Newton’s 2 nd Law: Relating Force, Mass, and Acceleration

Click on Sir Newton to move to the next slide Newton’s 2nd Law: Relating Force, Mass, and Acceleration Physical Science 9 Rochester High School

Return to previous slide Let’s Review… • We’ve discussed Newton’s 1st Law including: • Speed & Velocity • Force • Click on the links above to quickly review these topics. • After you are comfortable with these topics, click here.

Newton’s 1st Law • Also called the Law of Inertia • States an object in motion remains in motion and an object at rest remains at rest unless acted on by an outside force • Watch the Eureka Video about the relationship of mass and inertia

Speed & Velocity • Speed tells us the distance an object has traveled over a period of time • Velocity tells us the distance an object has traveled over a period of time AND the direction it traveled

Force • A force is a push or a pull on an object that causes a change in direction or speed • The net force tells us the total force on an object.

Comprehension Check:Speed What is the equation for speed? a. S = t x d b. S = t/d c. S = d/t

Not Quite! • Your choice: a. S = t x d • Think about what the US uses to measure speed in a car… Does the units of speed make sense with the equation you picked?

Take Another Glance… • Your Choice: b. S = t/d • Think about what the US uses to measure speed in a car… Does this make sense with the equation you picked?

You are Right! • S = d/t • The units for speed are miles per hour, meters per second, kilometers per hour, etc Move on to the Next Question!

Comprehension Check:Speed vs. Velocity A plane is traveling 50 km/s to the south. Is this an example of speed or velocity? Speed Velocity

Ask yourself…. • Is the magnitude included? • Is the direction included? • Speed only tells a magnitude (number) and velocity tells magnitude along with direction of motion.

Nice Job! • Since the magnitude (number= 50 km/s) and direction (south) are given, the data tells us the VELOCITY of the plane. • We call this a vector quantity (both a magnitude AND direction)

Comprehension Check:Speed What is the speed (in m/hr) of an object that travels 0.022 km in 180 seconds? a. 0.44 m/hr b. 440 m/hr c. 1.22 x 10-4 m/hr d. 0.122 m/hr

OOPS!a. 0.44 m/hr • Don’t forget to convert from 22 km into m! • 1 km = 1000 m

Great! b. 440 m/hr • You remembered to convert from km to m and from seconds to hours! • You are ready to move on to the new topics! Click on Newton above to move ahead.

TRY AGAINc. 1.22 x 10-4 m/hr • Don’t forget to convert • From 180 seconds into hours • From 22 km into m • 1 hour = 60 min ; 1 min = 60 seconds • 1 km = 1000 m

SO CLOSE!d. 0.122 m/hr • Don’t forget to convert from 180 seconds into hours before using the speed formula • 1 hour = 60 min • 1 min = 60 sec

New Topics • How is mass different from weight? • What is acceleration? • After you have completed the topics above, use your knowledge to learn about Newton’s 2nd law!

Mass vs. Weight • Mass is a measure of the amount of matter in an object. • - Measured in grams (lbs in US)

Mass vs. Weight • Weight is a measure of the forceof gravity on an object. - Since it’s a measure of force, weight is measured in Newtons (N) • Watch the Eureka video about mass vs. weight!

Comprehension Check: Mass vs. Weight What do you notice about the person in all the locations above? What does each location have in common? How are they different?

What do they have in common? In all locations, the person has the same mass of 63.5 kg.

How are they different? They all have different weights. The weight of the person changes based on the force of gravity present in each location.

Acceleration • You experience a change in velocity when you accelerate. • Since velocity includes both a speed and direction, acceleration occurs if speed and/or direction changes. • Since acceleration deals with a magnitude and a direction, it is a vector quantity!

Acceleration • The opposite of acceleration (speeding up) is deceleration (slowing down) - Deceleration is also called negative acceleration

Comprehension Check: Acceleration vs. Deceleration Is the car in Practice A accelerating or decelerating? Accelerating Decelerating

Congratulations! The car in practice A is accelerating because the velocity is increasing during each time interval.

