A fast pitch softball player does a “windmill” pitch, illustrated in Figure P6.18. moving her hand through a circular arc to pitch a ball at 70 mph. The 0.19 kg ball is 50 cm from the pivot point at her shoulder. At the lowest point of the circle, the ball has reached its maximum speed.
Figure P6.18
a. At the bottom of the circle, just before the ball leaves her hand, what is its centripetal acceleration?
b. What are the magnitude and direction of the force her hand exerts on the ball at this point?
Want to see the full answer?
Check out a sample textbook solutionChapter 6 Solutions
College Physics: A Strategic Approach, Books a la Carte Edition (4th Edition)
Additional Science Textbook Solutions
University Physics with Modern Physics (14th Edition)
Modern Physics
Applied Physics (11th Edition)
Conceptual Physical Science (6th Edition)
College Physics
Introduction to Electrodynamics
- A 5.00 kg satellite is launched from the north pole into a circular orbit 800 km above the surface of the earth. How much energy is required to achieve this orbit? (The following set of questions will guide you to the answer.) Me = 5.98x1024 kg; Re = 6.37x106 m. G = 6.67x10-11 N m2/ kg2. Note: The problem specifies that the satellite is being launched from the north pole so that we can ignore the initial circular motion and initial kinetic energy as it rotates once every day. In reality, space agencies choose to launch rockets from southern latitudes to take advantage of the initial velocity they have due to this motion. a. calculate the change in gravitational potential energy. (Give your answer in MJ.) b. What is the gravitational force on the satellite? (Give your answer in N.) c. What is the velocity of the satellite? (Give your answer in m/s.) Note: The weight force is equal to m v2/R. d. What is the kinetic energy in this orbit? (Give your answer in MJ.) e. how much total energy…arrow_forwardA comet orbits the sun (mass m_S) in an elliptical orbit of semi-major axis a and eccentricity e What is the kinetic energy of the comet at perihelion and aphelion in terms of its speeds at these points and its mass mm? (Express your answers in terms of the variables v_a, v_p, and m) What is the potential energy of the comet at perihelion and aphelion in terms of the sun–comet distances at these points, its mass m, and the mass of the sun m_S? (Express your answers in terms of the variables r_a, r_p, m, m_S and gravitational constant G) Derive expressions for the magnitudes of angular momenta with respect to the sun at perihelion and aphelion in terms of comets speeds and the sun–comet distances at these points. (Express your answers in terms of the variables v_a, v_p, r_a, r_p, and m separated by a comma)arrow_forwardConsider an object that is in an elliptical orbit with semimajor axis a = 7.9×106 m about a planet of mass M = 1.0×1023 kg. (a) What is the speed of the object when it is closest to the planet at r = a/4? (b) What is the speed of the object when it is furthest from the planet?arrow_forward
- A roller coaster at the Six Flags Great America amusement park in Gurnee, Illinois, incorporates some clever design technology and some basic physics. Each vertical loop, instead of being circular, is shaped like a teardrop (Fig. P5.22). The cars ride on the inside of the loop at the top, and the speeds are fast enough to ensure the cars remain on the track. The biggest loop is 40.0 in high. Suppose the speed at the top of the loop is 13.0 m/s and the corresponding centripetal acceleration of the riders is 2g. (a) What is the radius of the arc of the teardrop at the top? (b) If the total mass of a car plus the riders is M, what force does the rail exert on the car at the top? (c) Suppose the roller coaster had a circular loop of radius 20.0 m. If the care have the same speed, 13.0 m/s at the top, what is the centripetal acceleration of the riders at the top? (d) Comment on the normal force at the top in the situation described in part (c) and on the advantages of having teardrop-shaped loops.arrow_forwardA pendulum consists of a small object called a bob hanging from a light cord of fixed length, with the top end of the cord fixed, as represented in Figure OQ6.4. The bob moves without friction, swinging equally high on both sides. It moves from its turning point A through point B and reaches its maximum speed at point C. (a) Of these points, is there a point where the bob has nonzero radial acceleration and zero tangential acceleration? If so, which point? What is the direction of its total acceleration at (his point? (b) Of these points, is there a point where the bob has nonzero tangential acceleration and zero radial acceleration? If so, which point? What is the direction of its total acceleration at this point? (c) Is there a point where the bob has no acceleration? If so, which point? (d) Is there a point where the bob has both nonzero tangential and radial acceleration? If so, which point? What is the direction of its total acceleration at this point? Figure OQ6.4arrow_forwardModel the Moons orbit around the Earth as an ellipse with the Earth at one focus. The Moons farthest distance (apogee) from the center of the Earth is rA = 4.05 108 m, and its closest distance (perigee) is rP = 3.63 108 m. a. Calculate the semimajor axis of the Moons orbit. b. How far is the Earth from the center of the Moons elliptical orbit? c. Use a scale such as 1 cm 108 m to sketch the EarthMoon system at apogee and at perigee and the Moons orbit. (The semiminor axis of the Moons orbit is roughly b = 3.84 108 m.)arrow_forward
- Planetary orbits are often approximated as uniform circular motion. Figure P7.9 is a scaled representation of a planets orbit with a semimajor axis of 1.524 AU. a. Use Figure P7.9 to find the ratio of the Suns maximum gravitational field to its minimum gravitational field on the planets orbit. b. What is the ratio of the planets maximum speed to its minimum speed? c. Comment on the validity of approximating this orbit as uniform circular motion.arrow_forwardA roller coaster has a circular loop with a diameter (height) of 39 meters. When the coaster is upside down at the top of the loop, what is the minimum speed it must be traveling so that the passengers do not fall out?arrow_forward6. A popular trick of many physics teachers is to swing a pail of water around in a vertical circle fast enough so that the water doesn’t spill out when the pail is upside down. If Mr. Hopkinson’s arm is 0.60 m long, what is the minimum speed with which he can swing the pail so that the water doesn’t spill out at the top of the path? * Use g=9.8 a. 2.4 m/s b. 5.7 m/s c. 7.3 m/s d. 1.82 m/s e. 0.54 m/s 2. Hamlet, a hamster, runs on his exercise wheel, which turns around once every 0.5s. What is the frequency of the wheel? * Use g=9.8 a. 3 rev/s b. 3.5 rev/s c. 4 rev/s d. 4.5 rev/s e. 2 rev/sarrow_forward
- A satelite is in geostationary orbit. How much energy is required to move it to a circularorbit where it orbits the Earth once in 8 days? You may express your answer in terms ofthe total energy of the initial geostationary orbit.arrow_forward1.The planet Mercury has a mass of 3.30×1023 kilograms (kg) and a radius of 2440 kilometers (km). The universal gravitational constant is G = 6.67 × 10−11 Nm2/kg2. (a) If a is ball is launched upwards from the surface of Mercury with an initial speed of 2.15 kilometers per second (km/s), what height maximum height above the surface will it reach before falling back down? Give your answer in units of kilometers (km). Assume that the total mechanical energy of the ball is conserved. (b) What is the escape speed of Mercury? Give your answer in units km/s.arrow_forward
- Physics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
- College PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning