Module 02: Dynamics Flashcards
Lesson 2.1 - Newton’s First Law of Motion
What is force? Types?
Force: Any kind of push or pull on something
- Contact Forces: force is exerted when one object comes into contact with another
- Force of gravity: objects falls
- Force is required when accelerating from zero
- Force is required when changing direction
Lesson 2.1 - Newton’s First Law of Motion
How does one measure the magnitude (or strength) of a force?
Spiral Scale.
- Normally used to find the weight of an object
Weight: for force of gravity acting on an object
Lesson 2.1 - Newton’s First Law of Motion
How does the direction of the force affect it?
Force is a vector
- Represented by an arrow
- Arrow is the direction of the push or pull
Lesson 2.1 - Newton’s First Law of Motion
What is Newton’s First Law of Motion?
Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it
- consistent with Galileo’s observations
- The tendency of an object to maintain its state of rest or uniformity = INERTIA (called law of Inertia)
Lesson 2.1 - Newton’s First Law of Motion
What are the Inertial Reference Frames?
- New’s First Law does not hold in every reference frame
- Does not hold in an accelerating frame of reference
- Physics is easier in frames where the Law does hold
For most purposes, we usually make the approximation that a reference frame fixed on the Earth is an inertial frame
- Any reference frame that moves with constant velocity relative to an inertial frame is called an inertial reference frame
- Reference frame not hold = noninertial reference frame
Lesson 2.2 - Newton’s Second Law
What is mass? (According to Newton)
Mass = “quantity of matter”
- Measure of inertia in an object
- More mass = greater the force needed to give it a particular acceleration
- SI = kilogram (kg)
Lesson 2.2 - Newton’s Second Law
What is the difference between mass and weight?
- Mass: property of an object itself (Quantity of matter)
- Weight: a force (gravity pulling on an object)
Lesson 2.2 - Newton’s Second Law
What happens when a net force is exerted on an object?
- Net force exerted on an object increased its velocity (or reduce it if its in the opposite direction as the motion)
- If the net force acts sideways on a moving object, the direction of velocity changes
Generally speaking, the net force causes acceleration
Lesson 2.2 - Newton’s Second Law
What is the proportionality between net force and acceleration? How is this influenced by mass?
- Acceleration of an object is directly proportional to the next applied force
- Acceleration also dependent on mass: the greater the mass, the less acceleration for the same net force
The acceleration of an object is directly proportional to the net force acting on it, and is inversely proportional to the mass of the object.
The direction of the acceleration is the direction of the next force acting on the object
Lesson 2.2 - Newton’s Second Law
What is Newton’s Second Law of Motion?
- a: acceleration
- m: mass
- ΣF: vector sum of all forces on the object (net force)
- SI Units: newton (N)
- Only valid in inertial reference frames
Lesson 2.2 - Newton’s Second Law
What units are used in Newton’s Second Law
- SI units: newton (N)
- cgs units: mass in grams (g) and force is dyne
Dyne: net force needed to impart an acceleration of 1 cm/s2 to a mass of one gram
Thus,
(1) 1 dyne = 1 g*cm/s2
(2) 1 dyne = 10-5 N
Lesson 2.3 - Newton’s Thrid Law
What is Newton’s Third Law of Motion?
Whenever one object exerts a force on a second object, the second object exerts an equal force in the opposite direction on the first
“To every action there is an equal and opposite reaction”
- All materials, no matter how hard, are elastic to some degree
- A force influences the motion of an object only when its applied on that object
- A force exerted by an object does not influence that same object - only influences the object on which it is exerted
Ex: force exerted on the Person by the Ground
Lesson 2.3 - Newton’s Thrid Law
What is gravitational force? (g) How does it affect Newton’s first law?
- Objects dropped near the earth with the same acceleration (if air resistance is negligible)
- If gravitation force = acceleration, then:
FG = mg
- Force down to the center of the earth
- Weight: the magnitude of the force of gravity on an object
- SI units:
g = 9.80 m/s2 = 9.80 N/kg
Lesson 2.3 - Newton’s Thrid Law
What is contact force and normal force?
Contact Force:
- When two objects are in contact
Normal Force:
- Contact force acts perpendicular to the common surface(FN)
Lesson 2.4 – Newton’s Laws and Vectors
What is the net force of an object?
