40% of the course 4 Sub - Topics Projectiles
Attwood machines (inclined planes) Uniform Circular Motion
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Lesson 1.01 Intro to 2-D motion
Unit 1 - Force, Motion, Energy
Ex 1: How far does a truck move in 2.0 s if it is moving at a constant speed of 20.0 m/s?
Ex 2: A stone is dropped from a height of 6.0 m. What is its velocity when it is halfway down?
Assign:
p. 73 #37 - 41, 44 - 48 p. 74 #63, 65, 68-71
Lesson 1.02 Projectiles off a flat table
Projectiles
A projectile is any object which is __________________ or ____________________near the earth's surface.
Projectiles are a combination of two types of motion:
____________________________ in the x-direction and
____________________________ (acceleration) in the y direction.
Key assumptions:
1. ____________________________________________________________ 2. ____________________________________________________________ 3. ____________________________________________________________ 4. ____________________________________________________________ 5. ____________________________________________________________
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Examples of ____________________________________ (paths) of some projectiles
Free body diagram of each? The only force acting on a projectile is _______________________.
Ex 1: A projectile rolls _____________________________ off a 12.0 m high ledge with an initial velocity of 𝑣⃑𝑥 = 2.5𝑚𝑠.
a) Sketch the trajectory (path) of the projectile.
b) Sketch the velocity vectors of the projectile at 3 points in its path.
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c) Sketch the acceleration vectors of the projectile at 3 points in its path.
d) Calculate the __________________ (max horizontal displacement) of the projectile? STEP 1: ________________________________________________
STEP 2: ________________________________________________
Key Point!
Don't forget, range means "displacement in the x"
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Careful! There are *TWO* vectors here!
You already know the velocity in the x, it is
constant!
e) Find the net velocity (magnitude and direction) at t = 0.930 s
STEP 1: ________________________________________________
STEP 2: ________________________________________________
STEP 3: ________________________________________________
1. A ball rolls horizontally off an incline, as shown, at a velocity of 20.0 m/s.
a) How long is the projectile in the air? b) What is the range of the projectile?
c) What is the x-component of velocity at t = 0.42 s? d) What is the y-component of velocity at t = 0.42 s?
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1a 1.35s
b 27.2 m
c 20.0 m/s
d - 4.12 m/s
Lesson 1.03 Projectiles at an angle, same height
Ex 2: A football is kicked with an initial velocity of 20.0 m/s at an angle of 57°above the horizontal. It lands at the same height from which it was kicked.
a) Find the range of the football.
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35°
Practice: An object is thrown into the air with a velocity of 15.0 m/s and an angle of 35° with the horizontal and returns to the same height.
a) How long is the projectile in the air? b) What is the range of the projectile?
c) How long does it take to reach its max altitude? d) What is the max altitude?
e) What is the x-component of velocity at t = 0.62 s? f) What is the y-component of velocity at t = 0.62 s?
g) What is the net velocity at t = 0.62 s (magnitude and direction)?
2a 1.75 s
b 21.5 m c 0.88s d 3.77 m e 12.3 m/s f 2.5 m/s
Lesson 1.04 Projectiles from a Cliff
Warmup:A projectile is rolled horizontally off the top of a 6.2 m high ledge with an initial velocity of 4.8 m/s. Calculate:
a) The max range of the projectile
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Ex 3: A rock is thrown from the top of a 25.0 m high cliff with an initial velocity of 18.0 m/s [R61°U]. Find the time the projectile is in the air.
Practice Set - Projectile Motion
1. A projectile is shot horizontally at 20 m/s from a cannon located on a cliff 200.0 m high. a) How long is the projectile in the air?
b) What is the range?
c) What is the final velocity of the projectile? (ensure you include both magnitude and direction)
2. A cannonball is fired from a cannon at an angle of 38° to the horizontal at a velocity of 85.0 m/s. The cannon sits on a 100.0 m high cliff as in diagram 1, and the projectile lands on a 10.0 m high box.
a) Calculate the range to the box and max height the projectile reaches
3. A plane in horizontal flight at a velocity of 800 km/hr releases an “aid package”. From what altitude can the package be released in order to hit a target 1600 m ahead of the aircraft?
