Newton’s Laws Examples Physics 6A Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Newton’s Laws of Motion These three rules govern the motion of any object. 1: Law of Inertia The velocity of an object will not change unless it is acted upon by a nonzero net force. 2: This is the formula we will use to calculate the effect of forces on objects. 3: Forces always come in action-reaction pairs. You have probably heard this as “for every action there is an equal and opposite reaction”. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

v0 Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. v0 Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

v0 Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. v0 You may think that Newton’s first law (inertia) would tell us that the eraser should continue forward at speed v0 indefinitely. Does the eraser do this? Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

v0 Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. v0 You may think that Newton’s first law (inertia) would tell us that the eraser should continue forward at speed v0 indefinitely. Does the eraser do this? No, of course it slows down and then stops. So is Newton’s first law violated? Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

v0 1: Law of Inertia Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. v0 You may think that Newton’s first law (inertia) would tell us that the eraser should continue forward at speed v0 indefinitely. Does the eraser do this? No, of course it slows down and then stops. So is Newton’s first law violated? Here it is again – does the motion of the eraser follow this rule? 1: Law of Inertia The velocity of an object will not change unless it is acted upon by a nonzero net force. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

v0 1: Law of Inertia Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. v0 You may think that Newton’s first law (inertia) would tell us that the eraser should continue forward at speed v0 indefinitely. Does the eraser do this? No, of course it slows down and then stops. So is Newton’s first law violated? Here it is again – does the motion of the eraser follow this rule? 1: Law of Inertia The velocity of an object will not change unless it is acted upon by a nonzero net force. There must some net force acting on the eraser since it changed its velocity Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

v0 1: Law of Inertia Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. v0 You may think that Newton’s first law (inertia) would tell us that the eraser should continue forward at speed v0 indefinitely. Does the eraser do this? No, of course it slows down and then stops. So is Newton’s first law violated? Here it is again – does the motion of the eraser follow this rule? 1: Law of Inertia The velocity of an object will not change unless it is acted upon by a nonzero net force. There must some net force acting on the eraser since it changed its velocity What force(s) are exerted on the eraser? Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

