Motion

Unit 1: Motion Chapter 3: Laws of Motion 3.1 Newton's First Law 3.2 Acceleration and Newton's Second Law 3.3 Gravity and Free Fall

3.1 Investigation: Law of Inertia Key Question: Why are heavier objects harder to start or stop moving? Objectives: Apply an understanding of Newton’s first law to justify experimental data and observations. Explain the meaning of inertia. Distinguish between mass and weight.

Force changes motion A force is a push or pull, or any action that is able to change motion.

Law of inertia Newton’s first law says that objects continue the motion they already have unless they are acted on by a net force. If the net force is zero, an object at rest will stay at rest. If an object is acted upon by unbalanced forces, its motion will change.

According to these vectors, in what direction is the net force? Newton’s first law is often written in terms of the net force: “An object at rest will stay at rest and an object in motion will continue in motion at constant velocity UNLESS there is a net force.” According to these vectors, in what direction is the net force?

Force changes motion Forces can be used to increase or decrease the speed of an object, or to change the direction an object is moving.

Force, mass, and inertia Some objects resist changes in motion more than others. Inertia is the property of an object that resists changes in its motion. The greater an object’s inertia, the greater the force needed to change its motion. A bowling ball has more inertia than a golf ball.

Force, mass, and inertia Inertia comes from mass. Objects with more mass have more inertia and are more resistant to changes in their motion. A 5-kilogram bowling ball is 100 times as massive as a 50 gram golf ball, so it has 100 times the inertia.

Force, mass, and inertia For small amounts of mass, the kilogram is too large a unit to be convenient. A dollar bill has a mass of about a gram, and a liter of soda is 1,000 g. or 1 kg.

Units of force The pound is a unit of force commonly used in the United States. For smaller amounts, pounds are divided into ounces (oz.). There are 16 ounces in 1 pound.

Newtons Although we use pounds all the time in our everyday life, scientists prefer to measure forces in newtons. The newton (N) is a metric unit of force.

Unit conversions The newton (N) is a smaller unit of force than the pound (lb). If one pound of force equals 4.448 newtons, then a 100 lb person weighs 444.8 newtons.

The net force The motion of objects changes in response to the total force acting on the object, including gravity and any other forces that are present.

The net force in the horizontal direction The term net force is used to describe the total of all forces acting on an object. When used this way, the word net means “total.”

The net force in vertical direction Gravity exerts a force downward on the box. The floor exerts an equal and opposite force upward on the box.

The net force in vertical direction The net force on the box in the “up-down” direction is zero. When equal forces applied to the same object are in opposite directions they cancel.

Applications of Newton’s First Law Two very important safety features of automobiles are designed with Newton’s first law in mind: seat belts and air bags. Both supply a restraining force to counteract your inertia and to slow your body down.

Applications of Newton’s First Law Prior to the invention of cup holders, drink containers left on the dash obeyed the first law of motion and made quite a mess. Can you think of other applications of Newton’s first law?

Unit 1: Motion Chapter 3: Laws of Motion 3.1 Newton's First Law 3.2 Acceleration and Newton's Second Law 3.3 Gravity and Free Fall

3.2 Investigation: The Second Law: Force, Mass, and Acceleration Key Question: What is the relationship between force, mass, and acceleration? Objectives: Measure the acceleration for an Atwood’s apparatus of fixed total mass. Create a graph of force versus acceleration for the Atwood’s machine. Determine the slope and y-intercept of the graph and then relate them to Newton’s second law.

Newton’s second law Newton’s first law tells us that motion cannot change without a net force. According to Newton’s second law, the amount of acceleration depends on both the force and the mass.

Acceleration and force The second law says that acceleration is proportional to force. If force is increased or decreased, acceleration will be increased or decreased by the same factor.

The stronger the force on an object, the greater its acceleration. Force is directly proportional to acceleration. If twice the force is applied, the acceleration is twice as great.

The greater the mass, the smaller the acceleration for a given force. Mass is inversely related to force. An object with twice the mass will have half the acceleration if the same force is applied.

Applying the second law Keep the following important ideas in mind: 1. The net force is what causes acceleration. 2. If there is no acceleration, the net force must be zero. 3. If there is acceleration, there must also be a net force. 4. The force unit of newtons is based on kilograms, meters, and seconds.

Using units in calculations In terms of solving physics problems, use the following units when using force in newtons: mass in kilograms (kg) distance or position in meters (m) time in seconds (s) velocity in meters per second (m/s) acceleration in meters per second per second (m/s2)

Three forms of the second law When using the second law, the force that appears is the net force. Consider all the forces that are acting and add them up to find the net force before calculating any accelerations.

Using Newton’s second law A car has a mass of 1,000 kg. If a net force of 2,000 N is exerted on the car, what is its acceleration? Looking for: … the car’s acceleration. Given: …car’s mass (m= 1,000 kg) and the net force (Fnet = 2,000N). Relationship: Use: a = F m Solution: a = 2,000N = 2 kg• m/s2 = 2 m/s2 1,000 kg kg

Force and energy Forces are created any time there is a difference in energy. A stretched rubber band has more energy than a relaxed rubber band. The forces can transfer energy from one object to another.

