1 / 11

Section 8.5 Applications to Physics

Section 8.5 Applications to Physics. In physics the word “work” is used to describe the work a force has done on an object to move it some distance Work done = Force · Distance or W = F · D Units.

nash-harper
Download Presentation

Section 8.5 Applications to Physics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 8.5Applications to Physics

  2. In physics the word “work” is used to describe the work a force has done on an object to move it some distance • Work done = Force · Distance or W = F · D Units

  3. If an object of mass m moves along a straight line given by s(t), then the force (in the same direction) is defined by • What is the work required to raise a 5 kg mass up 10 meters?

  4. What if the force is not constant? • Consider a force that varies along a to b • Call if f(x) • Divide the interval a to b into n subintervals • Pick in the ith interval • Then is the force • The interval is then small enough so that the force is constant • Then • So

  5. Hooke’s Law • The force required to maintain a spring stretched x units beyond its natural length is proportional to x (let k be the constant of proportionality) so we get • F = kx

  6. Example • A spring has a natural length of 20 cm. If a 25 newton force is required to keep it stretched to 30 cm, how much work is required to stretch it from 20 cm to 25 cm?

  7. Example • A trough that has a triangular cross section that is 5m high, 3m wide at the top and 8m long is filled up to 3 meters with water. Given that the density of water is 1000 kg/m3, how much work is required in order to empty the trough?

  8. Force and Pressure • Can use a definite integral to compute the force exerted by a liquid on a surface • The force is directly related to the pressure • Pressure of a liquid is the force per unit area exerted by the liquid • It is equal in all directions • It increases with depth

  9. At a depth of h meters, the pressure, p, exerted by the liquid is given by computing the total weight of a column of liquid h meters high with a base of 1 square meter. • If the liquid has density δ then its weight per unit volume is δg where g is the acceleration due to gravity. The weight of the column is δgh so Pressure = Mass density ·g· Depth or P = δgh • Provided the pressure is constant over that area we have Force = Pressure · Area

  10. Units

  11. Example • #24 The Three Gorges Dam is currently being built in China. When it is finished in 2009, it will be the largest damn in the world: about 2000 m long and 180 m high, creating a lake the length of Lake Superior. Assume the damn is rectangular in shape. • Estimate the water pressure at the base of the dam • Set up and evaluate a definite integral giving the total force of the water on the dam

More Related