1a t = 6.4 s 1b Range = 128 m 1c v = 65.8 m/s [R72°D]
2a range = 812 m
2b dy = 138.0 m (above cliff)
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Lesson 1.05 Projectiles from a Cliff (Part 2)
Ex: A cannon on a 125 m high cliff fires a projectile with an initial velocity of 42 m/s at an angle of [R27°D].
Find:
a) range, and
b) final velocity at the bottom.
Assign:
p. 113 # 5, 6, 8 p. 114 # 16 - 30
Lesson 1.06 Normal Force
Warmup
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Forces
Normal Force (FN)
Force that the _____________ exerts on the object (perpendicular). Necessary for determining ________________________.
Frictional Force
Always opposes motion FF = μkFN
Normal force problems come in three flavors; a) ______________________
b) ______________________ c) ______________________
Elevators
A 50.0 kg man is standing in an elevator. Calculate the reading on a spring scale that he is standing on if the elevator is:
a) motionless
b) moving with uniform motion
c) accelerating upwards at a = 1.5 m/s/s
Steps to Determining Normal Force (FN)
1. Draw FBD 2. Fnet statement
3. Newton's 2nd Law (Fnet = ma)
Horizontal Surfaces
Ensure you draw good FBD for these, as they frequently involve components.
For each of the following, will the normal force be greater than, less than, or equal to gravity?
Horizontal Surfaces with Friction
Frictional force is determined from the normal force Ff = μFN. Because the Normal force can
vary, _______________ if there is a force component _________and _______________ if there is a force component _________, the frictional force can change as well.
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Ex: Calculate the acceleration of the 4.0 kg suitcase if the applied force is 18.0 N at an angle of 50° above the horizontal if the coefficient of friction, μk= 0.150.
*How would this change if the force were down at an angle? What happens to the normal force? to friction? to acceleration?
2. Determine FNet x
3. Determine ax
Practice Set – Normal force and friction
For each problem below, calculate:
a) the final velocity of the object after 1.2 s if the initial velocity is zero.
b) time taken to travel 6.2 m if the initial velocity was zero.
Assume that μk = 0.050 in each case.
1a 2.27 m/s 2a 9.10 m/s
Lesson 1.07 Inclined Planes
Warmup: Find the acceleration in the x direction.
Inclined Planes
Problems involving ramps or hills can be solved by using an inclined plane. In inclined plane problems, we rotate our x-y axes, and instead use axes that are perpendicular ( ) and parallel ( ).
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Ex1: Calculate normal force (m = 10.0 kg)
Ex 2: Calculate the acceleration of the 8.0 kg object if μk = 0.200. How far up the slope will the
Ex 3: A seal slides from rest down a 3.5 m long ramp where μk = 0.25. If the ramp is inclined at 32°, what is the final velocity of the seal?
Practice Set – Normal Force
1. A 50.0 kg man is standing in an elevator on a bathroom scale which reads Newtons. a) What does the scale read if the elevator is stopped? (490 N)
b) What does the scale read if the elevator is accelerating upwards at 1.5 m/s/s? (565N)
c) What does the scale read if the elevator is accelerating downwards at 1.5 m/s/s? (415N)
2. Calculate the normal force in each case. The answers are in brackets
a) (55N) b) (49.9 N)
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e) (25.3 N) f) (28.6 N)
Calculate the frictional force in each case if µk = 0.245. Unless otherwise indicated, assume that
motion is to the right, or downhill. The answers are given in brackets.
a) (13.4 N) b) (12.2 N)
c) (6.39 N) d) (36.5 N)
Assign
p. 196 #1 p. 224 #7-10
1.08 - Attwood Machines
A system of masses connected by string and pulleys.
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Ex: 3 Find the acceleration and the tension in the string.
Assign:
p. 202 a, b, c *note direction p. 225 11,12, 13, 14
Practice Set – Attwood Machines
1. Calculate the acceleration in the x direction if μk = 0.10 and the mass is 15 kg. (a = 2.32 m/s/s)
2. Calculate the acceleration and tension in each cord in the diagrams below. m1 = 5.0 kg, m2 = 10.0 kg μK = 0.24 (unless diagram is frictionless)
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3. A seal slides from rest down a 3.5 m long ramp into a pool of water. If the ramp is inclined at an angle of 25° above the horizontal and the coefficient of kinetic friction between the seal and the ramp is 0.20, how long does it take the seal to hit the water?
