Concept explainers
(a)
The terminal speed of the sphere.
(a)
Answer to Problem 35PQ
The terminal speed of the sphere is
Explanation of Solution
Write the given expression for resistive force on the sphere.
Here,
The negative sign indicates that the direction of the drag force is opposite to the velocity’s direction.
Write the velocity of the sphere.
Here,
If the time period
Rearrange the equation (II) for
Here,
If the object moves in its speed reaches one fourth of its terminal speed.
Substitute the equation (III) in equation (II).
Conclusion:
Substitute
Solve the above equation for
Substitute
Therefore, the terminal speed of the sphere is
(b)
The distance traveled by the sphere.
(b)
Answer to Problem 35PQ
The distance traveled by the sphere is
Explanation of Solution
Write the derivative form of the equation of velocity.
Here,
Compare the equation (II) and (V).
Rearrange the above equation for
Conclusion:
Substitute
Therefore, the distance traveled by the sphere is
Want to see more full solutions like this?
Chapter 6 Solutions
Physics for Scientists and Engineers: Foundations and Connections
- (a) When rebuilding her car's engine, a physics major must exert 300 N of force to insert a dry steel piston into a steel cylinder. What is the magnitude of the normal force between the piston and cylinder? (b) What is the magnitude of the force would she have to exert if the steel parts were oiled?arrow_forward(a) Estimate the terminal speed of a wooden sphere (density 0.830 g/cm3) falling through air, taking its radius as 8.00 cm and its drag coefficient as 0.500. (b) From what height would a freely falling object reach this speed in the absence of air resistance?arrow_forward(a) A very powerful vacuum cleaner has a hose 2.86 cm in diameter. With the end of the hose placed perpendicularly on the flat face of a brick, what is the weight of the heaviest brick that the cleaner can lift? (b) What If? An octopus uses one sucker of diameter 2.86 cm on each of the two shells of a clam in an attempt to pull the shells apart. Find the greatest force the octopus can exert on a clamshell in salt water 32.3 m deep.arrow_forward
- A 20.0-kg child sits on a four-legged stool. The radius of each of the stools feet is 0.022 m. a. Ignoring the mass of the stool, what is the force that is exerted on the floor? b. What is the pressure applied to the floor by the stool?arrow_forwardFast pls in 10 lin i will give u like for sure 17. Assume a water strider has a roughly circular foot of radius 0.0101 mm. The surface tension of water is 0.0700 N/m. What is the maximum possible upward force on the foot due to surface tension of the water? Narrow_forwardA helium-filled balloon, whose envelope has a mass of 25 kg, is tied to a 2.0-m-long , 0.050-kg string. The balloon is spherical with a radius of 0.40 m. When released, it lifts a length h of the string and then remains in equilibrium. Hint: Only that part of the string above the floor contributes to the load being supported by the balloon. a. Draw a free-body diagram for string-balloon systems, account for every force. b. Write an expression for the net force on this system. c. Determine the value of h in terms variables. d. If the density of air is ρ_{air}=1.29 kg/m3 and the density of Helium is ρ_{He}=0.179kg/m3, find h.arrow_forward
- The velocity of an object moving through a fluid can be modeled by the drag equation: dv/dt = −kv^2 where k is constant. A. Find the general solution to this equation. B. An object moving through the water has an initial velocity of 16 m/sec. After 2.0 seconds, the velocity has decreased to 12 m/sec. What will the velocity be after ten seconds?arrow_forwardAt its widest point, the diameter of a bottlenose dolphin is 0.50 m. Bottlenose dolphins are particularly sleek, having a drag coefficient of only about 0.090.a. What is the drag force acting on such a dolphin swimming at 7.5 m/s?b. Using the dolphin’s diameter as its characteristic length, what is the Reynolds number as it swims at this speed in 20° C water?arrow_forwardA closed cylindrical vessel of diameter 15 cm and length 100 cm contains water up to a height of 80 cm. The vessel is rotated at speed of 500 rpm about its vertical axis. Find the speed of rotation of the vessel in rpm, when the axial depth is zero. a. 891.7 b. 645.23 c. 20.4 d. 56.06 With Free Body Diagramarrow_forward
- The Zero Gravity Research Facility at NASA-operated Glenn Research Center in Ohio is used to test the behavior of fluids, flames, equipment and other objects in free fall. It consists of a 467-foot long, 12-foot diameter, steel vacuum chamber. The steel chamber resides inside of a concrete lined shaft which extends 510 feet below ground level. Objects falling through the tower experience free fall over a distance of 432 feet (132 meters). a. Determine the falling time for objects dropped from rest.b. Determine the final speed of the objects before the braking period begins.arrow_forwardA ping pong ball of mass 2.6 grams and 38 mm in diameter is supported by an air jet. The air has a density of 1.20 kg/m3 and kinematic viscosity of 1.5 x 10-5 m2/s. What is the speed of the air jet if the ping pong ball remains stationary? Assume a constant drag coefficient of 0.45. a. 3.021 m/s b. 288.610 m/s c. 9.127 m/s d. 83.302 m/sarrow_forwardA helium-filled balloon, whose envelope has a mass of 0.25 kg, is tied to a 2.0-m-long, 0.050-kg string. The balloon is spherical with a radius of 0.40 m. When released, it lifts a length h of the string and then remains in equilibrium. Hint: Only that part of the string above the floor contributes to the load being supported by the balloon. a. Draw a free-body diagram for string-balloon systems, account for every force. b. Write an expression for the net force on this system. c. Determine the value of h in terms of variables.arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax College