Download Unit IIIB Worksheet 1

Unit II: Newton’s Laws
Subunit B: Unbalanced Forces
Unit II-B Objectives
What you should know when all is said and done
By the time you finish all labs, worksheets and related activities, you should be able to:
1. Use Newton’s 2nd Law to qualitatively describe the relationship between m and a, F and a,
m and F. (e.g., if you double the mass, the acceleration will…)
2. Determine the net force acting on an object by:
a. drawing a force diagram for an object given a written description of the forces acting on it.
b. resolving forces into x and y components, then finding the vector sum of the forces.
c. analysis of the kinematic behavior of the object.
3. Solve quantitative problems involving forces, mass and acceleration using Newton’s 2nd Law.
a. Having determined the net force (as in #3), and given the mass, find the acceleration.
b. Continue to use the kinematical models from Unit I to determine the velocity or
displacement of the object, once the acceleration is known.
4. Differentiate between static and kinetic friction and describe what affects the frictional force.
5. Determine the magnitude of the frictional force and the effect it has on an object’s motion.
Unit II-B: Unbalanced Forces
Worksheet 1
1. Felicia, the ballet dancer has a mass of 45 kg. A) What is her weight on Earth?
B) What is Felicia’s mass on Jupiter, where the acceleration due to gravity is 26 m/s2?
C) What is Felicia’s weight on Jupiter?
2. Butch the 72 kg star quarterback collides with a stationary player and is brought to a stop with
an acceleration of -20 m/s2. A) What force does the stationary player exert on Butch?
B) What force does Butch exert on the stationary player?
3. A jumbo jet has a mass of 30,000 kg. The thrust for each of four engines is 15,000 N. What is
the jet’s acceleration when taking off?
4. A tow truck exerts a force of 3000 N on a car, accelerating it at 2 m/s2.
A) Find the mass of the car. B) If the force of friction on the car is now 1000 N and the tow truck
still pulls with 3000 N, what will be the acceleration of the car?
5. A rocket weighs 2 x 107 N. Its engines exert 25 x 106 N of force at lift-off.
A) What is the mass of the rocket? B) What is its acceleration when it lifts off?
6. An unbalanced force of 30 N gives an object an acceleration of 5 m/s2. What force would be
needed to give it an acceleration of 1 m/s2?
7. You stub your toe on the coffee table with a force of 10 N. A) What is the acceleration of your
1.8 kg foot? B) What is the acceleration of the table if it has a mass of 20 kg? (Ignore any frictional
effects.) C) Why would your toe hurt less if the table had less mass?
8. A 20-g sparrow flying toward a bird feeder mistakes the pane of glass in a window for an
opening and slams into it with a force of 2 N. A) What is the bird’s acceleration?
B) How many “g’s” is this?
9. You pull horizontally on a 50-kg crate with a force of 500 N, and the frictional force on the crate
is 250 N. What is the acceleration of the crate?
10. Two perpendicular forces, one of 45 N directed upward and the second of 60 N directed to the
right, act simultaneously on an object with a mass of 35 kg. What is the magnitude of the resultant
acceleration of the object?
Unit II-B: Unbalanced Forces
Worksheet 2
Multiple Choice.
1. What happens to the acceleration of an object when the net force exerted on it is doubled?
A) It doubles.
B) It is half as much.
C) It remains the same.
2. What happens to the acceleration of an object when the mass of the object is doubled?
A) It doubles.
B) It is half as much.
C) It remains the same.
3. If the mass of an object is cut in half, what happens to its weight (gravitational force)?
A) It doubles.
B) It is half as much.
C) It remains the same.
4. A woman exerts a constant horizontal force on a large box. As a result, the box moves across a
horizontal floor at a constant velocity. The constant force by the woman:
A) has the same magnitude as the weight of the box.
B) is greater than the weight of the box.
C) has the same magnitude as the total force which resists the motion of the box.
D) is greater than the total force which resists the motion of the box.
E) is greater than either the weight of the box or the total force which resists its motion.
5. If the woman in question 4 suddenly stops applying a horizontal force to the box, then the box
A) will immediately stop.
B) will continue moving at a constant speed for a while and then slow to a stop.
C) will immediately start slowing to a stop.
D) will continue at a constant speed.
D) will increase its speed for a while and then start slowing to a stop.
Short Answer.
6. Neglecting air resistance, why would an elephant and a mouse fall with the same acceleration?
7. State Newton’s 2nd Law of Motion.
Free Response. Show your work!!
8. How much would a 60 kg girl weigh on the moon where the acceleration due to gravity is 1.6
m/s2? What would her mass be?
9. You pull horizontally on a 50-kg crate with a force of 500 N. If it moves at a constant speed,
what is the magnitude of the frictional force acting on the crate? B) If the frictional force is now is
250 N, what is the acceleration of the crate?
10. A 900 kg car exerts 5000 N of traction force on a level road while being opposed by 1000 N of
friction and drag forces combined. What is the acceleration of the car?
11. A 70 kg skydiver jumps out of an airplane. Immediately after jumping, how large is the
skydiver's acceleration?
B) Upon reaching a downward velocity of 100 miles per hour, 300 Newtons of drag resist the
diver's motion. Draw a force diagram for the skydiver. How large is the skydiver's acceleration?
12. A firefighter with a mass of 80 kg slides down a vertical pole with an acceleration of 4 m/s2.
What is the frictional force that acts on the firefighter?
Unit II-B: Unbalanced Forces
Worksheet 3
1. An elevator is moving up at a constant velocity of 2.5 m/s, as illustrated in the diagram. The man
has a mass of 85 kg.
A) Construct a force diagram for the man.
B) How much force does the floor exert on the man?
2. The elevator now accelerates upward at 2 m/s2.
A) Construct a force diagram for the man.
B) How much force does the floor now exert on the man?
3. Upon reaching the top of the building, the elevator accelerates downward at 3 m/s2.
A) Construct a force diagram for the man.
B) How much force does the floor now exert on the man?
C) While descending in the elevator, the cable suddenly breaks. What is the force of the floor on
the man?
4. Consider the situation where a person that has a mass of 68 kg is descending in an elevator at
a constant velocity of 4 m/s. At some time “t”, the elevator starts to slow to a stop at the rate of 2
m/s2.
A) Construct, in the margin to the left, a qualitative motion map indicating the relative positions,
velocities, and accelerations of the elevator as it descends.
B) What is the magnitude of the net force acting on the person in the elevator when it is
descending at (a) constant speed and (b) as it accelerates?
C) Construct quantitative force diagrams (include magnitudes) for the person in the elevator as it
descends at (a) constant speed and (b) during its period of acceleration.
D) If the person in the elevator were standing on a bathroom scale calibrated in Newtons, what
would the scale read while the elevator was (a) descending at constant speed and (b) while
slowing down to a stop? Explain your answers.
Unit II-B: Unbalanced Forces
Worksheet 4
For each of the problems below, you must begin your solution with a force diagram. Some require
more than one diagram. For some questions, you will have to use kinematic equations as well as
Newton’s 2nd Law.
1. During a head-on collision, a passenger in the front seat of a car accelerates from 13.3 m/s (30
mph) to rest in 0.10 s.
A) What is the acceleration of the passenger?
B) The driver of the car holds out his arm to keep his 25 kg child (who is not wearing a seat belt)
from smashing into the dashboard. What force must he exert on the child?
C) What is the weight of the child?
D) Convert these forces from Newtons to pounds (1 lb = 4.45 N). What are the chances the driver
will be able to stop the child?
2. The maximum force that a grocery bag can withstand without ripping is 250 N. Suppose that
the bag is filled with 20 kg of groceries and lifted with an acceleration of 5.0 m/s2. Do the groceries
stay in the bag?
3. A 4-kg helicopter accelerates upward at 2 m/s2. How much lift force is exerted by the air on the
propellers?
4. A student, standing on a scale in an elevator at rest, sees that his weight is 840 N. As the
elevator rises, his weight increases to 1050 N, then returns to normal. When the elevator slows to
a stop at the 10th floor, his weight drops to 588 N, then returns to normal. Draw a motion map for
the student during his elevator ride. Determine the acceleration at the beginning and end of the
trip.
5. A racecar has a mass of 710 kg. It starts from rest and travels 40 m in 3 s. The car is uniformly
accelerated during the entire time. What net force is acting on the car?
6. Suppose that a 1,000 kg car is traveling at 25 m/s (55 mph). Its brakes can apply a force of
5,000 N. What is the minimum distance required for the car to stop?
7. A 65 kg person dives into the water from the 10-m platform.
A) What is her speed as she enters the water?
B) She comes to a stop 2 m below the surface of the water. What net force did the water exert on
the swimmer?
8. While chopping down his father’s cherry tree, George discovered that if he swung the axe with
a speed of 1.5 m/s, it would embed itself 2.3 cm into the tree before coming to a stop.
A) If the axe head had a mass of 2.5 kg, how much force was the tree exerting on the axe head
upon impact?