Review Sheet #01 – Projectiles and Attwoods
1. An object is fired with an initial velocity of 64 m/s [R25°U]. What are the initial components of its velocity?
2. An object rolls off the top of a flat table. Sketch the trajectory of this object and label the velocity vectors at three points.
3. An object is fired at an angle of 60° below the horizon. Sketch the acceleration vector for this projectile at three points in its trajectory.
4. A plane in horizontal flight at a velocity of 500 km/hr releases a projectile. From what altitude can the package be released in order to hit a target 2000 m ahead of the aircraft? 5. For each of the projectiles shown below, calculate:
a) time in the air b) max range
c) velocity when it hits the ground (magnitude and direction) d) max altitude only for iii)
6. A box is pulled as shown in the diagram below. If μk = 0.15, calculate the acceleration of
the box which has a mass of 5.5 kg.
1 x = 58 m/s; y = 27 m/s 5ii t = 0.938 s
2 Diagram, see notes dx = 8.12 m
3 Diagram, see notes v2 = 16.6 m/s [R59°D]
4 dy = 1016 m 5iii t = 6.15 s
5i t = 0.90 s dx = 105.5 m
dx = 10.8 m dy = 9.30 m (above ledge)
v2 = 14.9 m/s [R36°D] v2 = 49.4 m/s [R70°D]
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1. Calculate the normal force in each of the situations below. a) A 20.0 kg block in a stationary elevator.
b) A 20.0 kg block in an elevator accelerating up at 2.2 m/s/s. c) A 20.0 kg block in an elevator accelerating down at 2.2 m/s/s. 2. Calculate the normal force in each diagram.
3. For each of the diagrams in #2, calculate the frictional force if ìk = 0.37.
4. A penguin slides from rest down a 3.5 m long ramp into a pool of water. If the ramp is inclined at an angle of 35° above the horizontal and the coefficient of kinetic friction between the penguin and the ramp is 0.20, how long does it take the penguin to hit the water?
5. A box is pushed up a ramp with an initial velocity of 12.0 m/s. If the ramp is inclined at an angle of 25° above the horizontal and the coefficient of kinetic friction between the box and the ramp is 0.12, how far up the ramp will the box travel before stopping? 6. For each of the following diagrams calculate:
a) acceleration of the system b) tension in the rope.
1.09 - Uniform Circular Motion (UCM)
Motion in a circle at a __________________________________ *not uniform motion! Why?
Consider a stopwatch hand 2.0 cm long. Determine the speed of the tip of the stopwatch at 15.0 s and at 30.0 s. Determine the velocity at each of these times.
The speed is ______________________ at all points on the circle but the velocity is ________________. Any object undergoing UCM is _______________________________.
This acceleration is called the________________________, ac, and it always points towards the
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We are not introducing a new type of force but
rather describing the direction of the net force
acting upon the object which moves in the circle.
Without a centripetal force, an object in motion continues along a
straight-line path because of ________________. With a centripetal
force, an object in motion will be accelerated and change its direction.
Any object moving in a circle (or along a circular path) experiences a centripetal force. That is, there is some physical force pushing or pulling the object towards the center of the circle.
Whatever the object, if it moves in a circle, there is some _______________ acting upon it to cause it to deviate from its straight-line path, accelerate onwards and move along a circular path. Three such examples of
centripetal force are shown below.
As a car makes a turn, the _____________________ acting upon the turned wheels of the car provides centripetal force required for circular motion.
As a bucket of water is tied to a string and spun in a circle, the ____________________ acting upon the bucket provides the centripetal force required for circular motion.
As the moon orbits the Earth, the ______________________ acting upon the moon provides the centripetal force required for circular motion.
Equations for UCM
ac = centripetal acceleration (m/s2)
v = speed (tangential) (m/s) r = radius (m)
T = period (s)
For UCM problems assume the center of
the circle is the positive direction!
Convert frequency or period to speed.
Ex 1: A 32.0 kg mass moves in uniform circular motion at 4.1 m/s around a 12.0 m radius horizontal track.
a) What is the centripetal acceleration, ac
b) How much force is required to keep the object moving in a circle?
Ex 2: A 3.80 kg mass sits on a horizontal turntable with a radius of 1.95 m. Find the amount of friction required to keep the object in place if the turntable has a frequency of 0.13 Hz.
1. Draw FBD
2. List Givens
Remember the net force is the centripetal force.
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For UCM change Fnet into Fc!
