Chapter 4 Homework
Name: ______
Instructions: Print this document. Read and answer the assigned questions in the text book using the following format, in your own handwriting.
Exercise 1
First, draw a diagram below, indicating the horizontal plates, the electron beam, and the direction of the acceleration vector. Please also draw a coordinate system, a sign convention and an origin - think carefully about this. Where is the best place for the origin?
This question is very similar to a projectile problem in which the velocity parallel to the plates remains constant. Use this fact to write down an equation for the time that the electron beam is between the plates
t =
a) Use your equation to calculate the time.
t =
Write down one of the three equations of kinematics that will help you find the vertical displacement. Remember to use your coordinate system.
equation:
Now, make a list of the variables in your equation, and their values;
list:
b) Substitute the variables you identified above and solve the equation for the vertical displacement.
Use your coordinate system to identify the horizontal and vertical components of the velocity by adding the correct subscripts below;
V = horizontal
V = vertical
c) Using your notation, calculate the value of the horizontal component of the velocity
write down an equation that will help you find the vertical component of the velocity
Solve the equation for the vertical component of the velocity
Verify your answer is correct by checking the answer on the class web-site: erau.edu
Exercise 7
Draw a diagram, indicating all the forces (Hint, there are three).
Add an x - y coordinate system, with x indicating the horizontal direction and y the vertical direction, and a sign convention.
a) Resolve the forces in the x-direction and write down an equation for the acceleration, ax, using Newton’s 2nd law. Use symbols - no numbers yet.
Now solve the equation for ax,
b) Resolve the forces in the y-direction and write down an equation for the acceleration, ay, using Newton’s 2nd law.
What do you think is the value of ay just prior to the block moving up? This is the answer to part c)
Use this fact to solve for the force P needed to lift the block, this is the answer to part b) (I switched them around as the solution makes more sense this way).
Please verify your answers are correct before moving on.
Exercise 8
Draw a diagram indicating the forces acting on the block, a coordinate system and a sign convention.
a) Resolve the forces in the horizontal direction using your notation for the horizontal coordinate, and write down an equation for the acceleration, using Newton’s 2nd law. Use symbols - no numbers yet.
a =
(Use your notation to choose the correct subscript for a)
Now solve the equation for a,
a =
Now resolve the forces in the vertical direction using your notation for the vertical coordinate, and write down an equation for the acceleration, using Newton’s 2nd law. Use symbols - no numbers yet.
What can you say about the motion of the block in the vertical direction?
Repeat the previous page for the different mass implied in part b).
Start by calculating the “new” mass
m =
b) As before, resolve the forces in the horizontal direction using your notation for the horizontal coordinate, and write down an equation for the acceleration, using Newton’s 2nd law. Use symbols - no numbers yet.
a, =
(Use your notation to choose the correct subscript for a)
Now solve the equation for a,
a =
Now resolve the forces in the vertical direction using your notation for the vertical coordinate, and write down an equation for the acceleration, using Newton’s 2nd law. Use symbols - no numbers yet.
What can you say about the motion of the block in the vertical direction?
Please check your answer is correct before moving on to the next question.
Exercise 12
Draw a diagram indicating all the forces acting on the plane (Hint: there are three), a direction for the acceleration vector, a coordinate system and a sign convention.
a) Use Newton’s 2nd law to resolve the forces in the direction of the planes acceleration vector and find an equation for the thrust force, T.
T =
Now solve for T
T =
b) Use Newton’s 2nd law to resolve the forces in the direction perpendicular to the planes acceleration vector and find an equation for the lift force, L.
L =
Now solve for L
L =
Please verify your answer is correct before moving on.
Exercise 17
This question has to do with projectiles, and the question is asking for a symbolic answer, there are no numbers in the solution to this problem.
Start by looking at the equation given. Which of the 4 kinematic variables is missing? Next, use your three equations of kinematics to eliminate the missing variable, noting that the maximum altitude reached for a projectile occurs halfway through the time of flight, when the vertical velocity is zero.
Exercise 22
Another projectiles question. What I would like you to do is draw a simpler diagram than the one provided with the question. Let the horizontal range be 14 ft, the initial vertical height be 7ft and the final height when the ball goes through the basket be 10ft. The angle with which the ball is launched should also be indicated by the symbol θ.
Draw your diagram here.
