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Introductory Physics Hunter College Newton’s Laws and Forces in 1 Dimension Introduction Newton’s 3 Laws of Motion marks the foundation for nearly all of Classical Mechanics

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Introductory Physics Hunter College Newton’s Laws and Forces in 1 Dimension Introduction Newton’s 3 Laws of Motion marks the foundation for nearly all of Classical Mechanics. They describe the nature of how objects move, and are affected by external forces. To Review: 1. Newton’s 1st Law, also known as the law of Inertia, states that an object (in a constant frame of reference) at rest will stay at rest, whereas an object moving at a constant velocity (in a constant frame of reference) will keep moving at that velocity, unless acted upon by an external force. a. This is the reason that objects in deep space, relatively unaffected by the gravity of stars, can float off in one direction forever. 2. Newton’s 2nd Law, arguably the most famous, states that when multiple forces act on an object, the net force, equal to the vector sum total, is equal to the object’s mass times its net acceleration: ∑ ?? = ???? = ??????? ∗ ???? ? a. NOTE: Forces are vectors, and as such they add like vectors. In the case of 1-dimensional motion, this is easy to compute, but becomes non-trivial in 2 and 3 dimensions. b. Example: Gravity. The Earth constantly exerts a force on all objects around it, equal to the objects mass * the acceleration due to gravity, g: ?? = ??????? ∗ ? On the Earth’s surface, this value g is approximately equal to 9.8 m/s^2. 3. Newton’s 3rd Law, or the principle of action and reaction, states that any force between two objects exists in equal magnitude and opposite in direction. That is to say, if an object A exerts a force ?? on object B, then object B will exert a force ?? on object A. Newton’s 3rd Law states that these two forces are equal: ?? = −?? a. Example: Normal Forces. Normal Forces are the reason that objects that collide with one another, or are in contact, don’t go through one another. As an example, we stand on the ground because the force of gravity pulls us down. However, because we’re not just constantly sinking into the ground, there must exist a force exerted by the ground back at us, which leads to 0 net acceleration: ?? − ?? = 0 2 This normal force is a consequence of Newton’s 3rd Law. It is called normal, because the force is always perpendicular, or ‘normal’, to the point of contact. As a special case of normal forces, let’s look at friction. Friction arises when two objects move against one another, due to molecular interactions at the surface of two objects, and can differ depending on the types of objects involved. However, the friction force is always opposite the direction of the applied force/direction of motion. There are two types of friction: 1. Static Friction: Static Friction usually comes from the interlocking of edges or irregularities of two surfaces and can increase to prevent any relative motion between two objects, up to a point. The static friction force will increase to counteract the applied force, until it eventually fails, and the object begins to move. This force is proportional to the contact force between the two objects: ??????? ≤ ?? ∗ ?? where ?? is the coefficient of static friction. 2. Kinetic Friction: Once two objects are in motion against one another, friction still exists between them (e.g. rubbing your hands together produces heat from friction), although this force is constant and usually less than the force of static friction: ???????? = ?? ?? where ?? is the coefficient of kinetic friction. Pre-Lab Questions (show your work): 1. Imagine you are in a car without a seat belt, travelling at a constant speed. Suddenly, you traffic light turns red, and you are forced to brake, and you find yourself lurching forward. Why is that so? 2. A force F acts on a mass M, for some time interval T, giving it an initial speed v. If the same force acted on another mass 3M, what would be the initial speed of the new mass (in terms of v)? 3 Experiment: 1. Open the Simulation using this link. You should come across this window: This window contains a Force vs. time graph and a choice of objects to push. When the ‘Go’ button is pressed, the graph will begin recording Force v. time data. During this time, you can use the slider to the left, or click and drag the object on top to apply a force. The HELP Button on the bottom right gives helpful tips on working the simulation. 4 Imagine a 200 kg File Cabinet at rest on the ground. To push it forward, we apply a 600N force for 5 seconds Assuming there were no friction, how far would the cabinet have gone in that time? Test this out in the Simulation. Select the File Cabinet Object, and press GO on the left hand side. Apply a 600N force, and see how far the cart moves. Testing Static and Kinetic Friction 1. Imagine a 200 kg File Cabinet at rest on the ground. To push it forward, we apply a 600N force for 5 seconds Assuming there were no friction, how far would the cabinet have gone in that time? a. Test this out in the Simulation. Select the File Cabinet Object, and press GO on the left hand side. Apply a 600N force, and see how far the cart moves. 2. Press the Clear button. Now, Press the Go button to begin collecting data. Slowly increased the applied force via dragging the cabinet, or by using the slider next to the graph, and stop just after the object begins to move. (Include screenshots of the completed graph) a. What happened to the friction force? Why did this happen? b. Based off this graph, calculate the coefficient of static friction. 3. Clear the previous experiment. Now press go, and push the cabinet again until it begins moving. As it moves, play with the force (increase or decrease). How does the friction force change? (include screenshots of the completed graph) a. From this graph, calculate the coefficient of kinetic friction. 4. This time, switch to another object from the list. Repeat steps 2 and 3 with the new object, and calculate the coefficients of static and kinetic friction. 5 a. Are the coefficients the same compared to the cabinet? If they are not, why might that be? 5. This is an example that can be done at home. Find a small plastic object (such as a food container) and slide it on a kitchen table by giving it a gentle tap. Now spray water on the table, simulating a light shower of rain. What happens now when you give the object the same-sized tap? Now add a few drops of (vegetable or olive) oil on the surface of the water and give the same tap. What happens now? a. This latter situation is particularly important for drivers to note, especially after a light rain shower. Why? The Inclined Ramp 1. Let’s explore how Newton's laws and friction apply to inclined surfaces. Open the Inclined Ramp simulation, which can be found here. 2. Upon opening the simulation, set the ramp angle to 0°, using the slider on the right. Describe the forces on the file cabinet while it is on the ramp. 6 3. Reset the scenario using the RESET on the upper right-hand side. Now press go, and slowly lift the ramp. As you lift the ramp what do you notice happening to the forces on the file cabinet? Describe each change. Is there anything that does not change? a. At what angle does the cart begin to move? 4. This time replace the cabinet with the 300kg crate, and repeat step 3. Are there any notable differences? Post-Lab Questions (Show your work) 1. A 1200kg car is driving along a straight road at a speed of 50 m/s, when it brakes sharply. The resulting friction brings the car to rest. What is the frictional force if the coefficient of friction is 0.6, and how far does the car travel before it comes to rest? 2. A 12kg slab is being dragged across a dirt path with an applied force of 300N, and has a net acceleration of 5m/s^2. What is the coefficient of static friction between the slab and the ground? 3. Imagine a 60 kg skydiver free-falling to earth, when they pull their parachute. After pulling the parachute, they descend 46 meters in 4 seconds. Draw a free body diagram labelling all the forces on the skydiver. The relative magnitudes of all forces should be drawn to scale. What is the force of air resistance on the diver? 4. A toddler exerts a horizontal force of 20 N to pull a mass of 50 kg on a horizontal surface whose coefficient of static friction is 0.1. Find the static friction force and explain how you obtain your answer. 5. A 10 kg mass is placed on an incline as shown. The coefficient of static friction is 0.5. Will this mass slide? Find the frictional force and explain how you obtain your answer. F N =Mg cos20o Mg sin20o 20o Mg