement?
The reading on sensor 1 will be larger than the reading on sensor 2.
A rifle recoils while firing a bullet. The speed of the rifle's recoil is small because:
The rifle has a lot of mass
What is torque?
The rotational equivalent of force and the product of force and the perpendicular lever arm length
A large truck collides with a small car that is initially at rest. Which vehicle experiences the largest change in velocity?
The small car will experience the largest change in velocity. This is due to the conservation of momentum between two objects with unequal masses.
A pendulum with a mass if 0.8 kg and a rope length of 1.2 m is angled at 20 degrees relative to the vertical. What is the pendulum's oscillation frequency once it is released?
f = (1 / 2pi) x radical(g / L)
What is the equation for fundamental frequency?
f = v / 4L
One object is traveling at some speed to the right and another object is traveling at another speed to left. The objects collide. You are given the mass and velocity of both cars. What formula will be used to show what the speed of the cars would be after the collision?
(mv) + (mv) = (m + m)v
When trying to find how far a point on a hollow disk will travel in 1 minute of rotation, what do you do?
1st, find how many rads the disk turns in 1 second by multiplying w by 60 (theta) Then, find delta s (s = distance) s = theta(r) That will give you distance per minute of rotation.
How do you find the velocity of the flow rate as water exits a faucet? (Given Q)
Av = Av Q = Av
A student places two copper cubes with equal dimensions in a bucket of water. Both copper blocks sink to the bottom of the bucket. The first cube is solid copper and the second copper cube is hollow. What statement is accurate?
Both cubes experience the same, non-zero buoyant force.
An object is suspended from a spring scale. The scale reads the weight of the cube at 20 N. The cube is then submerged in water still attached to the scale, which now reads 15 N. What is the buoyant force on the object?
Buoyant force = 20 - 15 Bf = 5 N
A car turns a corner at a constant speed. Which of the following correctly identifies all of the non-zero acceleration terms experienced by the car?
Centripetal
What will result if a system experiences a net torque?
Changing the speed rotation
While pulling a nail out of a board, a student applies a downward force at a position 0.2m horizontal from the pivot point. The nail located 0.03 m measured horizontal from the pivot point. What is the mechanical advantage provided by the crowbar?
MA = F student / F nail
A baseball bat collides with a 0.145 kg ball moving w an initial velocity of 35 m/s to the left. If the collision lasts 0.005 s and the final velocity is 25 m/s, what was the force of the bat on the ball?
F = m(delta v) / delta t F = m(Vfinal - Vinitial) / t
What maximum horizontal force can a student apply to the top of a 2.0 m cubic box at rest on a rough surface before the box will start to tip over? The mass of the box is 100 kg.
Fd = mg(r/r)
To solve an equation to find the door's angular acceleration when two children push on opposite sides of the door:
First, find Impulse using the given equation (I = 1/3mL^2) Then, find the net torque on the door using the equation: (t = Frsintheta - Fr) Finally, solve for angular acceleration using the equation (t = Ia)
How do you find the net torque necessary to stop a rotating disk in a given time?
First, find the angular acceleration using the equation: (w = at + w_0) Then, plug that into the net torque equation (t = Ia) using the given angular speed.
How do you find the water pressure at the bottom of the container being used to catch water after 60 s?
First, find the height for the pressure equation. Q = Ah / t Then, use the equation P = pgh to find the pressure in Pa
What best defines "spring constant?"
Force per m of stretch or compression
What statement can best describe the energy transformations that occur when a pendulum swings back and forth?
Gravitational energy is converted to kinetic energy and back
What equation do you use to find the horizontal and vertical components of a given particle?
Horizontal: 0 = mvcos(theta) + mvcos(theta) + mv_x Vertical: 0 = mvsin(theta) + mvsin(theta) + mv_y
What is the equation for inertia?
I = 1/2mr^2
What is the equation for impulse or intensity?
Impulse = power / area To find the impulse for a circular area: I = P / (pi)r^2
Period and frequency have an ___________ relationship.
Inverse
What is the equation for impulse problems? For example, how would you find the average engine thrust provided by an engine?
J = Ft
What is the energy of motion?
Kinetic energy
What are the conditions for elastic kinetic energy?
Kinetic energy is conserved in the system
What are the conditions for inelastic kinetic energy?
Kinetic energy is not conserved in the system
A particular metal block has a mass of m and a volume of V. A student obtains the same metal that has a mass of 1/2 m. The volume of the sample must be:
Less than V.