B) How much force did the axe exert back on the tree?
Unit II-B: Unbalanced Forces
Worksheet 5
2. An applied 25 N force pushes on a 5.0 kg block resting on a frictionless horizontal surface. The
force is directed downwards at an angle of 20º.
A) Draw a force diagram of the block.
B) Determine the x-component of the applied force.
C) What is the acceleration of the block?
D) What is the normal force on the block?
3. A 70-kg box is pulled by a 400 N force at an angle of 30º to the horizontal. The force of kinetic
friction is 75 N. A) Draw the force diagram for the box.
B) What is the acceleration of the box?
C. What is the normal force acting on the box?
Unit II-B: Unbalanced Forces
Worksheet 6
1. A 50-kg sled is pulled horizontally along snow-covered, flat ground. The static friction
coefficient is 0.30, and the kinetic friction coefficient is 0.10.
A) What force is needed to start the sled moving?
B) What force is needed to keep the sled moving at a constant velocity?
C) Once moving, what force must be applied to the sled to accelerate is 3 m/s2?
2. A freshman is walking through the school cafeteria but does not realize that the person in front
of him has just spilled his glass of chocolate milk. As the freshman, who has a mass of 42 kg,
steps in the milk, the coefficient of friction between his feet and the floor is suddenly reduced to
0.040. What is the force of friction between his feet and the floor?
3. Unbeknownst to the students at AHHS, every time the school floors are waxed, Mr. Collins likes
to slide down the hallway in his socks. Mr. Collins weighs 850 N and the force of kinetic friction
between his socks and the floor is 102 N. What is the coefficient of kinetic friction that opposes Mr.
Collin’s motion down the hall?
4. As you take a shower, the soap falls out of the soap dish and you step on it with a force of 500
N. If you slide forward and the frictional force between the soap and the tub is 50 N, what is the
coefficient of friction between these two surfaces?
5. A 600 N cross-country skier is moving over packed snow. The coefficient of friction between the
skis and the snow is 0.11. What force is required to keep the skier moving at a constant speed?
6. Your 70-kg St. Bernard dog refuses to go out the back door to take a walk. If the coefficient of
static friction between the dog and the floor is 0.50, how hard must you pull in order to move the
dog to accelerate him by 1 m/s2? (Draw a force diagram!)
7. You are driving a 2500-kg car at a constant speed of 14 m/s along an icy, but straight and level,
road. You approach a traffic light that turns red, and slam on the brakes. Your wheels lock, and
the car skids to a halt in a distance of 25 m. What is the coefficient of friction between your tires
and the icy road?
Unit II-B: Unbalanced Forces
Worksheet 7
1. Suppose a hanging 1.0-kg mass is attached to a 4.0-kg block on the table.
A) If the coefficient of kinetic friction μk = 0.2, what is the acceleration of the block?
B) What would be the minimum value of the coefficient of static friction μs in order for the block to
remain motionless?
2. A block weighing 300 N is moved at a constant speed over a horizontal surface by a force of 50
N applied parallel to the surface.
A) Construct a force diagram for the block.
B) What is the coefficient of kinetic friction μk?
C) What would be the acceleration of the block if the μk = 0?
3. A 100 N force is applied to a 50-kg crate resting on a level floor. The coefficient of kinetic
friction μk is 0.15.
A) Draw a force diagram to represent the situation.
B) What is the acceleration of the crate?
4. In the situation described above, the coefficient of static friction μs = 0.25. Is the 100 N force
sufficient to cause the crate to accelerate? Draw a force diagram, then explain why or why not.
Unit II-B: Unbalanced Forces
Worksheet 8
1. You are dragging your desk again, but this time you remembered to empty the drawers so that
it is light enough to move. The desk has a mass of 30 kg and the coefficient of kinetic friction is
0.45. You pull with 250 N of force at a 30-degree angle.
A) Write the equation for the forces in the y-direction. Calculate
the Normal force.
B) Calculate the frictional force resisting your pull.
C) Write the equation for the forces acting in the horizontal direction. Calculate the acceleration of
the desk.
2. Now you decide to push that same blankety-blank desk instead of pull, but use the same 250 N
force at an angle of 30 degrees above the horizontal. The desk still has a mass of 30 kg and the
floor still has a coefficient of friction of 0.45.
A) Write the equation for the forces in the y-direction and calculate
the Normal force.
B) Calculate the frictional force on the desk.
C) Write the equation for the forces acting in the horizontal direction. Calculate the acceleration of
the desk. Is it better to push or pull the desk?
