Answer Key College Prep and Honors Questions 1. What is the difference between speed and velocity? Speed is a scalar quantity and has magnitude only while velocity is a vector and has both a magnitude and a direction. 2. In words, what is the definition of acceleration? Acceleration is the rate at which velocity changes over time. 3. When a projectile is shot at an angle from level ground, how does the horizontal velocity change during its flight? The horizontal velocity is unchanged (ax is zero). 4. What is the difference between a vector and a scalar? A vector has both magnitude and direction; a scalar is magnitude only. 5. State Newton’s First Law. Objects in motion tend to stay in motion and objects at rest tend to stay at rest unless acted upon by an outside force. 6. How are mass, inertia and weight similar? How are they different? All are measures of the relative heaviness or lightness of an object. Weight is dependent on gravity while mass and inertia are not. 7. If an applied force is perpendicular to its displacement, is any work done? What if the force and displacement are antiparallel? No work is done because the force and displacement must be in the same direction (cos 90 =0). If the force and displacement are anti-parallel, then negative work is done (cos 180 = -1). 8. If you push an object with 20 N of force to the left and the object does not move, how large is the force of static friction? In what direction does it act? 20 N; right 9. What is the rate at which work is done is called? Power. 10. State the Law of Conservation of Energy. In the absence of an external force, mechanical energy is conserved. Total energy is always conserved. 11. Is mechanical energy always conserved? Explain. No, only the absence of an external force (such as friction). 12. A plane flies with a speed of 400 mph at an altitude of 30,000 feet. Name the types of mechanical energy present in this example. Kinetic energy and gravitational potential energy. 13. Can the speed of an object change if no work is done? No, from the Work- Kinetic Energy Theorem, if no work is done than there is no change in kinetic energy. If KEi = KEf than there is no change in speed. 14. Explain conservation of energy as it relates to a polevaulter. As the polevaulter runs down the runway, he has no gravitational potential energy and his kinetic energy is increasing. When he plants the pole, the kinetic energy is converted into gravitational potential and elastic potential (from the pole). Above the bar, he has only gravitational potential energy. And, as he falls back to the mat, he loses gravitational potential energy and gains kinetic energy. 15. Is momentum conserved in two dimensions? Is momentum always conserved? Yes; only in the absence of an external force. 16. What is the name of a collision where two objects stick together? Perfectly inelastic. 17. Why do cars have air bags? According to the Impulse-Momentum Theorem, if you increase the stopping time, you decrease the force. Air bags bring your head to rest over a longer time period and reduce the force of impact. 18. A child swings a yo-yo in a circle with constant speed. Is it accelerating? Explain. Yes; the velocity is always changing direction. 19. Is there a force necessary to maintain circular motion? If so, in the case of planetary motion, what is this force? Yes; gravity. 20. As a passenger in car, why are you pushed to the outside as you round a turn? Because of centrifugal force, which is really the absence of a force rather than a true force. Also, by Newton I, your body wants to continue in a straight line. 21. Describe in words Newton’s Law of Universal Gravitation. Any two objects, by virtue of having mass, will attract each other. 22. Name the four fundamental forces. Gravity, weak, strong, electromagnetic. 23. Does the speed of the Earth depend on its mass? No, only on the mass of the Sun and the orbital radius. 24. How does a Black Hole form? When the fuel runs out in a star 3-4 times as massive as our own Sun, the gravitation process takes over, contraction begins and never stops. All the mass is concentrated into a point of about 9 mm. The point is infinitely dense and has so much gravity even light cannot escape. 25. What is an exoplanet? How are they discovered? An exoplanet is a planet outside of our solar system. They are discovered by looking for stars that wobble from its center of gravity—evidence that an object is rotating around it. 26. How does Einstein’s theory of gravity explain planetary motion? Mass curves spacetime and the Sun, being quite massive, makes an indention in space that the planets follow. 27. Both Work and Torque are the product of force and distance. How are they different? The parallel component of work causes work; the perpendicular component of force causes torque. 28. Why is the doorknob so far from the hinge of the door? Because of torque; by increasing the distance from the hinge, you reduce the force necessary to open the door. 29. State the Law of Rotation. An object that is rotating will keep rotating unless acted upon by an outside torque. 30. What causes a figure skater to spin faster when they pull their arms in? Conservation of angular momentum—as they pull their arms, more mass is distributed near their CG, causing their rotational inertia to decrease. In response, their angular speed will increase. 31. Why should you extend your arms when walking across a fence? By extending your arms, you distribute more mass further from your CG and increase your rotational inertia and therefore it is harder for you to rotate (fall). Problems Linear Motion 1. A ball is thrown up in the air with an initial velocity of 13 m/s. (a) What is the maximum height the ball attains? 