Unit 1: Motion Chapter 3: Laws of Motion 3.1 Newton's First Law 3.2 Acceleration and Newton's Second Law 3.3 Gravity and Free Fall

3.3 Investigation: Free Fall Key Question: What kind of motion is falling? Objectives: Explain the meaning of falling is a physics sense. Determine an equation for the velocity in free fall. Use the equation to make predictions.

Gravity and Free fall An object is in free fall if it is accelerating due to the force of gravity and no other forces are acting on it. A ball thrown upward is also in free fall after it leaves your hand.

Free fall Falling objects increase their speed by 9.8 m/s every second, or 9.8 m/s2

Upward launches If you throw a ball upward, the ball will slow down as it moves upward, come to a stop for an instant, and then fall back down. As it moves upward, the speed decreases by 9.8 m/s every second until it reaches zero. The ball then reverses direction and starts falling down. As it falls downward, the speed increases by 9.8 m/s every second.

Changes in velocity Recall that velocity is speed with direction. The positive sign means upward and the negative sign means downward.

Changes in velocity In free fall and other situations when there is constant acceleration, the average velocity is the average of the starting or initial velocity (vi ) and the final velocity (vf )

Using average velocity A rock falls off a cliff and splashes into a river 5 seconds later. What was the rock’s average velocity? Looking for: … for average velocity in m/s. Given: …the time (5s) and assume the rock was at rest on the cliff, so it’s vi = 0. Relationships: Use: v = gt and vavg = vi – vf 2 Solution: v = (9.8 m/s2) (5 s) = 49 m/s vavg = 0 – 49 m/s = 24.5 m/s

Calculating distance Using the average velocity to calculate the distance traveled by an object in free fall requires multiple steps.

Calculating distance If the initial velocity is zero and the object falls for t seconds, then the final velocity is gt. The average velocity is half the final velocity or 1/2 gt. The distance is the average velocity multiplied by the time or 1/2 gt2. The general formula is therefore: d = 1 gt2 2 *This formula only works when the object starts at rest and is in free fall.

Using average velocity A skydiver falls for 6s before opening her parachute. Calculate her actual velocity at the 6-second mark and the distance she has fallen in this time. Looking for: … velocity in m/s after 6 seconds and distance fallen. Given: … the time (6s) and assume skydiver was at rest, so it’s vi = 0. Relationships: Use: v = gt ; vavg = vi – vf and d = vavgt 2 Solution: v = (9.8 m/s2) (6 s) = 58.8 m/s vavg = 0 – 58.8 m/s = 29.4 m/s d = (29.4 m/s) (6 s) = 176 m

Gravity and Weight The force of gravity on an object is called weight (Fw). At Earth’s surface, gravity exerts a force of 9.8 N on every kilogram of mass.

Weight vs. mass Weight and mass are not the same. Mass is a fundamental property of matter measured in kilograms (kg). Weight is a force measured in newtons (N). Weight depends on mass and gravity.

Weight depends on mass and gravity A 10-kilogram rock has the same mass no matter where it is in the universe. On Earth, the10 kg. rock weighs 98 N.. On the moon, the same rock only weighs 16 N.

Weight and mass Legend says that about 1587, Galileo dropped two balls from the Leaning Tower of Pisa to see which would fall faster. Suppose the balls had masses of 1.0 kg and 10 kg. a. Use the equation for weight to calculate the force of gravity on each ball. b. Use your answers from part a and Newton’s second law to calculate each ball’s acceleration. Looking for: … the force due to gravity (Fw) and the acceleration for each ball Given: … one ball’s mass = 1.0 kg. Relationships: Use: Fw = mg and a = F ÷ m Solution: For the 1.0 kg ball: a) Fw = (1.0 kg)(9.8 m/s2) = 9.8 N b) a = (9.8 N) ÷ (1.0 kg) = 9.8 m/s2

Summary: Both balls have the same acceleration! Weight and mass a. Use the equation for weight to calculate the force of gravity on each ball. b. Use your answers from part a and Newton’s second law to calculate each ball’s acceleration. Given: …the other ball’s mass = 10 kg. Relationships: Use: Fw = mg and a = F ÷ m Solution: For the 10 kg ball: a) Fw = (10 kg)(9.8 m/s2) = 98 N b) a = (98 N) ÷ (10 kg) = 9.8 m/s2 Summary: Both balls have the same acceleration!

Air resistance When something falls through air, the air exerts an additional force. This force, called air resistance, acts opposite to the direction of the object’s motion.

Terminal velocity Objects only accelerate until the force of air resistance equals the force of gravity. The net force then becomes zero and the object reaches a constant velocity called the terminal velocity. The terminal velocity depends on the ratio of an object’s weight to its air resistance.

Parabolic Flights NASA has been conducting parabolic flights since the 1950s to train astronauts. Scientists and college students have also gone on parabolic flights to perform a wide variety of chemistry, biology, and physics experiments. ZERO-G flights contain three types of parabolas: Martian gravity (1/3 Earth gravity), Lunar gravity (1/6 Earth gravity), and zero gravity.