Force and weight Objectives Explain the difference between
Force and weight
Objectives • Explain the difference between weight and mass. • Calculate weight from mass or mass from weight.
Assessment 1. If you take a trip from Earth to the Moon, which statement below is correct? A. Your mass and weight both decrease. B. Your mass stays the same and your weight decreases. C. Your mass decreases and your weight stays the same. D. Your mass increases and your weight decreases.
Assessment 2. What is the weight of this dumbbell, in newtons? 3. A person weighs 150 lbs. What is this weight in newtons? What is this person’s mass in kilograms? A 10 kg dumbbell resting on a table is partly supported by a spring that pulls upward with a force of 50 N.
Physics terms • mass – measurement of the quantity of matter. (SI kg; English slugs) • force – action on a body that causes a change in motion. (SI Newtons) • weight – downward-acting force created by gravity acting on the mass of an object. Equal to mg, where g is the local strength of gravity at the Earth’s surface. Weight has the units of force • newtons – Si unit of force equivalent to 1 kg m/s 2 • pound (lb) – English unit of force equal to 4. 448 N. The force due to Earth’s gravity is often expressed in pounds.
Equations Weight is mass multiplied by the strength of gravity. At Earth’ s surface the strength of gravity is 9. 8 newtons per kilogram.
Explaining motion Isaac Newton was the first person to explain WHY objects move the way they do. He based his laws of motion on two key concepts: • mass • force
What is mass? All matter has mass and takes up space. A solid rock has mass. So do gases and liquids. With your hand out the window of a moving car, you feel the mass in the air pushing against you.
Measuring mass The SI unit for mass is the kilogram. This object has a mass of 2 kilograms.
What is force? The concept of force: A force is a push or a pull.
What is force? The concept of force: A force is a push or a pull. Forces can cause an object to change its motion. Can you give some examples of forces?
Types of forces The concept of force: A force is a push or a pull. Forces can cause an object to change its motion. Can you give some examples of forces? Examples of forces: • • • weight friction tension from rope force from a spring electric force
Units of force Quantitative: Force is measured in newtons.
Units of force
Weight is a force Weight is the force of gravity acting on objects with mass. How is weight different from mass?
Weight vs. mass Mass is an intrinsic property that measures the quantity of matter in an object. • Your mass does NOT change if you go into space.
Weight vs. mass Mass is an intrinsic property that measures the quantity of matter in an object. • Your mass does NOT change if you go into space. Weight is an extrinsic property that depends on the gravity force. • Your weight changes if you go into space. Your weight depends on your location.
Weight vs. mass Mass is a scalar quantity. It has a magnitude (such as 60 kg), but no direction. Weight is a vector. It has magnitude AND direction. For objects on Earth, it always points straight down toward the center of the Earth. Fw
Weight is the force of gravity acting on objects with mass. Weight is mass multiplied by the strength of gravity. At Earth’s surface the strength of gravity is 9. 8 newtons per kilogram.
Weight One kilogram of mass weighs 9. 8 N. This is roughly the mass and weight of a one liter water bottle. 1 kg
Weight One kilogram of mass weighs 9. 8 N. 1 kg This is roughly the mass and weight of a one liter water bottle. Force is a vector, so it has a direction. The force of weight always points straight down. Fw = 9. 8 N
Weight One kilogram of mass weighs 9. 8 N. 1 kg This is roughly the mass and weight of a one liter water bottle. What changes if you bring this bottle to the Moon? Fw = 9. 8 N
Weight One kilogram of mass weighs 9. 8 N. 1 kg This is roughly the mass and weight of a one liter water bottle. What changes if you bring this bottle to the Moon? Fw = 1. 6 N
What is a pound? The pound is the English unit of force. The person standing on this scale is pushing down on it with a force of 125 pounds.
What is a pound? The pound is the English unit of force. Pounds are a unit of force, not mass. One pound = 4. 448 N The newton is a smaller unit of force than the pound. One newton = 0. 225 lbs (~3. 6 ounces)
Example problem If a person has a weight of 125 pounds, what is her mass in kilograms?
Convert to SI units If a person has a weight of 125 pounds, what is her mass in kilograms?
Calculate the mass Mass is weight divided by g.
Weight and mass Whenever you know the mass of an object, you can calculate its weight. Whenever you know the weight of an object, you can calculate its mass.
Exploring the ideas Click this interactive calculator on page 135.
Engaging with the concepts Use the weight calculator to check your work when solving problems on the student assignment.
Test your knowledge How many newtons of gravitational force is exerted on a man with a mass of 80 kg who is standing on the Moon, where g = 1. 6 N/kg? a. 128 N b. 64 N c. 784 N d. 50 N
Test your knowledge How many newtons of gravitational force is exerted on a man with a mass of 80 kg who is standing on the Moon, where g = 1. 6 N/kg? a. 128 N b. 64 N c. 784 N d. 50 N The answer is a. Force = (mass) × (acceleration due to gravity) = 80 kg × 1. 6 N/kg = 128 N
Assessment 1. If you take a trip from Earth to the Moon, which statement below is correct? A. Your mass and weight both decrease. B. Your mass stays the same and your weight decreases. C. Your mass decreases and your weight stays the same. D. Your mass increases and your weight decreases.