8.6 m (b) How long is the ball in the air? 2.65 s 2. A car accelerates from rest to a speed of 70 mph in 12 s. (a) What is the acceleration of the car in m/s2? 2.59 m/s2 (b) How far did the car travel in this time? 187 m 3. Derive the time independent linear motion equation. See solutions. Vectors 4. A plane flies 25 km at angle of 35° above the horizontal then changes course and flies 212 km at an angle of 12° above the horizontal. What is the total displacement of the plane? 235 km; 14.4° above the horizontal 5. A soccer ball is kicked with a velocity of 20 m/s at angle of 20° above the horizontal. (a) What is the maximum height the ball attains? 2.39 m (b) How far does it travel? 26.1 m 6. A daredevil is shot out of a cannon at an angle of 45° above the horizontal with a speed of 50 m/s. A net is to be placed 10 m above the ground to catch him. How far away from the cannon should the net be placed? 245 m 7. A baseball is hit and just clears an 8 m wall, 125 m from home plate. If the ball was hit at a 40 degree angle, find its initial speed. v = 36.7 m/s Forces 8. A box is pushed across a frictionless floor with an applied force of 80 N at angle of 30° above the horizontal. If the box has a mass of 18 kg, what is the acceleration of the box? 3.85 m/s2 9. A 70 kg greased pig is in the back of a pickup truck where the coefficient of static friction between the truck and pig is 0.205. What acceleration can the truck have before the pig slides and falls out? 2.00 m/s2 10. An object slides down a 30° incline with an acceleration of 2.40 m/s2. What is the coefficient of kinetic friction on the incline? 0.295 11. Show the relationship between the critical angle for an object overcoming friction to slide down an incline is given by tan θc = μs. See solutions. Work and Energy 12. A lawnmower is pushed with a force of 25 N at angle of 40° above the horizontal. (a) How much work is required to push the lawnmower 1 km? 19,150 J (b) If the job is completed in 15 minutes, how much power is required? 21.2 W 13. A toy gun has a spring constant of 65 N/m. If the spring is compressed 2.54 cm, (a) how much elastic potential does a dart in the gun have? .02 J (b) If the dart has a mass of 10 g, what velocity does the gun have when fired horizontally? 2 m/s (Assume mechanical energy is conserved) 14. How much mechanical energy does an air maiden swallow (African, not European) have if it has a mass of 1 kg and flies with a speed of 10 m/s at a height 30 m above the ground? 344 J 15. A hobbit (m=30 kg) slides down a 20° hill that is 15 m long where the coefficient of kinetic friction is 0.25. (a) How much work does gravity do on the hobbit? 1508 J (b) How much work does friction do on the hobbit? -1036 J (c) What is the change in kinetic energy? 472 J (d) What is the hobbit’s velocity at the bottom of the hill? 5.6 m/s Momentum and Impulse 16. A cannon (m=1000 kg) fires an 8 kg cannonball with a velocity of 140 mph. What is the recoil velocity of the cannon? 1.1 mph 17. A 200 kg golf cart traveling at 40 m/s collides with a parked school bus with a mass of 6000 kg. (a) If the two objects stick together after the collision, what is their velocity? 1.29 m/s (b) If the golf cart is at rest after the collision, calculate the speed of the bus. 1.33 m/s 18. A cue ball with mass 0.25 kg strikes a stationary red ball of equal mass with a speed of 4 m/s. After the collision, the cue ball goes off at an angle 30° above its original path will the red ball travels at angle of 60° below the original path. Find the velocity of each ball after the collision. 3.46 m/s for cue ball; 2 m/s for red. 19. A 15 g marble moving at 20 cm/s collides with a second marble that is 10 g and moving in the same direction at 5 cm/s. Treat the collision as elastic and find the velocity of each ball after the collision. v1’= 8 cm; v2’ = 23 cm/s Circular Motion 20. Find the angular speed of the Earth around the sun in rad/s. 1.99 x10-7 rad/s 21. A 0.50 kg yo-yo is spun in a horizontal circle of diameter 1.8 m and with a speed of 10 m/s. (a) What is the period for the yo-yo? 0.57 s (b) What is the centripetal force? 55.6 N 22. What maximum speed can a car negotiate a flat turn of radius 20 m without slipping if the coefficient of static friction is 0.25? v = 7 m/s 23. A curve is banked so that a car will not have to rely on friction to round a turn without skidding. Show that the angle of such a banked turn is given by tan θ = v2/gr. See solutions. Universal Gravitation 24. Find the force of attraction between Mr. Zlatin (m= 85 kg) and Natalie Portman (m=52 kg) if the two are separated by a distance of 4000 km. 1.84 x10-20 N 25. Joe Torre steers the Yankees charter plane to within 12 km of a Black Hole of mass 8.3 x1030 kg. Find the Event Horizon and determine the fate of the 2000 World Champions. 12,302 m; Yankees are all dead! 26. Find the orbital speed and period of a planet orbiting the Black Hole in Problem 19 if the planet has a mass of 2.004 x 1025 kg and has an average radius of 1.23 x 109 m. 670,900 m/s; 11,519 s (about 3.2 hrs) 27. A golf ball is hit on Mars at a 45 degree angle with a speed of 50 m/s. How far does it go? 662 m Rotational Mechanics 28. Our fat 4th grade friend (180 kg) sits on a seesaw 2 m from the fulcrum. Where should his voluptuous girlfriend (35 kg) sit to balance? 10.3 m 29. A plane lands with a speed of 55 m/s and each of the plane’s wheels has a radius of 1.10 m, with a moment of inertia of 100 kg x m2. Friction causes the wheels to spin upon landing when a 16,000 N force is supported by each wheel. If the wheels attain their angular speed in 0.30 s, find the coefficient of friction between the wheels and the runway. 0.95 30. Use conservation of mechanical energy to show the speed of a solid sphere at the bottom of a ramp h is given by v = √[(10/7)gh]. See solutions.
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