What can be used as a measure of an object's inertia?
Mass
What is the definition of density?
Mass / Volume
Two masses are allowed to oscillate on identical springs. Mass A has a mass of m and mass B has a mass of 2m. If the two oscillate for the same amount of time, which mass will travel a greater total distance?
Mass A will travel a greater total difference.
The law of conservation of mass states that:
Mass cannot be created or destroyed
What is the best definition of pressure?
Mass per Area
A simple, uniform bridge has a length of 8.0 and a mass of 15000 kg. What is the normal force on the *LEFT* side of the bridge when as 1200 kg car is at a position of 6.0 m on the bridge?
N(8) = (15000 x 4 + 1200 x 2)(9.8) N = (60,000 + 2400 / 8) (9.8) N = 7.6 x 10^4
What is the equation to find friction force given the weight of an object, length of an object, and the degree of the angle the object is resting on? ex: a 15 kg ladder w/ a length of 2.0 m is placed against a smooth wall. The ladder forms a 75 degree angle. What is the friction force on the ladder?
N2 = wcostheta / rsintheta
What is the equation for Poiseuille's Law, or the equation for laminar flow in a pipe?
Q = (delta)P(pi)r^4 / 8(nu)(l)
What is the equation for the volume flow rate of water as it leaves the tank?
Q = Av Q = (pi)r^2v
What is the equation for laminar flow rate?
Q = P(pi)r^4 / 8nl
What is the equation for volumetric fluid flow rate?
Q = V/t
A cylindrical column of liquid applies a pressure of 120 Pa to the bottom of the container. If the liquid has a mass of 25 kg, what is the cross-sectional radius of the container?
P = F / A A = (pi)r^2 120 = (25)(9.8) / (pi)r^2
Use the given density and height to determine the pressure of the gas surrounding the barometer.
P = pgh
What is the fluid pressure at the bottom of a 2.0 m column of water (density = 1000 kg/m^3)?
P = pgh
A student measures the fluid pressure at the bottom of a column of fluid at 5.0 kPa. The atmospheric pressure is 101 kPa. What is the absolute pressure?
Pabs = Pgauge + Patm
What is the equation for wave period?
Period = 1 / frequency (frequency = waves / second)
What depth of water (density = 1000 kg/m^3) will result in a fluid pressure of 5000 Pa?
Pfluid = pgh 5000 = (1000)(9.8)(h)
Use the manometer to determine the gas pressure in the container. Atmospheric pressure is 101 kPa and the fluid is mercury with a density of 13560 kg/m^3. Hg = 5.0 cm = .05 m
Pgas = Patm + pgh *Remember to convert 101 kPa to Pa (101,000 Pa)
A student measures the fluid pressure at the bottom of a column of fluid at 3.0 kPa. The atmospheric pressure if 101 kPa. What is the gauge pressure?
Pgauge = Pfluid Pgauge = 3.0 kPa
A spring with a mass of 7.0 kg and a spring constant of 200 N/m is compressed 0.7 m. When released, the spring-mass system will oscillate horizontally on a frictionless surface. What is the frequency of oscillation?
Remember that frequency is the inverse of the equation for period, T. f = (1/2 pi)(rad(k/m))
A student creates a position vs. time graph for the oscillation of an object. The equation for the graph is determined to be: x = (.25)cos(3.0 t). What is the period of oscillation?
Remember that x = Acoswt and w = 2pi / T So, plug in the known variables & solve: 3.0 = 2pi / T T = 2.09 s
A pipe with some radius has fluid moving through it with velocity v. The radius of the pipe halves. Which statement is most accurate?
Since mass must be conserved, all the mass that enters the pipe every second must equal the mass that exits the pipe every second. The fluid flow rate will remain the same.
Examples of longitudinal waves include:
Sound, transmission of an earthquake
Two identical spring-mass systems are allowed to oscillate. System A oscillates vertically while system B oscillates horizontally. If both systems have the same initial spring stretch, which system will experience the largest maximum velocity?
System A will have the largest maximum velocity.
What mass attached to a spring constant of 50 N/m will have an oscillation period of 3.0 s?
T = (3pi)radical (m/k)
What is the equation for the friction force for torque?
T = (inertia)(acceleration)
The equation for period for a spring oscillator is:
T = 2(pi)radical m/k
A large truck collides with a small car that is initially at rest. Which vehicle experiences the largest collision force?
The force of the truck on the car is equal to the force of the car on the truck.
