General Physics I: Day 12 Review for Exam 1 "A gem cannot be polished without friction, nor a [person] perfected without trials." ~ Lucius Annaeus Seneca

Sample Problem - Banked Curve A car drives around a curve with radius 410 m at a speed of 32 m/s. The road is banked at 5.0°. The mass of the car is 1400 kg. What is the frictional force on the car? At what speed could you drive around this curve so that the force of friction is zero? This question gets messy! Start with FBD. Discuss how friction could be up, down or zero. Choose up (the “too slow” version). Do NSL for x & y, COMPACTLY. Both have F_f and F_N in them. 2 eq. 2 unknowns Combining them is ugly, so plug values in first! Should come up with F_f = -2288 N

Concepts of Kinematics Position (vector!) Displacement (vector!) Velocity (vector!) Acceleration (vector!) Understand the relationships among these How does the direction of each relate to what is happening to the object? Be competent with vectors and vector mathematics

Motion With Constant Acceleration We can handle constant acceleration (or averaged) in one dimension. Four equations apply. For two dimensions, each component must be treated separately using the same tools. For projectile motion: Must split into horizontal & vertical parts. 𝑎 𝑦 =−9.8 𝑚 𝑠 2 and 𝑎 𝑥 =∅ ( 𝑣 𝑥 is constant!) Do not mix horizontal & vertical quantities! You will usually need to tackle both

Newton’s Laws of Motion Conceptually describe Newton’s three laws in your own words. Can you offer examples? Newton’s first law is mostly conceptual. Inertia should inform how you think about motion. Newton’s second law is the workhorse. Must be split into components! Newton’s third law is mostly conceptual. Only applies if concerned with more than one object!

Catalog of Forces Weight ( 𝐹 𝑔 or 𝑤 ) is the force of gravity (different than mass). 𝐹 𝑔 =𝑚𝑔 on Earth. Always down! Springs ( 𝐹 sp. ). Springs will push out when compressed or pull back when stretched. Lots of other things behave the same way (trampolines!). Tension ( 𝐹 T 𝑜𝑟 𝑇 ). Ropes, etc. Pull only. Always equal at both ends if ropes & pulleys are ideal. Normal ( 𝐹 N ). Force caused by contact with a surface. Always perpendicular to the surface.

Catalog of Forces Friction ( 𝐹 f,k and 𝐹 f,s , or 𝑓 k and 𝑓 s ). Sometimes present objects touch. Parallel to the surface. Static: Surfaces do not slide against each other. Kinetic: They do slide. Drag ( 𝐹 D ) is similar to friction, caused by air, water or other fluids. Only used if explicitly discussed Thrust ( 𝐹 thrust ). Contact force created by expelling gas out the back of a rocket or other engine. Rolling friction ( 𝐹 f,r ). Acts to slow down rolling.

Forces in Circular Motion For objects moving in a circle we know they must have an acceleration pointing toward the center of the circle: As with all force problems, use Newton’s 2nd Law: Can you describe why can stay in the bucket? Why your coffee falls over? Why you feel pressed into the door of the turning car?

Sample True/False F F F T T An object that moves in a circle at constant speed is accelerating forward. The net force on an object is always in the same direction as its velocity. In uniform circular motion the acceleration is constant, so the equations for constant acceleration can be applied. Immediately after opening her parachute the net force on a skydiver will be upward. As a car goes around a banked turn, if the force of static friction points inward then the car is going faster than the “safe” speed for that curve. F F F T T

Sample Multiple Choice 6. Two equal masses are connected by a light cord passing over a pulley of negligible mass. At the moment the system is in motion, with the right-hand block moving downward at 1.2 m/s. Which of the following is the correct free-body diagram for the two masses?

Sample Multiple Choice 7. You throw a ball up very high in the presence of air resistance. Which takes longer, the trip to the top of its motion, or the return trip back to your hand? The trip upwards takes longer. The trip back down takes longer. They take the same amount of time. We cannot tell without knowing the mass and cross-sectional area of the ball.

Sample Short Answer 8. A young boy takes a heavy ball that is attached to a rope and swings it around himself by holding his arms out forward and turning his body in place (much like you do when you swing a 3 year old around you by their arms). The ball moves in a horizontal circle as it goes around you. a) To start, draw a free body diagram for the ball at some instant (use a side view). Label each force with the type of force, the object exerting the force and the object on which the force is exerted.

Sample Short Answer (8 continued) b) Can the rope connecting his hand to the ball be horizontal? Explain. c) If he were to swing the ball faster and faster the angle that the string makes with the horizontal will get smaller and smaller. Explain why this happens.

Sample Quantitative 9. A true story: A fungus projects its spores… In the process of launching, the spore reaches a speed of 25.0 m/s (around 56 mph) in just 14.0 millionths of a second (that is, 14.0 × 10-6 sec). Assuming constant acceleration during its launch, what is the magnitude of the acceleration?

Sample Quantitative (9 continued) For the real spore, air resistance is a huge effect, so the spore doesn’t go all that far. How far would the spore go if it were launched in an airless environment (still on Earth) at an angle of 50.0º above level ground?

Sample Quantitative 10. An 8.6 kg box is resting on a conveyor belt when the belt lurches into motion. For 1.5 seconds the belt accelerates to the right at a rate of 1.3 m/s2. The coefficient of static friction between the box and belt is 0.55 and the coefficient of kinetic friction is 0.22. a) Will the box slip at first, or not?

Sample Quantitative (10 continued) What is the final speed of the box? If you were to reach out and push backwards on the box, keeping it from moving (with the belt sliding along underneath it), how hard would you have to push?

Sample Quantitative 11. A boy is pushing a moving box down a ramp angled 33.5º above the horizontal. The box has a mass of 35 kg and doesn’t slide very easily against the ramp, having a coefficient of static friction of 0.71 and a coefficient of kinetic friction of 0.52. At the moment, the box is sliding down at 0.65 m/s and the boy is pushing down the ramp (parallel to the ramp) with 17 N.

Sample Quantitative (11 continued) What is the acceleration of the box? Assuming that the forces on the box have not changed, describe the box’s motion 2.0 seconds later.

Sample Quantitative 12. A Ping-Pong ball has a diameter of 4.0 cm and a mass of 2.47 g. Assume the air resistance coefficient for a Ping-Pong ball is given by D = 0.00040 kg/m. What is the terminal velocity of the ball?

Sample Quantitative (12 continued) If the ball were launched upward at twice its terminal speed, what would its acceleration be at that moment? If the ball were launched downward at twice its terminal speed, what would its acceleration be at that moment?

Topics Missing? Rolling friction Others?

Coming up… Tuesday (9/30) → Exam 1 (Ch. 1-5) Warm-Up due Wednesday night Extra credit due Wednesday by 9:50 AM. Exam Expectations: Use the bathroom before we start. You only need a pencil and calculator. Bring your Student ID. Never look at another student’s paper.