Newton’s second law states that the acceleration is proportional to the net force of an object
- NET FORCE: vector sum of all the forces acting on the object
Lesson 2.4 – Newton’s Laws and Vectors
What are free-body (force) diagrams?
* Choose one object and draw an arrow to represent the force acting on it
- Include every force acting on the object
- Not include forces acting on other objects
Add different diagrams for different objects
Forces like gravity and contact forces (one object pushing or pulling another, normal force, friction)
Lesson 2.4 – Newton’s Laws and Vectors
What are the steps to create a Free-Body Diagram for problems requiring the use of Newton’s Laws?
- Draw a sketch of the situation
- Consider only one object (at a time) and draw its corresponding free-body diagram
* (a) All the forces acting on it
(b) Include unknown forces
(c) Not include forces acting on other objects***- Draw the arrow for each force vector with reasonably accurate direction and magnitude
- Lable each force
- Only forces acting on a given object can be included in ΣF = ma for object
- Newton’s second law involves vectors, so it’s usually important to resolve vectors into components. Choose x and y axis
- For each object, apply Newton’s second law to the x and y component separately
- Solve the equation(s) for the unknown(s)
Lesson 2.4 – Newton’s Laws and Vectors
What is tension in a flexible cord?
- Flexible cord pulls on an object, the cord is said to be under tension
Force exerts on the object is the tension FT - Has negligible mass = force exerted at one end is transmitted undiminished to each adjacent piece of cord along the entire
- ΣF = ma = 0
- If the cord’s mass is zero (or negligible) no matter what a is
- Force pulling on the cord at two ends must add up to zero:
FT and -FT
Lesson 2.5 – Newton’s Laws with Friction, Inclines
What is friction?
- Exists between two solid surfaces (even the smoothest looking surfaces is rough on a microscopic scale)
- Microscopic bums impede the motion
- Rolling Fiction: when an object rolls over the surface
- Kinetic Friction: sliding friction
Lesson 2.5 – Newton’s Laws with Friction, Inclines
How does (sliding) kinetic friction work?
- Object slides across a surface, forces of kinetic friction acts opposite to the direction of the objects’ velocity
- The magnitude of friction: depends on the two surfaces
The friction force is approximately proportional to the normal force between two surfaces (which is the force that either object exerts on the other and is perpendicular to their common surface and contact)
Proportionality between the magnitudes of the friction force [Ffr] and the normal force [FN] as an equation by inserting a constant of proportionality µk:
Ffr = µkFN
- Not a fundamental law, its experimental relationship between the magnitude and force of friction
- Ffr: acts parallel to the two surfaces
- FN: acts perpendicular to the surfaces
- Not a vector equation
- µk: coefficient of kinetic friction (roughly independent of sliding speed as well as the area in contact)
Lesson 2.5 – Newton’s Laws with Friction, Inclines
What is static friction?
Force parallel to the two surfaces that can arise even when there is no sliding.
-
Ex: The desk is resting on the floor and there is no horizontal force exerted on the dest, so it doesn’t move. You exert a horizontal force, bt the dest isn’t movies, so there is another force keeping it in place (net force is zero at rest).
If you push with greater force without moving it, then the static friction increased
Push hard enough, kinetic friction takes over = exceeded the maximum force of static friction
Maximum force of static friction:
(Ffr)max = µsFN
- µs: coefficient of static friction
- Since the static friction can vary from zero to this maximum value:
Ffr ≥ µsFN
Lesson 2.5 – Newton’s Laws with Friction, Inclines
How can friction be a hindrance and how can it be reduced?
- Slows down moving objects and causes heating and binding of moving parts in machinery
- More effective in reducing friction: oil or other gas between them
Lesson 2.5 – Newton’s Laws with Friction, Inclines
How can friction be useful?
Walking depends on the friction between the soles of our shoes and the ground (static friction)
Lesson 2.5 – Newton’s Laws with Friction, Inclines
What is an incline and how does it affect physics?
The object slides down an incline, such as a hill or ramp
- Gravity is an accelerating force - yet the acceleration is not vertical
- Change the axis, so the x-axis points along the incline and the y-axis is perpendicular
Lab: Pulleys
What is a Pulley?
Simple machine consisting of a grooved wheel on an axle
Lab: Pulleys
What is a fixed Pulley?
