Newton's Second Law

Author: Maddie Van Beek


Last week, we learned about Newton’s First Law of Motion, or the Law of Inertia. You learned that an object in motion will stay in motion, or an object at rest will stay at rest, unless affected by an outside force. If you missed us last week, check out http://discoveryexpress.weebly.com/…/demonstrating-the-law-…. 




Newton’s Second Law tells us that the acceleration of an object--as produced by a net force--is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object. 




What does that even mean?! 




It can be simplified into this equation:




F = m * a




F = force

- Force is measured in Newtons. 

m = mass

- Mass is measured in kilograms. 

a = acceleration 

- Acceleration is measured in meters per second squared. 







Before you try using this equation, here’s a great example from howstuffworks.com. 

http://s.hswstatic.com/gif/newton-law-of-motion-one-dog.jpg

Let’s say you are trying to calculate the acceleration for this dog sled. As you can see, the force is 100 newtons, and the mass is 50 kilograms. 




Before you plug the numbers into the equation, isolate acceleration, since that is what you are trying to find. 




F = m * a




Take the force divided by mass to get acceleration by itself. 




a = F/m




Next, plug the numbers into the equation. 




a = 100N/50kg




Now, divide! 




a = 2 m/s^2 




You’ve calculated the acceleration of the sled! 




But what if another dog that pulls with equal force is added to the team? 

http://s.hswstatic.com/gif/newton-law-of-motion-two-dogs.jpg

Try calculating the acceleration this time! 




F = 200 N

m = 50 kg

a = ? 




a = F/m

a = 200 N/50 kg

a = 4m/s^2




What would have happened if you had doubled both the force and the mass? 




F = 200 N

m = 100 kg

a = ? 




a = F/m

a = 200 N/ 100 kg

a = 2m/s^2




You’d be right back to an acceleration of 2m/s^2.  




This example demonstrates how the acceleration is proportional to the force. 

http://s.hswstatic.com/gif/newton-law-of-motion-four-dogs.jpg

The picture above illustrates the idea of net force. If two equal forces are opposing each other, the net force becomes zero. In this picture, you see that there are two dog sled teams pulling with a force of 200 N on either side of the sled, so the net force is zero. This means that the sled would not move. If the sled team on the right were bigger and were pulling with a force of 300 N, then the sled would move to the right. Make sense? 




You now have plenty of information to complete the practice equations and the activity below, but for further description of Newton’s Second Law of Motion, check out this helpful video from KhanAcademy: 

Newton's second law of motion: Newton's Second Law of Motion: F=ma

Now that you have seen a few demonstrations, let’s practice:




1. Erin and Andrew are playing tug of war. Erin is pulling to the right with a force of 100 N. Andrew is pulling to the left with a force of 200 N. What is the net force? What direction would they move? 

2. Grady is pulling a wagon that has a mass of 30 kilograms. Grady is pulling with a force of 300 N. What is the acceleration? 


3. Ashley is pushing a stroller that has a mass of 20 kilograms. The stroller is accelerating at 3 m/s^2. 
Use F = m * a to find the force. 


4. Deidre is pulling her puppy’s leash with a force of 50 N, but the puppy is pulling in the opposite direction with a force of 25 N. What is the net force? 

5. Josiah is pushing a shopping cart with a force of 75 N at a rate of 1 m/s^2. What is the mass of the shopping cart? 




Activity




YOU WILL NEED:

• 2 marbles of the same size, but different masses. Both should be lighter than the ball bearings. 
• 2 identical ball bearings
• Ramp (could be constructed out of poster board) 
• Tape Measure
• Scale
• Stopwatch

Here’s what to do!

1. Use the scale to determine the mass of each marble and ball bearing. Record these masses in your observation journal. 
2. Use a tape measure to create two meter-long ramps. You could use heavy poster board to make the ramp. Make sure you fold up the sides so the marble won’t roll off. 
3. Place one end of the first ramp on top of a stack of books to create an approximately 10 degree incline. 
4. Mark the first ramp at 30cm and 60cm. 
5. Place the end of the second ramp at the bottom of the incline of the first ramp. Make sure the marble will be able to roll smoothly from one ramp to the next. You could place a piece of tape to connect the two ramps and make sure it’s a smooth transition. 
6. Now that you’ve made your ramp, place one ball bearing at the base of the first ramp, right where the second ramp starts. Here is what your final set-up should look like: 

http://swift.sonoma.edu/education/newton/newton_2/html/Newton2.html

1. Place the marble with the smallest mass at the top of your ramp. What do you think will happen when it hits the ball bearing? Try it out! 
2. As you can see, the ball bearing moves when it is struck by the marble. Think back to Newton’s First Law, an object at rest stays at rest until enacted upon by an outside force. 
3. Try this again, except this time, use the stopwatch to time how long it takes the marble to travel from the top of the ramp to the ball bearing at the bottom of the ramp. 
4. Do this three times and then calculate the average time. 
5. Repeat step 8 and 9 with first the second marble and then the ball bearing. 
6. Next, repeat step 8-10, except start at the 30cm mark. 
7. Last, repeat steps 8-10, except start at the 60cm mark. 

Record your data and calculate the acceleration in this chart: 
 

To calculate acceleration, subtract the ball’s initial speed (zero) from its final speed and divide by the time it took to hit the target ball. 




Example: 

Speed:          100cm/2sec

Simplified:      50cm/sec

Acceleration:  (50cm/sec - 0cm/sec) / 2 sec

                      25cm/sec^2




Part 2

What’s happening when the first ball hits the second ball? 

So now that you’ve determined acceleration for each impact ball, let’s focus on what happens when each ball hits the target ball bearing at the bottom of the first ramp. As you have seen, the force of the accelerating ball causes the once-stationary target ball to move. 




How do you think the mass of the impact ball affects the time it takes the target ball to travel down the second 1m ramp once it is struck? 




Let’s find out! 




1. Just as you did before, start with the lightest marble at the top of the ramp. This time, you are using the stopwatch to measure the time it takes the target ball to travel from its starting point to the end of the second 1m ramp. You will start the stopwatch once the target ball is struck and stop the stopwatch once it reaches the 1m mark. 


2. Repeat step 1 three times and record the average time. 


3. Repeat steps 1-2 with the second marble. 


4. Repeat steps 1-2 with the other ball bearing. 


5. Record in the table below: 

http://swift.sonoma.edu/education/newton/newton_2/html/Newton2.html

Record your observations. Did the mass of the impact ball affect the average time the target ball took to travel 1m? Why do you think this is? 

You should have found that the more mass the impact ball had, the faster the target ball rolled 1 meter. This explains Newton’s Second Law: Larger mass means larger force, which then means larger acceleration. This demonstrates how the variables of mass, acceleration, and force are proportional with one another. 




Extension: 

Now that you have the mass and the acceleration of the impact balls from part one, you can calculate the force with which they hit the target ball bearing. Remember, the force is found by multiplying the mass and the acceleration. 

http://s2.quickmeme.com/img/52/5274cc91d666865736eada8deec07a9192cd33f893051bbf6624822e0e24a7e0.jpg

References

http://science.howstuffworks.com/innovation/scientific-experiments/newton-law-of-motion3.htm

http://www.physicsclassroom.com/class/newtlaws/Lesson-3/Newton-s-Second-Law

http://swift.sonoma.edu/education/newton/newton_2/html/Newton2.html

http://www.physicsclassroom.com/class/1DKin/Lesson-1/Acceleration