3. Fnet statement
Assign:
p. 206 #1 - 6 (show 6 next day) p. 226 #15-17
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Key Point! When weightless, set your
centripetal acceleration to 9.8 m/s
2Ex 4: A 1.2 kg mass is swung at the end of a 0.50 m long string in a vertical circle with a speed of 4.3 m/s. Calculate the tension in the string at the top and bottom of the circle.
Apparent Weight and Weightlessness
Your "weight" is a measure of the force of gravity acting upon you, and is reflected in the magnitude of the
normal force, FN. Any acceleration, such as from an elevator, can make you "feel" heavier or lighter. This
new normal force is your "apparent weight"
*notice that if you are stationary or moving with uniform motion, your apparent weight is the same as your actual weight.
If you are moving in a vertical circle with ____________________, this normal force will reduce to zero. When this happens you are said to be "weightless", and your centripetal acceleration is 9.8 m/s/s.
*it doesn't mean you have no mass, but that if you were sitting on a bathroom scale at that time it would read "zero".
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Assign: p. 226 #20-22
Look at the reading on the bathroom scale in each situation. In cases a and b the object is accelerating in the indicated direction. In case c, the person is in freefall, with an acceleration of 9.8 m/s2.
Ex: A 65.0 kg person is moving through a vertical circle of radius 35.0 m at a speed of 27.0 m/s.
a) Find her apparent weight at the top and at the bottom of the loop.
b) What speed would be required in order for her to feel weightless?
This phrase must be in the problem to use this equation.
This phrase indicates that we must do a FBD.
Frictionless banked curves
The component of the normal force provides the centripetal force.
Ex: A speeding family van is heading around a banked frictionless turn at 260 km/hr. What is the angle of the bank if the radius of the turn is 930 m?
Ex: What is the maximum speed at which a car can round a 90.0 m horizontal curve if the coefficient of static friction is 0.50?
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Practice Set – Uniform Circular Motion Ensure that you draw completed diagrams and list all givens for each problem.
1. How fast must a plane be flying in a loop-the-loop of radius 2.0 km if the pilot feels weightless? (There is no normal force from the seat)
2. A string used to make a pendulum has a breaking strength of 12.0 N and a length of 0.80 m. A 1.00 kg bob is set in motion.
a) If the bob moves with a speed of 1.00 m/s at the bottom will the string break? b) What is the highest speed at which the bob can move?
3. A 1.5 kg object is swinging from the end of a 0.62 m string in a vertical circle. If the period is 1.2 s, what is the max and min tension in the cord?
4. A 2.0 g raisin is sitting on a turntable. What is the frictional force that must be provided to keep the raison on the turntable if it spins at 45 rpm at a radius of 3.0 cm?
5. A car goes around a banked curve at an angle of 30°. The car will stay on the road with no friction at a speed of 22.0 m/s. What is the radius of the curve?
6. Calculate the angle at which you must bank a frictionless curve such that a car can round it safely at 100.0 km/hr if the radius of the curve is 500.0 m.
7. What is the max speed at which a car can still stay on a racetrack banked at 30° if the radius of the track is 0.800 km?
1.10 - Static Equilibrium and Torque
Center of mass: An imaginary point where you assume ____________________________. (This is where you draw the force of gravity)
For uniform objects (spheres, squares, etc) the center of mass is the _______________________ of the object. For non-uniform masses, the center of mass is not near the center.
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Assign:
p. 237 # 1-3 p. 266 # 1
p. 267 # 18 - 20, 25
*18. Ans = 196 N 19. Ans = 170 N
Hanging Picture Problems
1.11 - Hanging Picture Problems, Unequal Angles
Ex: Calculate the tension in each string.
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Practice Set – Hanging Picture Problems Find the tension in each string in the following diagrams.
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1.12 – Torque
Torque (τ)
The _____________________________________ caused by a ________________________ acting some _______________________ from the center of mass is a _____________________, measured in Nm.
Ex 1: How much torque is created about the nut in each case?
(which way would the bolt *tend* to rotate...torques are caused even when there is no rotation, much like forces can exist even when there is no acceleration)
Whenever the forces act some distance away from each other, the problem may require torque!
Static Equilibrium and Torque
definitions
Translational equilibrium
FNET = 0 (hanging picture problems)
Rotational equilibrium τNET = 0 (net torque is zero)
Static equilibrium FNET = 0
τNET = 0
Ex 2: A 20.0 kg board acts as a seesaw. One child has a mass of 30.0 kg and sits 2.5 m away from the fulcrum. Where must a 25 kg child sit in order to attain static equilibrium?