Fixed Pulley: Stationary and does not move when a string or rope runs through it
Assume that they are massless: rotation of the pulley itself does not need to be taken into account during calculations
Lab: Pulleys
What is a movable pulley?
Movable Pulley: Moves as an object
Mass must be accounted for
Lab: Pulleys
What is a compound pulley system?
Compound Pulley System: Combination of fixed and movable pulley system
Single Fixed Pulley: change direction of the force applied
Single Movable Pulley and Compound: change direction and magnitude of the force
Lab: Pulleys
What is tension (in a pulley system)?
🔬 Tension: Pulling force exerted by a string or rope
Assume strings and ropes are massless - tension same all areas of the rope
Lab: Pulleys
Describe the free-body diagram of a single fixed pulley:
- Tension is the same magnitude on both sides of the pulley
- equal to the weight of the object
Lab: Pulleys
Describe the free-body diagram of a single movable pulley or compound pulley system:
The direction and magnitude of the tension on each side of the string are different
Single Movable Pulley: The weight of the object is evenly distributed to the two sides
- Weight is canceled by the sum of the tensions on each side
- Weight each side = half of total object
Lab: Pulleys
What is Mechanical Advantage?
🔬 Mechanical Advantage (MA): Measure of the multiplication factor for the input force
- The ratio of the output force to the input force:
MA = Fout / Fin
- Output Force: Corresponds to the load - object being moved by the machine
- Input Force: Corresponds to the applied force required to use the machine and move the load
Lab: Pulleys
What is Theoretical Mechanical Advantage?
🔬 Theoretical Mechanical Advantage (TMA): Ideal mechanical advantage of the machine
- The ratio of the theoretical output force to the theoretical input force:
TMA = Fout theory / Fin theory
- Also equals the number of string segments directly supporting the load (number of pulleys supporting the load + 1):
TMA = n + 1
- n = the number of pulleys supported
Lab: Pulleys
What is Actual Mechanical Advantage?
🔬 Actual Mechanical Advantage (AMA): Measured mechanical advantage for the machine
- Less than TMA (loss due to friction)
- Calculated using the measured input force (EFFORT) and measured output force (LOAD)
Lab: Pulleys
What is Efficiency (in a pulley system)?
🔬 Efficiency: Ratio of AMA to TMA
Efficiency = AMA/TMA * 100%
- the efficiency of a pulley system is effectively a measurement of the amount of friction in the system, or how close to an ideal system a real system is
- The more efficient the system, the smaller the amount of friction in the system, and the closer to ideal the system becomes
- Efficiency increases by increasing the actual mechanical advantage, accomplished by reducing the friction present in the system.
- Real systems are never 100% efficient because some friction always exists in real systems.
Lab: Pulleys
What is the Law of Conservation of Energy?
Law of Conservation of Energy: Total energy in an (isolated) system is constant
Lab: Pulleys
Define Work (in a pulley system):
Work: Measure of Energy (Joules) and is the force multiplied by the distance over the force acts:
W = Fd
In a pulley system: W(in) = W(out)
Machine MA > 1:
- Input force is less than the output force
- Input force must be larger than the distance over which the output force acts:
- Therefore, load moves over a smaller distance than the effort or applied force
- The larger the mechanical advantage of a machine, the smaller the effort required and the greater the distance the applied force must act over in order to move the load a given distance
Fout / Fin = din / dout = MA
Lab Experiment: Friction
How do you calculate the coefficient of kinetic friction?
Lab Experiment: Friction
How do you calculate the coefficient of static friction using the angle of Repose?
Angle of Repose: the angle at which an object rests on an inclined surface
Lesson 2.3 Questions
1. (I) What force is needed to accelerate a sled (mass = 55 kg) at 1.4 m/s2 on horizontal frictionless ice?
Lesson 2.3 Questions
3. (I) How much tension must a rope withstand if it is used to accelerate a 1210-kg car horizontally along a frictionless surface at 1.20 m/s2?
Lesson 2.3 Questions
5. (II) Superman must stop a 120-km/h train in 150 m to keep it from hitting a stalled car on the tracks. If the train’s mass is 3.6 × 10<span>6</span> kg, how much force must he exert? Compare to the weight of the train (give as %). How much force does the train exert on Superman?