v0 1: Law of Inertia Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. v0 You may think that Newton’s first law (inertia) would tell us that the eraser should continue forward at speed v0 indefinitely. Does the eraser do this? No, of course it slows down and then stops. So is Newton’s first law violated? Here it is again – does the motion of the eraser follow this rule? 1: Law of Inertia The velocity of an object will not change unless it is acted upon by a nonzero net force. There must some net force acting on the eraser since it changed its velocity What force(s) are exerted on the eraser? We can draw a picture of the eraser and all the forces that act on it. This is one of your most important tools – we call it a “free-body diagram” Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. Normal force Here is the force diagram for the eraser friction weight Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. Normal force ‘Normal’ means perpendicular Here is the force diagram for the eraser Assuming that the normal force and the weight are the same magnitude, which direction is the net force on the eraser? friction weight Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. Normal force ‘Normal’ means perpendicular Here is the force diagram for the eraser Assuming that the normal force and the weight are the same magnitude, which direction is the net force on the eraser? The net force is to the left (in the direction of the friction force). What does this tell you about the acceleration of the eraser? friction weight Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. Normal force ‘Normal’ means perpendicular Here is the force diagram for the eraser Assuming that the normal force and the weight are the same magnitude, which direction is the net force on the eraser? The net force is to the left (in the direction of the friction force). What does this tell you about the acceleration of the eraser? Yes, the acceleration is also to the left. This will always happen – the acceleration will be the same direction as the net force (this is from Newton’s 2nd law) friction weight Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. Normal force ‘Normal’ means perpendicular Here is the force diagram for the eraser Assuming that the normal force and the weight are the same magnitude, which direction is the net force on the eraser? The net force is to the left (in the direction of the friction force). What does this tell you about the acceleration of the eraser? Yes, the acceleration is also to the left. This will always happen – the acceleration will be the same direction as the net force (this is from Newton’s 2nd law) At this point it should be clear why the eraser slowed down and stopped. The acceleration was to the left – opposite the velocity, so the speed decreased. We will return to this example and do some calculations after we learn more about friction. friction weight Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. Normal force One more idea with this eraser example: How does Newton’s 3rd law apply here? Does each force in our diagram have an ‘equal and opposite’ reaction force? friction weight Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. Normal force One more idea with this eraser example: How does Newton’s 3rd law apply here? Does each force in our diagram have an ‘equal and opposite’ reaction force? Let’s think about the friction force first. What objects are interacting to make the friction force happen? friction weight Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. Normal force One more idea with this eraser example: How does Newton’s 3rd law apply here? Does each force in our diagram have an ‘equal and opposite’ reaction force? Let’s think about the friction force first. What objects are interacting to make the friction force happen? It is the rough surface of the eraser rubbing against the metal chalk rail. How would you describe the ‘reaction’ to this force? Frail on eraser weight Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. Normal force One more idea with this eraser example: How does Newton’s 3rd law apply here? Does each force in our diagram have an ‘equal and opposite’ reaction force? Let’s think about the friction force first. What objects are interacting to make the friction force happen? It is the rough surface of the eraser rubbing against the metal chalk rail. How would you describe the ‘reaction’ to this force? The ‘reaction’ is always the same 2 objects, with their roles reversed. So we can consider the force that the eraser exerts on the rail as the corresponding reaction. This was not in our free-body diagram because our diagram only had forces on the eraser. F rail on eraser F eraser on rail,x weight Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. Normal force One more idea with this eraser example: How does Newton’s 3rd law apply here? Does each force in our diagram have an ‘equal and opposite’ reaction force? What about the weight? What is the reaction to that force? F rail on eraser F eraser on rail,x weight Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. Normal force One more idea with this eraser example: How does Newton’s 3rd law apply here? Does each force in our diagram have an ‘equal and opposite’ reaction force? What about the weight? What is the reaction to that force? What objects are interacting to make the weight of the eraser? F rail on eraser F eraser on rail,x weight Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. Normal force One more idea with this eraser example: How does Newton’s 3rd law apply here? Does each force in our diagram have an ‘equal and opposite’ reaction force? What about the weight? What is the reaction to that force? What objects are interacting to make the weight of the eraser? The weight is the force of gravity exerted on the eraser by the earth. F rail on eraser F eraser on rail,x Fearth on eraser Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. Normal force One more idea with this eraser example: How does Newton’s 3rd law apply here? Does each force in our diagram have an ‘equal and opposite’ reaction force? What about the weight? What is the reaction to that force? What objects are interacting to make the weight of the eraser? The weight is the force of gravity exerted on the eraser by the earth. So how would you describe the reaction force? Is it the normal force? F rail on eraser F eraser on rail,x Fearth on eraser Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. Normal force One more idea with this eraser example: How does Newton’s 3rd law apply here? Does each force in our diagram have an ‘equal and opposite’ reaction force? What about the weight? What is the reaction to that force? What objects are interacting to make the weight of the eraser? The weight is the force of gravity exerted on the eraser by the earth. So how would you describe the reaction force? Is it the normal force? NO (why not??) F rail on eraser F eraser on rail,x Fearth on eraser Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

EARTH (not to scale) Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. Normal force One more idea with this eraser example: How does Newton’s 3rd law apply here? Does each force in our diagram have an ‘equal and opposite’ reaction force? What about the weight? What is the reaction to that force? What objects are interacting to make the weight of the eraser? The weight is the force of gravity exerted on the eraser by the earth. So how would you describe the reaction force? Is it the normal force? NO (why not??) The reaction has to be the same objects with their roles reversed. The weight was the earth pulling downward on the eraser, so the reaction should be the eraser pulling upward on the earth. (same 2 objects, opposite direction) F rail on eraser F eraser on rail,x Fearth on eraser Feraser on earth EARTH (not to scale) Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

EARTH (not to scale) Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. Normal force One more idea with this eraser example: How does Newton’s 3rd law apply here? Does each force in our diagram have an ‘equal and opposite’ reaction force? Ok, last one – what is the reaction that corresponds to the normal force? First identify which 2 objects are interacting. F rail on eraser F eraser on rail,x Fearth on eraser Feraser on earth EARTH (not to scale) Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

EARTH (not to scale) Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. Frail on eraser,y One more idea with this eraser example: How does Newton’s 3rd law apply here? Does each force in our diagram have an ‘equal and opposite’ reaction force? Ok, last one – what is the reaction that corresponds to the normal force? First identify which 2 objects are interacting. This time it is the eraser and the chalk rail, but in the vertical (y) direction. F rail on eraser,x F eraser on rail,x Fearth on eraser Feraser on earth EARTH (not to scale) Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