3. That darn man with a broom is back pushing his 2.0 kg broom across the floor in the same
bored way he does every night cleaning up after you slobs. The broom handle makes a 50 angle
with the floor. He pushes the broom with a 20.0 N force. The floor has a coefficient of kinetic
friction of 0.22.
A) Write the equation for the forces in the y-direction. What is the value
of the normal force?
B) How much friction opposes the motion?
C) Write the equation for the forces in the x-direction. Calculate the acceleration of the broom.
Unit II-B: Unbalanced Forces
Review Worksheet
EQUATIONS
F = Fnet = ma
Fg = mg = Weight
Fs = μs FN
Fk = μk FN
Fnet = the sum of all forces, m = mass, a = acceleration
Fg = the force of gravity, g = 10 m/s2
Fs = Static friction, μs = the coefficient of friction, FN = Normal force
Fk = Kinetic friction, μk = the coefficient of friction, FN = Normal force
CONCEPTS COVERED
 Newton’s 2nd Law
 Meaning of Inertia, Mass, Weight, Acceleration, and Force
 Units: mass (kg), weight (N), acceleration (m/s2), Force (N), N = kg m/s2
 Types of Forces and drawing force diagrams
 Adding Force vectors, finding components
 The effect of force on different masses, the effect of different forces on the same mass (the
relationship between force, mass, and acceleration)
 Setting up and solving problems with Fnet = ma (1-D and 2-D)
 Using Fnet = ma with kinematic equations to solve problems
 Friction - Static and kinetic – coefficient of friction problems
 Review concepts from previous units - kinematic relations and graphs, Newton’s 1st and 3rd
Laws.
PROBLEM SOLVING HINTS
1. Sketch a free-body diagram
2. Knowns: write down everything you know (F = , m = , a = , etc.)
3. Applicable equations:
 The main equation to use is Fnet = ma.
 Add up all your forces together (this is Fnet), and set it equal to ma.
 Write down everything symbolically (using letters to represent all the forces) first.
 Don’t put in any numbers until the end.
 In some problems, you might also have to use your kinematic equations as well. Use Fnet =
ma to find acceleration, then your kinematic equations (or visa-versa).
 Separate vertical and horizontal forces. Then Fnet (x) = ma(x) and Fnet (y) = ma(y).
 With multiple masses: apply Fnet = ma to each mass separately, or to the whole system.
 Pulleys - Remember that pulleys just change the direction, not the magnitude of force.
4. Rearrange the equation to solve for the variable you want to know
5. Solve the problem!
PRACTICE QUESTIONS
1. State Newton’s 2nd Law.
2.
A 10 kg armadillo and a 5 kg armadillo are each pushed with a force of 20 N. Which armadillo
will have a greater acceleration? Why?
3. A 10kg armadillo and a 5 kg armadillo both fall from the same tall building at the same time.
Which will have a greater acceleration? Why?
4. What type of relationship exists between mass and acceleration? Draw a rough graph.
5. If the force acting on a cart doubles, what happens to its acceleration?
PRACTICE PROBLEMS - Draw a force diagram, show all work, and include units
6. How much would a 60 kg girl weigh on the moon, where the acceleration due to gravity (g moon)
is 1.6 m/s2? What would her mass be?
7. A force of 6 N pushes a bug to the north. A force of 4 N pushes the bug to the west. A force of
3 N pushes the bug to the south. A) What is the net force acting on the bug? (Magnitude and
direction) B) If the bug’s mass is 0.1 kg, what is the bug’s acceleration? (Magnitude and
direction)
8. A net force of 250 N accelerates a bike and rider at 2.0 m/s2. What is the combined mass of
bike and rider?
9. A 0.2 kg baseball traveling at 45 m/s strikes the catchers mitt. The mitt recoils back 11 cm
before coming to rest. What force did the baseball exert on the mitt?
10. A 20-kg block slides down a frictionless ramp. The normal force on the block is 189 N. Draw
a force diagram for the block. Determine the acceleration of the block.
11. A car has weighs 15,000 N and the coefficient of static friction between the tires and the dry
road is 0.8. A) Find the static frictional force. B) If the car hits a wet spot and the tires slide,
the coefficient of kinetic friction is reduced to 0.5. Find the kinetic frictional force.
Answers to Problems: 6) 96 N, 60kg; 7) 5 N, NW, 50 m/s2 NW; 8) 125 kg; 9) 1840 N; 10) 3.27
m/s2; 11) 12,000 N, 7500 N