Part A and B
Lesson 2.3 Questions
9. (II) A 0.140-kg baseball traveling 35.0 m/s strikes the catcher’s mitt, which, in bringing the ball to rest, recoils backward 11.0 cm. What was the average force applied by the ball on the glove?
Lesson 2.3 Questions
13. (II) A 75-kg petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg. How might the thief use this “rope” to escape? Give a quantitative answer.
Lesson 2.3 Questions
17. (II) (a) What is the acceleration of two falling sky divers (total mass = 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of their weight? (b) After opening the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute? See Fig. 4–44.
(B)
N - FN = ma
1293.6 N - FN = m(0)
FN = 1293.6 N
Lesson 2.4 Questions
23. (II) Arlene is to walk across a “high wire” strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is 10.0°, as shown in Fig. 4–47. If her mass is 50.0 kg, what is the tension in the rope at this point?
Lesson 2.4 Questions
27. (II) A train locomotive is pulling two cars of the same mass behind it, Fig. 4–51. Determine the ratio of the tension in the coupling (think of it as a cord) between the locomotive and the first car (FT1), to that between the first car and the second car (FT2), for any nonzero acceleration of the train.
Lesson 2.4 Questions
31. (II) An object is hanging by a string from your rearview mirror. While you are decelerating at a constant rate from 25 m/s to rest in 6.0 s, (a) what angle does the string make with the vertical, and (b) is it toward the windshield or away from it? [Hint: See Example 4–15.]
(b)
The object will swing towards the windshield, since it has a positive acceleration, so it moves forwards
Lesson 2.4 Questions
33. (II) (a) If mA = 13.0 kg and mB = 5.0 kg in Fig. 4–53, determine the acceleration of each block. (b) If initially mA is at rest 1.250 m from the edge of the table, how long does it take to reach the edge of the table if the system is allowed to move freely? (c) If mB = 1.0 kg, how large must mA be if the acceleration of the system is to be kept at 1/100 g?
Part A and B
Lesson 2.5 Questions
37. (I) A force of 35.0 N is required to start a 6.0-kg box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor? (b) If the 35.0-N force continues, the box accelerates at 0.60 m/s2. What is the coefficient of kinetic friction?
Part A and B
Lesson 2.5 Questions
39. (II) The coefficient of static friction between hard rubber and normal street pavement is about 0.90. On how steep a hill (maximum angle) can you leave a car parked?
Lesson 2.5 Questions
41. (II) A 2.0-kg silverware drawer does not slide readily. The owner gradually pulls with more and more force, and when the applied force reaches 9.0 N, the drawer suddenly opens, throwing all the utensils to the floor. What is the coefficient of static friction between the drawer and the cabinet?
Lesson 2.5 Questions
43. (II) A 1280-kg car pulls a 350-kg trailer. The car exerts a horizontal force of 3.6 × 103 N against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.
Lesson 2.5 Questions
51. (II) A child on a sled reaches the bottom of a hill with a velocity of 10.0 m/s and travels 25.0 m along a horizontal straightaway to a stop. If the child and sled together have a mass of 60.0 kg, what is the average retarding force on the sled on the horizontal straightaway?
Lesson 2.5 Questions
57. (II) The block shown in Fig. 4–59 has a mass m = 7.0 kg and lies on a fixed smooth frictionless plane tilted at an angle θ = 22.0° to the horizontal. (a) Determine the acceleration of the block as it slides down the plane. (b) If the block starts from rest 12.0 m up the plane from its base, what will be the block’s speed when it reaches the bottom of the incline?
Lesson 2.5 Questions
59. (II) The crate shown in Fig. 4–60 lies on a plane tilted at an angle θ = 25.0° to the horizontal, with mk = 0.19. (a) Determine the acceleration of the crate as it slides down the plane. (b) If the crate starts from rest 8.15 m up along the plane from its base, what will be the crate’s speed when it reaches the bottom of the incline?
A push of magnitude P acts on a box of weight W as shown in the figure. The push is directed at an angle θ below the horizontal, and the box remains a rest. The box rests on a horizontal surface that has some friction with the box. The friction force on the box due to the floor is equal to
Module 02 Exam
Two blocks, A and B, are being pulled to the right along a horizontal surface by a horizontal 100-N pull, as shown in the figure. Both of them are moving together at a constant velocity of 2.0 m/s to the right, and both weigh the same.
