Lesson 24: Newton's Second Law (Motion) To really appreciate Newton s Laws, it soeties helps to see how they build on each other. The First Law describes what will happen if there is no net force. The Second Law describes what will happen if there is a net force. The Second Law (The Law of Motion) When an external, unbalanced force acts on an object, the object will accelerate in the sae direction as the force. The acceleration varies directly as the force, and inversely as the ass. When an external, unbalanced force We are still talking about these external forces, but now we ve added in the idea of unbalanced. Unbalanced just eans that there isn t anyone (or anything) pushing against the force hard enough to cancel it out. There is a net force acting on the object. accelerates in the sae direction as the force Soe people think this eans that the object will ove in the sae direction as the force not necessarily! The object ight be oving to the right, while a force is pushing left. That eans the object will slow down. It s acceleration is in the direction of the force (to the left), but it is still oving to the right. The acceleration varies directly as the force This just eans that if the force increases, the acceleration will increase. If the force decreases, the acceleration decreases. This akes sense push soething harder and it will accelerate ore! They depend directly on each other. and inversely as the ass. This eans that if the ass is bigger, the acceleration is less. If the ass is less, the acceleration is ore. This akes sense also if soething has less ass, it is easier to ake it ove faster! They depend inversely on each other. Matheatically this would be written as a αf a α 1 The little swiing fish sybol ( α ) is the Greek letter alpha and eans varies as in ath. It does not ean they are equal to each other, but it does show they are related to each other in 10/30/2017 studyphysics.ca Page 1 of 5 / Section 3.3
soe way. We are showing that acceleration is directly related to force If the net force exerted is increased, the acceleration will also increase. Acceleration is inversely related to ass. If the ass increases, the acceleration will decrease. If the ass is bigger, the object will have ore inertia, so it will resists changes to its otion ore. When you cobine these two relations, you get one of the ost basic and iportant forulas ever discovered in physics. = net force (Newtons, N) = ass (kg) a = acceleration (/s 2 ) The unit of force is called the Newton. It's equivalent to kg /s 2. It was naed in honor of the outstanding work that Newton did in physics. By definition a one kilogra ass will be accelerated at 1 /s 2 if a 1 Newton force is applied to it. Exaple 1: Deterine the force acting on a 5.46kg object if it is accelerated at 17/s 2. =a =(5.46)(17) =92.82=93N Exaple 2: Deterine the acceleration of a 1000 kg car if a 2.5e3 N force acts on it? =a = 2.5e3 1000 =2.5/s2 Applications of Newton's Second Law It is best to start the ore coplex diagras by analyzing what forces are involved, coe up with a net force forula, and draw a free body diagra. In these exaples the forces will all be acting vertically or horizontally, not both. 10/30/2017 studyphysics.ca Page 2 of 5 / Section 3.3
Exaple 3: A kg elevator is being raised by a cable that exerts a 4.00e4 N force upwards. Deterine the acceleration of the elevator. There are only two forces acting on the elevator, the force of tension in the cable pulling it up and the force of gravity acting down. It is the net force that causes the acceleration of the elevator, so we're basically solving for that. We can substitute in = a Reeber to use negative for down and positive for up. F T + F T g+ F T g+ F T ( 9.81)+ 4.00e4 36297+ 4.00e4 3703 1.0008108=1.00 / s 2 Drawing 1: Free body diagra of elevator. The acceleration of the elevator is 1.00 /s 2 [upwards]. Exaple 4: Deterine the acceleration of the elevator fro Exaple 3 if the tension in the cable is only 3.30e4 N. + F T g+ F T g+ F T g+ F T ( 9.81)+ 3.30e4 36297+ 3.30e4 3297 0.8910810811= 0.891 /s 2 The acceleration of the elevator is now 0.891 /s 2 [down]. 10/30/2017 studyphysics.ca Page 3 of 5 / Section 3.3
Exaple 5: A 0.0500 g piece of paper is dropped. If it falls with an acceleration of 0.390 /s 2 [down] deterine the friction acting on the paper. The frictional force ust be pointing upwards since it will resist the otion of the paper falling down. Don't forget to turn the ass into kilogras. + g+ Drawing 2: Free body a g= of falling sheet of =a g paper. =(a g) =5.00e-5( 0.390 ( 9.81)) =4.71e-4N The fricition acting on the paper is 4.71e-4 N [up]. Exaple 6: Two boxes are attached by a thin wire as shown in Drawing 3. A person pulls on the wire attached to the yellow box. There is a force of friction 25.0 kg 5.0 kg of 213 N acting on the boxes. Deterine the force applied to the boxes if they accelerate to the right at Drawing 3: Two boxes attached by wire. 2.45 /s 2. Since the boxes are attached by a wire, they ust accelerate at the sae rate. We can also treat the as one big ass instead of two sall asses. We will assue that the wires have no ass. and F N cancel each other vertically, so we can ignore the. To the right is positive, and to the left is negative. = + + = a =30.0(2.45) ( 213) =286.5=287 N The applied force is 287 N [right]. 30.0 kg F N Drawing 4: Free body diagra of single ass. Exaple 7: Atwood's Pulley is a classic physics proble involving two unequal 12.00kg 10/30/2017 studyphysics.ca Page 4 of 5 / Section 3.3 7.50kg Drawing 5: Atwood's Pulley.
asses hanging fro a wire over a pulley. Since one of the asses is heavier, the whole thing will ove so that the heavier ass oves down and the lighter ass oves up. If ass one is 12.00 kg and ass two is 7.50 kg, deterine the acceleration of each ass. Since we are dealing with two asses that are attached, we will do the sae thing as Exaple 6 and add the asses. We will need to be careful, since the net force is pulling the blue box down and the yellow box up, but is ade up of two forces due to gravity pulling down on different sides. To siplify this, we will take our single ass and pretend that one force due to gravity is pulling it to the left, while the other force due to gravity is pulling it to the right. 1 2 1 19.50kg 2 Drawing 6: Rotate the two forces due to gravity horizontally, and show the acting on the cobined Mass One ass. 1 = g 1 =12.00 9.81 1 = 117.72 N Pulls to the left with 117.72N. Mass Two = g =7.50 9.81 =73.575N Pulls to the right with 73.575N. Hoework 12.00kg 1 = 117.72 73.575 = 44.145 = 44.15N 7.50kg = a = 44.15 19.50 a = 2.26 / s 2 p149 #1,2 p150 #1 p152 #2 p158 #5, 8, 9 The inus sign, based on Drawing 6, just shows that ass one will drop as ass two rises. Both will have an acceleration of 2.26 /s 2. When doing questions that involve a pulley, just reeber that a pulley kind of changes the direction a force is acting in. That's why we can change the directions soe of the forces are pointing in these questions, even though we typically can not change the direction of vectors. 10/30/2017 studyphysics.ca Page 5 of 5 / Section 3.3