Next, clearly identify on your diagram, with appropriate labels,
1. the initial velocity vector
2. the direction of the acceleration vector
3. a sign convention
4. a coordinate system. Let x be the horizontal coordinate and y be the vertical coordinate, but you choose where to place the origin.
Using your coordinate system and sign convention, write down the information you know about the x and y motion;
X Y
The question does not ask for the time, nor does it give you the time, so, I don’t want to see any calculations of the time. Instead, carefully choose some equations that will allow you to eliminate the time variable. Here’s how;
First, write down an equation of kinematics that describes the x motion
Next, write down the corresponding equation for the y motion.
Now eliminate the time variable, t, between the two equations.
Still using symbols, re-arrange your equation to make vo the subject, since this is the variable the question is asking for
vo =
Finally, substitute the appropriate numbers for the variables, being careful to use SI units, and calculate the value of vo.
vo =
Please verify your answer is correct before moving on.
Exercise 24
Another projectiles question. What’s different about this one is the jet is pointing downwards, which will result in a negative initial velocity, for a sign convention where up is positive.
As with the previous question, draw a diagram. Let the angle with which the decoy is launched be indicated by the symbol θ.
Draw your diagram here.
Next, clearly identify on your diagram, with appropriate labels,
1. the initial velocity vector
2. the direction of the acceleration vector
3. a sign convention
4. a coordinate system. Let x be the horizontal coordinate and y be the vertical coordinate, but you choose where to place the origin.
Using your coordinate system and sign convention, write down the information you know about the x and y motion;
X Y
a) The first part of the question asks about the time of flight. Which coordinate are you going to start with, X or Y ?
Which equation of kinematics are you going to start with?
Equation:
Still using symbols, re-arrange the equation to make t the subject, since this is what the question is asking for,
Be careful now to use the correct numbers, in SI units. Do your unit conversions here;
Finally, calculate the value of the time variable t
t =
b) The next part of the question asks you to find the altitude of the jet at the time the decoy was released
Which coordinate are you going to start with, X or Y ?
Which equation of kinematics are you going to start with?
Equation:
Still using symbols, re-arrange the equation to make the initial vertical displacement the subject, since this is what the question is asking for. Also, be sure to use the origin that you chose for your coordinate system.
Be careful now to use the correct numbers, in SI units. Do your unit conversions here;
Finally, calculate the value of the initial vertical displacement
yo =
Please verify your answer is correct before moving on.
Exercise 41
This question is a one-dimensional relative velocity problem that involves a transatlantic flight where the plane files with the wind on the outward leg and against the wind on the inbound leg.
The first thing to do is decide for yourself which way is east and which way is west and identify those directions with right and left.
Make your choice below in a diagram
Next, choose a sign convention because the plane travels in both directions but the wind is blowing in one direction only, so the wind helps on one leg of the journey, but not the other.
The question asks about an assumption to do with the wind velocity. (Hint: Which of the four kinematic variables can you assume is zero? )
Next, write down two equations, one describing the planes ground velocity on the outbound leg and the other describing the planes ground velocity on the inbound leg,
Equation 1:
Equation 2:
Next, write down two equations for the time each leg takes,
Equation 1:
Equation 2:
You are told something about the time difference, so subtract the two equations above,
What you should end up with, after some algebra, is a quadratic equation involving the square of the wind velocity. Show the algebra and derive the quadratic equation
Now solve the quadratic equation for the wind velocity.
Please verify your answer is correct before moving on.
Exercise 44
This is another relative velocity problem. The place to start is with a diagram. Be sure to label the tips and tails of the velocity vectors as this will help you arrange them in the correct orientation.
The solution to the problem involves the sine and cosine rules. Also, be sure to convert the velocities to SI units.
The question asks for the wind vector velocity, so I’m looking for the size and direction of the vector.
Please check that your answer is correct.
Problem 15
You may find that reading section 4-4 useful before attempting to solve this problem.
As always, the place to start is with a diagram identifying the forces acting on the object, an acceleration vector, direction of motion, and a sign convention.
a) If you assume that the object is released from rest, then the drag force initially is zero, since the object has no velocity. So, the initial acceleration would be?
b) After some time, the drag force builds up with the increasing velocity, and eventually equals the objects weight. Now the weight and drag forces are balancing each other and the object is no longer accelerating. So, write down Newton’s second law for the object and solve for the velocity, v.
c) The object is accelerating before it reaches terminal velocity. So, write down Newton’s second law for the object and solve for the acceleration.
Phew ! You are now done with the fourth homework. Well done.
1