EARTH (not to scale) Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. Frail on eraser,y One more idea with this eraser example: How does Newton’s 3rd law apply here? Does each force in our diagram have an ‘equal and opposite’ reaction force? Ok, last one – what is the reaction that corresponds to the normal force? First identify which 2 objects are interacting. This time it is the eraser and the chalk rail, but in the vertical (y) direction. The opposite to this force is a downward force on the chalk rail due to the eraser. F rail on eraser,x F eraser on rail,x Fearth on eraser Feraser on rail,y Feraser on earth EARTH (not to scale) Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Example: Pushing a box across the floor. A 60 kg box is at rest on a frictionless horizontal floor. It is pushed to the right by a 120-Newton force. Draw a free-body diagram for the box. Find the resulting acceleration. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Example: Pushing a box across the floor. A 60 kg box is at rest on a frictionless horizontal floor. It is pushed to the right by a 120-Newton force. Draw a free-body diagram for the box. Find the resulting acceleration. y x Normal force 120 N weight Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

We can use Newton’s 2nd law to calculate the acceleration. Example: Pushing a box across the floor. A 60 kg box is at rest on a frictionless horizontal floor. It is pushed to the right by a 120-Newton force. Draw a free-body diagram for the box. Find the resulting acceleration. y x Normal force We can use Newton’s 2nd law to calculate the acceleration. 120 N weight Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

We can use Newton’s 2nd law to calculate the acceleration. Example: Pushing a box across the floor. A 60 kg box is at rest on a frictionless horizontal floor. It is pushed to the right by a 120-Newton force. Draw a free-body diagram for the box. Find the resulting acceleration. y x Normal force We can use Newton’s 2nd law to calculate the acceleration. 120 N We can write down separate equations for the x- and y-directions: weight Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

We can use Newton’s 2nd law to calculate the acceleration. Example: Pushing a box across the floor. A 60 kg box is at rest on a frictionless horizontal floor. It is pushed to the right by a 120-Newton force. Draw a free-body diagram for the box. Find the resulting acceleration. y x Normal force We can use Newton’s 2nd law to calculate the acceleration. 120 N We can write down separate equations for the x- and y-directions: weight Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

We can use Newton’s 2nd law to calculate the acceleration. Example: Pushing a box across the floor. A 60 kg box is at rest on a frictionless horizontal floor. It is pushed to the right by a 120-Newton force. Draw a free-body diagram for the box. Find the resulting acceleration. y x Normal force We can use Newton’s 2nd law to calculate the acceleration. 120 N We can write down separate equations for the x- and y-directions: weight Notice that we could determine that the normal force equals the weight, but in this problem we don’t really care (if there were friction we would need this fact) Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Example: An eraser sliding on the chalk rail. A 0.1kg eraser is given an initial velocity of 4 m/s along the chalk rail. It slows down and comes to rest in a distance of 3 m. Find the magnitude of the friction force that acts on the eraser. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Example: An eraser sliding on the chalk rail. A 0.1kg eraser is given an initial velocity of 4 m/s along the chalk rail. It slows down and comes to rest in a distance of 3 m. Find the magnitude of the friction force that acts on the eraser. Here is the free-body diagram again. Notice that the only horizontal force is friction. Normal force friction weight Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Example: An eraser sliding on the chalk rail. A 0.1kg eraser is given an initial velocity of 4 m/s along the chalk rail. It slows down and comes to rest in a distance of 3 m. Find the magnitude of the friction force that acts on the eraser. Here is the free-body diagram again. Notice that the only horizontal force is friction. We can write down Newton’s 2nd law for the x-direction: Normal force friction weight Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Example: An eraser sliding on the chalk rail. A 0.1kg eraser is given an initial velocity of 4 m/s along the chalk rail. It slows down and comes to rest in a distance of 3 m. Find the magnitude of the friction force that acts on the eraser. Here is the free-body diagram again. Notice that the only horizontal force is friction. We can write down Newton’s 2nd law for the x-direction: Normal force friction We can use kinematics to find the acceleration: weight Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Example: An eraser sliding on the chalk rail. A 0.1kg eraser is given an initial velocity of 4 m/s along the chalk rail. It slows down and comes to rest in a distance of 3 m. Find the magnitude of the friction force that acts on the eraser. Here is the free-body diagram again. Notice that the only horizontal force is friction. We can write down Newton’s 2nd law for the x-direction: Normal force friction We can use kinematics to find the acceleration: weight Put this value in to find the friction force: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB