Concept explainers
Suppose the object in Problem 70 had an initial velocity in the horizontal direction equal to the terminal speed, vx0 = mg/b. Show that the horizontal distance it can go is limited to xmax = mvx0/b, and find an expression for its trajectory (y as a function of x).
70. Moving through a liquid, an object of mass m experiences a resistive drag force proportional to its velocity, Fdrag = −bv, where b is a constant, (a) Find an expression for the object’s speed as a function of time, when it starts from rest and falls vertically through the liquid, (b) Show that it reaches a terminal velocity mg/b.
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
Essential University Physics: Volume 1 (3rd Edition)
Additional Science Textbook Solutions
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
Chemistry: An Introduction to General, Organic, and Biological Chemistry (13th Edition)
Cosmic Perspective Fundamentals
Microbiology with Diseases by Body System (5th Edition)
Human Physiology: An Integrated Approach (8th Edition)
Organic Chemistry (8th Edition)
- A 10.0 kg ball is released from rest in an ocean. As it falls, the water applies a resistive force R = −bv, where v is its velocity. At a time 6.14 s after its release, the ball is moving at half of its terminal speed. (Ignore any buoyant force.) (a) What is the ball's terminal speed (in m/s)? m/s (b) At what time after release (in s) is its speed three-fourths of its terminal speed? s (c) How far (in m) has the ball moved in the first 6.14 s of its motion?arrow_forwardA 60 kg skydiver can be modeled as a rectangular "box" with dimensions 22 cm × 40 cm × 1.8 m. What is his terminal speed if he falls feet first? Suppose that the density of air is 1.2 kg/m3.arrow_forwardThe drag force, Fa, imposed by the surrounding air on a vehicle moving with velocity Vis given by Fa Ca ApV²/2 where Ca is a constant called the drag coefficient, A is the projected frontal area of the vehicle, and p is the air density. An automobile is moving at V = 40 miles per hour with C = 0.28, A = 24 ft², and p = 0.075 lb/ft³. Determine the force, in lbf, and the power, in hp, required to overcome aerodynamic drag.arrow_forward
- A racquetball has a radius of 0.0295 m. The drag coefficient of the ball is 0.35, and the density of the air is 1.29 kg/m3. What would be the terminal speed for the racquetball if it were dropped from a very high cliff, assuming it has a mass of 0.0394 kg?arrow_forwardA paratrooper and his 8-m-diameter parachute weigh 950 N. Taking the average air density to be 1.2 kg/m3, determine the terminal velocity of the paratrooper.arrow_forwardA skydiver of mass m = 60 kg jumps out of an airplane. At some moment before the 5. parachute opens, while falling in a spread-eagle formation, her instantaneous velocity is = (0,-20,0) m/s. (The coordinate system is one for which skyward is the +y direction.) What is the acceleration (a vector) of the skydiver at that moment? Include air drag in your calculation. Put your numerical vector answer in component form. Constants: In this formation her drag coefficient is C = 1.0. Her area that "catches" the air is A 1.5 m2. The density of air is p= 1.22 kg/m³.]arrow_forward
- Simulate projectile motion with air resistance in PhysLab. A shuttlecock is launched from the ground with an initial speed of 36.8015 m/s at an angle of 7.0734 degrees with respect to the horizontal. The shuttlecock experiences air resistance with a drag coefficient of 0.1937 in an environment where the air density is 0.2178 kg/m3. If the shuttlecock has a radius of 3.4 cm and a mass of 5.2 grams, what is the maximum height reached by the shuttlecock? Assume that the experiment is done near the surface of the earth.arrow_forwardA falling body on Earth will generally not fall at constant acceleration in reality, due to air resistance (or drag). The equation for the drag force Fd isFd = 0.5 (Cd A) ρ v2where Cd is the unitless drag coefficient of a body (which depends on the body's density and other properties), A is its cross-sectional area as it falls, ρ is the density of the air, and v is the body's velocity with respect to the atmosphere. Now, you may need to look up a couple of things to get a reasonable answer here, but anyway: The drag force on a person falling belly-first (as shown) at a speed of 30.0 m/s through the atmosphere is approximately a 500 N b 50 N c 5 N d 5000 Narrow_forwardEstimate the speed at which the drag on a 150-g steel ball becomes equal to about 1% of its weight. (The density of steel is about 7900 kg/m3, and C for a sphere is about equal to 0.5.) Take the density of air to be 1.2 kg/m3. The speed is m/s. 34. A space probe near the earth has values of E, L, and m such that L/m = 7.5 × 1010 m2/s and 2E/m = 0. Find the eccentricity of this orbit and the radius of the closest point of the orbit to the earth, and classify the orbit as elliptical, parabolic, or hyperbolic. The eccentricity of the orbit is______ and the orbit is ______Choose one (.Elliptical, Parabolic, Hyperbolic) The radius of the closest point of the orbit to the earth is _______ km.arrow_forward
- Boxes are transported by a conveyor belt with a velocity vo to a fixed incline at A, where they slide and eventually fall off at B. Knowing that μk = 0.40, determine the velocity of the conveyor belt if the boxes leave the incline at B with a velocity of 11 ft/s. 20 ft 15° The velocity of the conveyor belt is 4.08 ft/s 15°.arrow_forwardFrozen rain with spherical shape falls from 3.00 km, what is its velocity if the diameter is 0.3 mm? with air drag (density of air=1.225 x kg/ m3arrow_forwardA tennis ball is thrown at 25 m/s on a day when the wind speed is 0 m/s. What is the drag force acting on the tennis ball if the coefficient of drag is 0.4 and the reference area is 0.005 m2? The density of air is 1.2 kg/m3.arrow_forward
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning