3. An object with mass m is dropped from rest. (a) Write an expression for the net force on the object, assuming that the downwards force (due to gravity) is proportional to the object's mass and the upwards force (due to air resistance) is proportional to the square of the object's velocity. (b) Write a different expression for the net force on the object based on Newton's Second Law, (force) = (mass) (acceleration). (c) Write a differential equation for the object's velocity based on parts (a) and (b), and use it to find the object's velocity v at time t.

3. An object with mass m is dropped from rest. (a) Write an expression for the net force on the object, assuming that the downwards force (due to gravity) is proportional to the object's mass and the upwards force (due to air resistance) is proportional to the square of the object's velocity. (b) Write a different expression for the net force on the object based on Newton's Second Law, (force) = (mass) (acceleration). (c) Write a differential equation for the object's velocity based on parts (a) and (b), and use it to find the object's velocity v at time t.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

A skydiver weighing 178 lbf (including equipment) falls vertically downward from an altitude of 5000 ft and opens the parachute after 17s of free fall. Assume that the force of air resistance, which is directed opposite to the velocity, is 0.76 |v| when the parachute is closed and 12 |v| when the parachute is open, where the velocity v is measured in ft/s. Use g = 32 ft/s². Round your answers to two decimal places. (a) Find the speed of the skydiver when the parachute opens. v(17) = i ft/s (b) Find the distance fallen before the parachute opens. x(17) = i ft (c) What is the limiting velocity v after the parachute opens? VL = i ft/s
A stack of two crates is being accelerated upwards by two cables. The cables are directly attached to crate 1 and the tension in each cable is 3248 N. You may assume that the masses of the cables are negligible compared to the masses of the crates. The acceleration of the crates is? bottom crate crate 1 is 109 kg. the top crate is 248 kg.
An airplane has a mass of 3.39 × 104 kg and takes off under the influence of a constant net force of 2.57 x 104 N. What is the net force that acts on the plane's 71.9-kg pilot? Number Units
Newton's 2nd Law can be symbolized as EF = ma Let mass A = 100 kg Let mass B = 1 kg What is true about an object of large mass versus an object of small mass? The more massive object has more inertia. The objects have the same inertia. The more massive object has less inertia. The objects have the same weight near Earth's surface. The more massive object has a larger weight near Earth's surface. V If the same net force is applied to both then the larger mass has the larger acceleration. O If the same net force is applied to both then the objects will haye the same acceleration. O If the same net force is applied to both then the larger mass has the smaller acceleration.
No need to explain, just choose one of the options please: 1. A person is standing on a bathroom scale in an elevator. As the elevator is accelerating downwards (at a rate that is less than g), the person looks down at the scale and notices that it reads: a) Zero. b) less than their actual weight. c) greater than their actual weight. d) the same as their actual weight. e) it is not possible to tell.
4.3 kg A 4.3 kg object hangs at one end of a rope that is attached to a support on a railroad boxcar. When the car accelerates to the right, the rope makes an angle of 37° with the vertical. The acceleration of gravity is 9.8 m/s² . Find the acceleration of the car. Answer in units of m/s². (
When a certain force is applied to an object with a mass of 2 kg, its acceleration is 10.0 m/s2. When the same force is applied to a different object, its acceleration is 4.0 m/s2. The mass of second object is 10.0 kg 2.5 kg 8.0 kg 1.25 kg 5.0 kg
A flea jumps by exerting a force of 1.28 × 10-5 N straight down on the ground. A breeze blowing on the flea parallel to the ground exerts a force of 0.660 x 10-6 N on the flea. Find the direction and magnitude of the acceleration of the flea if its mass is 6.50 x 10-7 kg. Do not neglect the gravitational force. (Assume that the breeze blows in the +x-direction and that the +y-direction is up.) magnitude m/s2 direction o counterclockwise from the +x-axis Additional Materials
An object is at rest on a table. The earth is pulling this object down with a force of magnitude m · g. If we consider this force as the action of an action-reaction pair, what is the reaction force of this force m · g? a) The table pushes the object up b) The object pulls up to the ground c) The earth pushes up the table d)The object pushes the table down e)The table pushes down to the ground
The acceleration due to gravity on planet Z is 1.81 m/s^2 A) if a rock weighs 28.0 N at the surface of the earth what is its mass on the earth’s surface? B) What is the mass of the rock on Planet Z? express answers in Kilograms
please help with questions 42 and 43
In an experiment performed in a space station, a force of 49 N causes an object to have an acceleration equal to 9 m/s2. What is the object's mass? (a) What is the person's mass? kg(b) The elevator accelerates upward momentarily at the rate of a = 4 m/s2. What does the scale read then? N(c) The elevator then moves with a steady speed of 7 m/s. What does the scale read now? N