Ask yourself… • Does the velocity of the car in Practice A increase or decrease? • Is car A speeding up or slowing down?

Calculating Acceleration • We can solve for acceleration using the following formula:

Units for Acceleration • The units for acceleration are distance/time/time. • For example: m/s/s, km/min/min, mi/hr/min • m/s/s can be written as m/s2, km/min/min can be written as km/min2, etc • Watch the Eureka video about units of Acceleration (part 2)!

Acceleration If I rearrange the equation, I find that:

Acceleration Example Calculation • How long does it take for a car to change its velocity from 10 m/s to 25 m/s if the acceleration is 5 m/s2? Equation: T = ∆ V/A T = (25 m/s – 10 m/s) / 5 m/s2 = 15 m/s / 5 m/s2 = 3 s

Comprehension Check: Acceleration Calculation As a shuttle bus comes to a normal stop, it slows from 9.00m/s to 0.00m/s in 5.00s. Find the average acceleration of the bus. • 45 m/s2 • -1.8 m/s2 • 1.8 m/s2 • -45 m/s2

Good Try! • Your Choice: a. 45 m/s2 • Remember: The equation for acceleration is

Nice! • You used the correct equation and noticed the car was decelerating therefore making your answer negative. • You can move on to a different topic!

So Close! • Your Choice: c. 1.8 m/s2 • You used the correct equation (below) but is the car accelerating or decelerating?

Take Another Look • Your Choice: d. -45 m/s2 • Remember: The equation for acceleration is

Newton’s 2nd Law • Combines our knowledge of force, mass, and acceleration. • States: The force acting on an object equals the object’s mass times its acceleration.

Newton’s 2nd Law • In an equation, this law means: Force = mass * acceleration F = m * a • Watch the Eureka Video about this equation and Acceleration (Part 1)!

Newton’s 2nd Law • So what in the world does that mean to us? Consider the following example…. • You have a full shopping cart and an empty one. Which requires more force to push? *Obviously the full cart is harder to push because it has more MASS.

Newton’s 2nd LawExample Calculation A Zoo keeper lifts a lion on a stretcher with a combined mass of 175kg . The upward acceleration is 0.657m/s2. What force is necessary to produce this acceleration? F = m * a F = (175 kg) * (0.657 m/s2) F = 114.975 kg*m/s2 or 114.975 N UPWARD *Recall: Force is a vector quantity which requires a magnitude AND direction!

Comprehension Check: Newton’s 2nd Law Calculation A sailboat and crew have a combined mass of 695kg. If the boat experiences an unbalanced force of 895N pushing it forward, what is the boat’s acceleration? • 0.777 m/s2 • 622,025 m/s2 • 1.29 m/s2

Try Again! Your Choice: a. 0.777 m/s2 • Remember: Newtons (N) are a unit of force and kg are a measure of mass. • Rearrange your F = m*a equation to solve for a!

Hmm… Your Choice: b. 622,025 m/s2 • Remember: Newtons (N) are a measure of force and kg are a measure of mass. • Rearrange your F = m*a equation to solve for a!

Wonderful! Your Choice: c. 192.1 m/s2 • The work is shown below F = m*a 895 N = 895 kg*m/s2 = (695 kg)*(a) a = (895 kg*m/s2)/695 kg a = 192.1 m/s2

Congratulations! • You have completed the assignment. • If you feel prepared, see your teacher for the quiz. You will get only two chances to get at least an 85% on the quiz- so make sure you are ready! • If you want to review the topics or review the Eureka videos, click here!

Need More Review? How is mass different from weight? What is acceleration? Review Newton’s 2nd law! You can also review the Eureka Videos to go along with these topics!

Mass vs. Weight • Mass is a measure of the amount of matter in an object. • - Measured in grams (lbs in US)

Mass vs. Weight • Weight is a measure of the forceof gravity on an object. - Since it’s a measure of force, weight is measured in Newtons (N)

Newton’s 2 nd Law: Relating Force, Mass, and Acceleration