Test Corrections Use these concepts to explain corrected answers. Make sure you apply the concepts to the specific situation in each problem. Circular Motion Concepts When an object moves in a circle, the net force on the object points toward the center of the circle. Net force for circular motion is called centripetal force. When an object moves in a circle, the velocity of the object points tangent to the circle. Example: A marble moving inside a pie pan is kept in a circle by the normal force F N of the pan walls on the marble, pushing the marble toward the circle center. The net force is perpendicular to the velocity of the object at any point on the circle. The net force Fnet acting on an object moving in a circle can be F g, F N, F T, or F fs.(static friction force, such as on car tires while the car turns). The net force can also be a combination of several forces added together (e.g., F g and F N for a car moving on a hill, like in class notes). The net force vector must point to the center of the circle. Skills: Draw the centripetal force vector at a specific point for an object moving in a circle Draw the velocity vector at a specific point for an object moving in a circle Label the specific force name (F g, F N, F T, F fs ) causing circular motion 1
Newton s Law of Universal Gravitation Fg is the force of gravity, which is the same as weight. Skill: Draw Fg vector on a mass due to another mass. The direction of Fg on one object is toward the center of the 2 nd object. If you know the value of g on a planet (e.g., on Earth it s 10 m/s 2, you can find the weight in Newtons using F g = mg. Example: What is the weight of a 2-kg book? F g = mg = (2kg) (10m/s 2 ) = 20 N Newton s Law of Universal Gravitation gives a detailed descriptions for Fg. Fg is directly proportional to the 2 masses pulling on each other. mm where m is the mass of an object and M is the mass of a planet, Fg for example. Directly proportional means: if you multiply the left side by a number (e.g., planet mass M doubles), the right side (F g, weight) is also multiplied by the same number. Example: If Earth and Planet X are the same size, and the same rock is placed on each planet, Fg of the rock will change. If Planet X is 2x the mass of Earth, the rock s Fg is 2x. The mass of the rock m does not change with location. Fg is inversely proportional to the square of the distance between masses. F g mm 2 d where m is the mass of an object and M is the mass of a planet, and d is the distance between the object center and the mass center. 2
Inversely proportional means: If the right side increases (distance), the left side decreases (Fg), and vice versa. Example: Compare the rock s weight on the surface of the Earth to the rock s weight in orbit around the Earth. Because Fg is inversely proportional to the distance between masses, the weight of the rock decreases when it moves farther away from the Earth. Newton s 1 st Law Concepts Skill: Be able to identify and draw an FBD on the object and label the forces (F g, F N, F T, F fs, F fk ). Make the horizontal forces balance, and the vertical forces balance. Draw larger forces as longer vectors. N1L: Fnet = 0 means a = 0 (no change in velocity) N1L: When an object moves at constant velocity, all the forces on the object balance (Fnet = 0). N1L for circular motion: When the net force on an object moving in a circle suddenly becomes zero (e.g., string breaks) the object s a = 0 and velocity is constant. The object continues moving at constant velocity (straight line/constant speed). The object s velocity is the same as it was at the point the net force was removed. 3
N1L: Object can look like they suddenly move without being pushed. Use Newton s Law of Inertia (N1L) to reason what happens: By N1L, objects want to move the at constant velocity or stay at rest. If an object suddenly moves without an applied force, the object must be inside something that just accelerated (e.g., in a train, a car, a plane, the back of a truck). Example: If you apply a force on the accelerometer to the right, the hanging mass wants to stay in place and appears to move left. Example: If a box sits in the back on a truck and suddenly moves forward without a force, the truck must have accelerated backwards. By N1L, the box wants to stay in its original location and there wasn t enough static friction force from the truck to accelerate the box with the truck. Newton s 2 st Law Concepts Skill: Be able to identify and draw an FBD on the object and label the forces (F g, F N, F T, F fs, F fk ). Draw larger forces as longer vectors. N2L: Fnet 0 means a 0 and velocity changes. The direction of a is the same as the direction of Fnet. N2L: When an object s velocity is not constant, the forces on the object do not balance (Fnet 0). N2L is an equation: Fnet = ma Fnet means total force. m is the mass of the object. a is the acceleration. 4
You can find Fnet 2 ways: o From an FBD, add horizontal forces separately. Add vertical forces separately. Be careful to use correct signs (+/-) for the forces when adding them, based on their direction. o If you are given mass m and acceleration a, plug in to get Fnet Fnet = ma To find acceleration a, you must know Fnet and m (mass in kg). Then, plug into Fnet = ma. You may need to find Fnet from a given FBD. Fnet = ma is not the same as Fg = mg!!! Fnet = ma is a general equation that relates total force (Fnet), mass (m), and the acceleration. Fg = mg is a specific equation used to find weight (Fg) from mass, or mass from weight. On Earth, g = 10 m/s 2. Is an object speeding up or slowing down? Negative acceleration does NOT always mean an object is slowing down. You must compare the direction of velocity AND direction of acceleration. Speeding up: If v and a point in the same direction, speed increases. Slowing down: If v and a point in opposite directions, speed decreases. Newton s 3 rd Law Concepts 2 object interacting N3L: 2 objects exert equal and opposite forces on each other. Example: Earth pulls on the apple with Fg toward the center of the Earth. Apple pulls of the Earth with an equal Fg toward the center of the apple. 5
Identify the 2 interacting objects and name them. Example: You push on create G. The objects are you and G. Action force is F You on G Reaction force is F G on You Be able to draw FBDs for 2 interacting objects. Clearly label the action/reaction forces. If the 2 objects have different masses, they will have different acceleration. N3L: Objects exert equal and opposite forces on each other. N2L: For a given force, the smaller mass will have greater acceleration and greater speed change. Example: Notice the action and reaction forces and their names. 6