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Ex 3: A uniform 20.0 m long beam has a mass of 1500 kg. It supports a 4200 kg mass as shown. Calculate the force on each support.
Assign: P. 266 Theory Questions! #3, 5, 6, 7, 8, 15 Student Practice:
1. Mitch (m = 35 kg) and Tim (m = 22 kg) are playing on a seesaw. If the length of the seesaw is 6.0 m and it has a mass of 15.0 kg, calculate:
a) The torque generated by each boy if they sit on the end of the seesaw, b) Where must Mitch sit to balance Tim, if Tim sits at one end, and c) The normal force on the seesaw by the support.
ANS: τm = 1030 Nm, τt = 648 Nm, d = 1.89 m, Fn = 706 N
2. A uniform 1500 kg steel beam, 20.0 m long, supports a 6.00 x 103 kg piece of machinery. Calculate the
force in each support.
Ex 4: A uniform cantilever beam in static equilibrium (aka diving board) has a mass of 255 kg, and the
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Ex 5: A uniform beam 2.20 m long with a mass of 25.0 kg is mounted on a hinge and supports a 42.0 kg mass as shown. Determine the components of the force, F, on the hinge, and the tension, T, in the wire.
The wall is frictionless, but the floor is not.
Ladder problems typically involve some trig to determine
the required angles.
Ex 6: A 5.0 m long uniform ladder has a mass of 12.0 kg. It leans against a frictionless wall as shown. Find: a) the force of friction on the ground
b) the normal force of the wall on the ladder c) the normal force of the floor on the ladder
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Solving Torque Problems
1.
Draw a FBD
* always of the uniform beam
2.
Identify torques
* pick a pivot, place it so as to eliminate variables
* be sure to sketch torques relative to the pivot you have selected.
3.
Calculate torques
* start at pivot and work your way across
* make sure all distances are measured from pivot.
4.
Solve for unknown
* Generally this will get you an unknown force or radius
5.
Check that you have solved the question
* may need another force!
Practice Set – Torque
1. A uniform cantilever beam of mass 1200 kg and length 15.0 m is set up as below. Calculate the forces in each support. (Be careful of the directions)
2. A uniform beam, 3.5 m long with mass m = 15.0 kg, is mounted on a hinge on a wall that supports a mass M = 110.0 kg. The beam is held horizontal by a wire that makes an angle of 30° with the beam. Determine:
a) the components of the Tension Tx, and Ty,
b) the tension T,
c) the components of the Force of the wall on the beam Fx, and Fy, and,
b) the resultant Force F.
3. A 6.0 m long ladder leans against a wall at a point 3.0 m above the ground as seen in the diagram. The ladder is uniform and has a mass of 6.0 kg. Assuming the wall is frictionless (but the floor is not)
determine the forces exerted on the ladder by the ground and the wall.
4. A 1.5 x 103 kg car is crossing a 120 m long bridge which is supported at both ends. If the mass of the bridge is 4.8 x 103 kg, what is the force provided by each support when the car is 32 m from one end?
1 F
a = 5880 , Fb = 17640 N
2 T
x = 1997 N, Ty = 1153 N, T = 2305 N, Fy = 73.6 N, Fx = 1997 N, F= 1998 N [R2.1°U]
3 F
normal from wall = 51.0 N, F Normal from Floor = 58.9 N, FF = 51.0 N
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r = 22 .0 m
Review Sheet – UCM and Torque
1. Calculate the centripetal acceleration of a car travelling at 85 km/hr around a circular track of radius 0.900 km. 1. What centripetal force is exerted on a 2.5 kg mass spinning in a circle of radius 1.5 m at 12.0 m/s?
2. A 5.0 kg mass is attached to a wire cable spinning in a vertical circle of radius 1.2 m. If the mass is spinning at 75 km/hr; calculate:
a) max tension b) min tension
3. The end of a lawnmower blade rotates with a frequency of 75 Hz.
a) What is the centripetal acceleration if the blade has a radius of 32 cm? b) How fast is the tip of the blade moving?
4. A plane flying at 475 km/hr flies over the top of a circular path.
a) What must be the radius of the circle to just achieve weightlessness? (Normal force = 0)
b) What would be the normal force on a 75 kg pilot in the same plane if it flies the bottom of the circular path at the same speed?
5. A roller coaster ride makes a loop-the-loop as seen below. If the radius of the coaster is 22.0 m, a) How fast must the coaster be going so that the people don't fall out?
b) At the bottom of the coaster, what is the normal force on a 75 kg person if the speed is 85 km/hr?
6. A car drives around a horizontal curve with a frictional coefficient of 0.58. What is the maximum safe speed for the car if the radius of the turn is 125 m?
7. A 2.5 g raisin is sitting on a turntable of radius 12 cm. If the turntable rotates at a frequency of 77 RPM, what frictional force is required to keep the raison on the turntable?
8. A car is traveling at 120 km/hr around a frictionless turn of radius 115 m. What must be the angle of the bank to keep the car on the road?
9. A frictionless turn is banked at 35° to the horizontal. What is the maximum speed at which the car can stay on this road if the radius is 225m?
1 0.619 m/s2 6a 14.7 m/s 2 240 N 6b 2636 N 3a 1852 N 7 26.7 m/s 3b 1754 N 8 0.0195 n 4a 71, 000 m/s2 9 45∘
4b 151 m/s 10 39.3 m/s 5a 1776 m
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30
m = 5.2 kg
60
m = 5.2 kg
60
Fg = 200 N
50
M 25
0.15 m
F = 5 5 N
Θ =65°
0.15 m
F = 5 5 N
0.85 m F =120 N
F =120 N
m = ? 55 k g
1.1 m
3.15 m
1. A lever arm 2.5 m long has a force of 175 N applied to it right angles. What is the torque generated? 2. What are the conditions for translational equilibrium?
3. What are the conditions for static equilibrium?
4. What is the tension in each of the strings below? The beam in part C is massless.
a) b) c)
5. What must be the tension in each string if the mass M = 12 kg?
6. Calculate the torque generated about the bolt in each wrench below.
a) b)
7. Calculate the total torque generated about the lug nut in the problem below.
8. Kahlil (m = 125 kg) and Ghibran (m = 75 kg) are sitting on a 4.0 m long massless seesaw. If Ghibran sits on the end of the seesaw, how far from the pivot must Kahlil sit to balance him?
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75 m
15 m
A B M 35 ° 78 ° H inge T FA 75 cm
10. The 12.0 m long I-Beam (m = 650 kg) in the diagram is secured as a cantilever beam. A construction worker (m1 = 75 kg) is sitting on the beam as indicated, with his gear hanging over the side (m2 = 275 kg). What is the force in each support?
11. The wheelbarrow shown is carrying a mass of 75 kg. The centre of mass is located 55 cm behind the front wheel. What must be the force exerted by the man on the handle at a distance of 1.75 m behind the front wheel?
12. A truck of mass 1200 kg is at rest on a uniform bridge of mass 1700 kg. The bridge is 75 m in length. If the truck is 15 m from support "A", what is the force in each support?
13. The crane derrick below has a mass of 125 kg and an overall length of 5.5 m. M = 2500 kg a) What is the Tension T, in the cable?
14. A duck holds a hanging window in static equilibrium with a horizontal force of 125 N. If the window is 95 cm long, what is the mass of the window?
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3. 0 m 5. 0 m
4. 0 m
15. A 5.0 m long ladder with a mass of 22 kg is leaning against a frictionless wall at a point 4.0 m above the floor. A boy of mass 42 kg is standing 4.0 m from the bottom of the ladder.
a) What must be the force of the wall on the ladder? b) What must be the force of friction on the ladder? c) What must be the force of the floor on the ladder?
1 437.5 N 9 19.2 kg
2 FNET = 0 10 Fa = 16 170 N [down] FB = 25 970 N [up] 3 FNET = 0
Τnet = 0
11 231 N [up]
4a 29.4 N 12 Fa = 17 738 N Fb = 10682 N 4b 231 N
115 N
13a T = 18 000 N
4c 102 N 5 T1 = 78.3 N
T2 = 110 N
6a 8.25 N 14 m = 35 kg 6b 7.47 N 15a FW = 580 N 7 102 Nm 15b F Fr = 580 N 8 1.20 m 15c FN = 627 N
This is the end of Unit 1 – Force, Motion, and Energy. 40% of the year is now complete. Congrats.