What is the force on A?
No horizontal force acts on A.
Module 02 Exam
A push of magnitude P acts on a box of weight W as shown in the figure. The push is directed at an angle θ below the horizontal, and the box remains a rest. The box rests on a horizontal surface that has some friction with the box. The friction force on the box due to the floor is equal to
- P cos θ + W
- P + W
- P cos θ
- P sin θ
- 0
- P cos θ
Module 02 Exam
In the figure, what does the spring scale read? The pulleys are ideal and the strings and scale are also massless.
- 0.50 N
- more than 19.6 N
- exactly 1.0 N
- 0.00 N
- exactly 2.0 N.
- exactly 1.0 N
Module 02 Exam
Two boxes, A and B, are connected by a horizontal string S on a horizontal floor. A very light wire pulls horizontally on box B, as shown in the figure, with a force of 100 N. The reaction force to this pull is
- the pull that string S exerts on box A.
- the force that box A exerts on box B.
- the pull that box B exerts on string S.
- the pull of box B on the wire.
- the pull that string S exerts on box B.
- the pull of box B on the wire
Module 02 Exam
A flatbed truck is carrying an 800-kg load of timber that is not tied down. The maximum friction force between the truck bed and the load is 2400 N. What is the greatest acceleration that the truck can have without losing its load?
Module 02 Exam
A box of mass 72 kg is at rest on a horizontal frictionless surface. A constant horizontal force of magnitude F then acts on the box, accelerating it to the right. You observe that it takes the box 3.4 seconds to travel 13 meters. What is the magnitude of the force F?
Module 02 Exam
A 30.0-kg load is being held in place using massless wires in the ideal pulley arrangement shown in the figure. What is the magnitude of the force F?
Module 02 Exam
The figure shows a block of mass M hanging at rest. The light wire fastened to the wall is horizontal and has a tension of 38 N. The wire fastened to the ceiling is also very light, has a tension of 59N and makes an angle θ with the ceiling. Find the angle θ.
50°
Module 02 Exam
A 5.0-kg block and a 4.0-kg block are connected by a 0.6 kg rod, as shown in the figure. The links between the blocks and the rod are denoted by A and B. A vertical upward force of magnitude F of magnitude 150 N is applied to the upper block. What magnitude force does each of the links A and B exert?
*************
Module 02 Exam
Three blocks, light connecting ropes, and a light frictionless pulley comprise a system, as shown in the figure. An external force of magnitude P is applied downward on block A, causing block A to accelerate downward at a constant 2.5 m/s2. The tension in the rope connecting block B and block C is equal to 60 N.
(a) What is the magnitude of the force P?
(b) What is the mass of block C?
Module 02 Exam
A 55-kg box rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.30, and the coefficient of kinetic friction is 0.20. What horizontal force must be applied to the box to cause it to start sliding along the surface?
Module 02 Exam
You push horizontally on a 120-N box that is initially resting on a horizontal table. The coefficient of static friction between the box and the table is 0.75, and the coefficient of kinetic friction is 0.40. Find the friction force on the box if the push is equal to (a) 84 N; (b) 94 N.
Module 02 Exam
As shown in the figure, block B on a horizontal tabletop is attached by very light horizontal strings to two hanging blocks, A and C. The pulleys are ideal, and the coefficient of kinetic friction between block B and the tabletop is 0.100. The masses of the three blocks are mA = 12.0 kg, mB = 7.00 kg, and mC = 10.0 kg. Find the magnitude and direction of the acceleration of block B after the system is gently released and has begun to move.
Block B has an acceleration of 0.44m/s2 and moves in the left direction.
Module 02 Exam
A system consisting of blocks, a light frictionless pulley, a frictionless incline, and very light connecting wires is shown in the figure. The wires pull on the left-hand blocks parallel to the surface of the ramp. The 9.0-kg block accelerates downward when the system is released gently from rest.
(a) What is the magnitude of the acceleration of the 9.0-kg block?
(b) What is the tension in the wire connecting the two blocks on the incline?
Module 02 Exam
A 7.5-kg stone moves up frictionless hill that slopes upward at 41° above the horizontal. If the stone has an initial velocity of 8.5 m/s at the bottom, how far (as measured along the surface of the hill) will it go before stopping?