A student places a block of wood in a bucket of water where the block floats half above the surface. The student then places a second, larger block of wood in the bucket. The second block of wood also floats half above the surface. Which statement is true?
The buoyant force on the larger block of wood is greater than the buoyant force on the smaller block of wood.
Inertia is a measure of...
The difficulty of changing an object's motion
What is one definition for wavelength?
The distance between two crests
Describe the effect on the flow rate when the radius of the pipe decreases.
The flow rate decreases
Describe the effect on the flow rate when the pressure difference decreases.
The flow rate will decrease.
Describe the effect on the flow rate when the fluid viscosity decreases.
The flow rate will increase
Describe the effect on the flow rate when the length of the pipe decreases.
The flow rate will increase
What is the equation for the velocity of the water as it leaves the hole near the bottom of the tank?
The long pressure equation starting with 1/2
A large truck collides with a small car that is initially at rest. Which vehicle experiences the largest change in momentum?
The momentum lost by the truck is equal to the momentum gained by the car.
What will result if the net force of an object is not zero?
The object will accelerate.
What will result if the net force on an object is zero?
The object will remain motionless or move at a constant speed.
A hot air balloon with several people inside of it has a total mass of 3000 kg. If the density of air is 1.2 kg/m^3, what volume must the balloon have in order to float?
p = m / V 1.2 = 3000 / V
What is the equation for momentum?
p = mv
A student uses a wrench to tighten a particular bolt. Which of the following changes would allow the student to use a smaller force without changing the torque?
The student should move his hand further away from the bolt.
What is the best definition of an oscillation period?
The time to complete one oscillation
What statement is accurate concerning simple harmonic motion of a pendulum?
The total energy in the system remains constant throughout oscillations.
Two equal mass disks are rotating about an axis through their centers. Disk A is hollow while disk B is solid. Both disks have the same starting angular velocity. Equal sized frictional torques are applied to both disks. Which disk will stop first?
The two objects have the same mass, but that mass is distributed about the axis of rotation differently. The cover the mass to the axis, the smaller the moment of inertia and the easier it becomes to change the rotation of the object. Since disk B has some mass near the axis where disk A has none of its mass near the axis, disk B will have a smaller moment of inertia. Disk B will have rotational motion that is easier to change; therefore, it will stop first.
A student places a block of wood in a bucket of water. The block of wood floats so that half of the volume is below the water line and half the wood is above the water line. What is accurate about this relationship?
The upward force of the water is equal to the weight of the wood.
What is an example of an oscillating object?
The vibration of a string, a guard marching back and forth between two points, a child swinging on a swing set
What conditions must be met for a system to experience a constant velocity?
There must be no net force on the system.
How do you find the difference in pressure between two parts of a pipe?
Use long equation that starts with 1/2 and fill in missing variables. Remember p = 1000 kg/m^3. The answer should be P1 - P2
The slope of a position vs. time graph is best defined as:
Velocity
What is the formula for momentum?
p = mv
What is the equation for wave frequency?
frequency = # of waves / second Units = Hz
What is the equation for determining wavelength?
lambda = distance / frequency (1.5)
What is the maximum velocity of a pendulum that has a starting height 0.5 m above the equilibrium?
mgh = 1/2mv^2 *m cancels out gh = (1/2)v^2
A 0.15 kg arrow moving with an initial velocity of 30 m/s passes through a 3.0 kg block initially at rest on a frictionless surface. If the final speed of the arrow is 25 m/s, what is the speed of the block?
mv + mv = mv + mv
A 25 kg child rides a 3.0 kg skateboard with an initial velocity of 2.0 m/s. The child jumps backward off the board in a way that she has no final velocity. What is the resulting speed of the skateboard?
mv + mv = mv + mv
What is the formula for angular velocity?
omega (w) = (delta)theta / t
What is the equation for finding the speed of a traveling wave?
velocity = lambda x frequency
A solid 50 kg disk (I = 1/2mr^2) with a radius of 0.7 m rotates from rest to a final angular velocity of 20 rad/s/s in 4.0 s. What is the disk's angular acceleration?
w = at + w_0
What is the equation to find the time it takes for an object (i.e. a rocket) to reach maximum velocity?
w = at + w_0
What is the formula for angular distance?
w = at + w_0
A student attaches a 2.0 kg mass to a spring constant of 70 N/m. The student stretches the spring 0.15 m and then releases the spring. The spring-mass system oscillates horizontally on a frictionless surface. What is the position of the mass at time 1.5 s?
w = rad(k / m) x = Acoswt