Assessment 1. If you take a trip from Earth to the Moon, which statement below is correct? A. Your mass and weight both decrease. B. Your mass stays the same and your weight decreases. C. Your mass decreases and your weight stays the same. D. Your mass increases and your weight decreases.
Assessment 2. What is the weight of this dumbbell, in newtons? A 10 kg dumbbell is resting on a table partly supported by a spring that pulls upward with a force of 50 N.
Assessment 2. What is the weight of this dumbbell, in newtons? Fw = mg = (10 kg)(9. 8 N/kg) = 98 N
Assessment 3. A person weighs 150 lbs. What is this weight in newtons? What is this person’s mass, in kilograms?
Assessment 3. A person weighs 150 lbs. What is this weight in newtons? What is this person’s mass, in kilograms?
Assessment 3. A person weighs 150 lbs. What is this weight in newtons? What is this person’s mass, in kilograms?
Normal forces and free-body diagrams • The meaning of a free-body diagram – A geometric sketch of an object isolated from everything else except for the forces that act on it. – Every interaction the object has with the environment is replaced by the force that interaction makes on the object.
Normal Forces (sometimes called support forces) • If a ball is resting on a table, then the free-body diagram replaces the table with a force that allows the ball to remain at rest – called a normal force – Force perpendicular to a surface (where objects touch other objects, such as floors or walls)
Normal forces and free-body diagrams Drawing Normal Forces Drawing free-body diagrams outline of the object that • Normal forces provide a push • An shows the approximate locations and assumed directions & point perpendicular to the and names of the forces acting surface of contact on each single object
Test your knowledge Which forces are drawn on a free-body diagram of an object? a. only those forces that are exerted by the object b. only those forces that are exerted on the object c. all forces exerted on or by the object
Test your knowledge Which forces are drawn on a free-body diagram of an object? a. only those forces that are exerted by the object b. only those forces that are exerted on the object c. all forces exerted on or by the object The answer is b. Only those forces that act on the object should appear on its free-body diagram. The forces that act on an object determine its motion.
Center of Mass • The center of mass is the average location of all the mass contained in the object • Where is the center of mass of a ring? • For rigid objects it is usually accurate to consider the weight force to act on an object’s center of mass.
Weight on freebody diagrams • weight force is drawn downward from the center of mass • Solve the Example problem below • • • You can find the center of mass of an irregular object by hanging it from a string. The center of mass will always lie directly below the line of the string. If you choose three different points, the intersection of the three lines (one for each string choice) shown in the diagram (above) locates the center of mass.
ways to draw free-body diagrams • Free-body diagrams are used for describing forces and objects. • Outline method – more practical applications • Point-mass method used more in theoretical application
Which is best? • Which point-mass is right for m 1? • Draw an Outline method for m 1
What is a “net force”? • The net force is the total, or sum, of all forces acting on an object • Can the same forces make different net forces?
Force is a Vector • The direction of a force matters when determining the net force. • Force, like position, is a vector. In one-dimensional problems positive and negative signs are used to indicate direction. • Forces should be assigned positive and negative values that correspond to direction. • When solving problems involving forces and free-body diagrams, you must choose which direction is positive.
What is Equilibrium F 1+F 2+F 3+⋯=0 (5. 2) F 1, F 2, F 3, . . . = force (N) • This is a vector equation! That means that equation (5. 2) holds separately for each direction relevant to the situation. • The total force in the x-direction must be zero. • The total force in the y-direction must be zero. • The total force in the z-direction must be zero.
Test your knowledge Nina is pulling on a box with a force of 250 N, but the box isn’t moving. What is the force of friction on the box? • 0 N • 250 N • 500 N • Not enough information
Test your knowledge Nina is pulling on a box with a force of 250 N, but the box isn’t moving. What is the force of friction on the box? • 0 N • 250 N • 500 N • Not enough information The answer is b, 250 N. If the box is not moving, then there is no net force on it. This means that Nina’s pulling force must be canceled out by friction.
How do I solve an Equilibrium Problem? 1. Draw a free-body diagram including forces from ropes, attached supports, weight, and normal forces. 2. Assign positive and negative directions. 3. Use the equilibrium equation by setting the net force to zero independently for each direction. Each direction equation can be solved for one unknown force. 4. If there are still unknown forces then you may need more information
Test your knowledge • If, while moving at 9 m/s, a box experiences a friction force of 40 N, how much force do you need to apply to the box for it to be in equilibrium? • 0 N • 20 N • 40 N • 80 N
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