Physics General Physics

Transcription

1 Physics General Physics Lecture 16 Chapter 5 & 6 Feb 4, 014 Announcements Course webpage: Syllabus, lecture note, etc Online homework: HW.5 is placed on WebAssign and is due by March 3. HW.5: Ch.5 1, 6, 16, 18, 0, 35, 44, 50 Sung-Won Lee Sungwon.Lee@ttu.edu Chapter. 5 Circular Motion & Gravitation Kepler s Laws Kepler s laws describe planetary motion. 1. The orbit of each planet is an ellipse, with the Sun at one focus. An ellipse is a closed curve such that the sum of the distances from any point P on the curve to fixed points (F 1 and F ) remains constant. That is, the sum of the distances, F 1 P + F P, is the same for all points on the curve.

2 Kepler s Laws. An imaginary line drawn from each planet to the Sun sweeps out equal areas in equal times. 3. The square of a planet s orbital period is proportional to the cube of its mean distance from the Sun. Kepler s Laws The two shaded regions have equal areas. The planet moves from point 1 to point in the same time as it takes to move from point 3 to point 4. Planets move fastest in that part of their orbit where they are closest to the Sun. Kepler s Third Law of Planetary Motion The square of the period of an orbit is proportional to the cube of the orbital radius For simplicity, apply to a circular orbit Period is T and the gravitational force supplies a centripetal force Squaring both side and solving for T gives π r G M M M v T = and F = = S un planet planet grav v r r T " 4π # = $ % r & G M S un ' 3 Orbit Examples In the log T vs log r plot, the data for the planets of the solar system fall on a power-law straight line specified by: T 4π = r GM 3 Also applies to satellites with M Sun replaced by M planet The square of the period is proportional to the cube of the radius: Kepler s Section 3 rd Law!! 5.4 Section 5.4

3 Extra-solar Planets Astronomers, using the most advanced telescopes, have recently seen evidence of planets orbiting nearby stars. These are called extra-solar planets. Suppose a planet is observed to have a 100 day (T = 1.037x 10 8 s) period as it orbits a star at the same distance that Jupiter is from the Sun. What is the mass of the star in solar masses? 1 solar mass is defined to be the mass of the sun. Extra-solar Planets Astronomers, using the most advanced telescopes, have recently seen evidence of planets orbiting nearby stars. These are called extra-solar planets. Suppose a planet is observed to have a 100 day (T = 1.037x 10 8 s) period as it orbits a star at the same distance that Jupiter is from the Sun. What is the mass of the star in solar masses? 1 solar mass is defined to be the mass of the sun. 3 4π 3 4π r 31 T = r M = = kg GM GT kg M / M S = = 13 solar masses kg Example: Where is Mars? Mars period (its year ) was first noted by Kepler to be about 687 days (Earth-days), which is (687 d/365 d) = 1.88 yr (Earth years). Determine the mean distance of Mars from the Sun using the Earth as a reference. Example: Where is Mars? Mars period (its year ) was first noted by Kepler to be about 687 days (Earth-days), which is (687 d/365 d) = 1.88 yr (Earth years). Determine the mean distance of Mars from the Sun using the Earth as a reference.

4 Example: The Sun s mass determined. Determine the mass of the Sun given the Earth s distance from the Sun as r ES = 1.5 x m. Example: The Sun s mass determined. Determine the mass of the Sun given the Earth s distance from the Sun as r ES = 1.5 x m. T 4π = r GM 3 Tides Tides are the fluctuations of the level of the Earth s oceans Tides are due to the Moon s gravitational force on the oceans Also exerts a force on the solid Earth Tides, cont. One high tide occurs when the Moon is directly overhead There are generally two high tides per day, 1 hours apart Section 5.5 The Sun also affects tides Its effects are smaller than the Moon s When the Sun and the Moon are aligned and on the same of the Earth, the tide is higher than when produced by the Moon alone Section 5.5

5 Work The work done by a constant force is defined as the distance moved multiplied by the component of the force in the direction of displacement: The product of F Δx is called work Chapter 6 Work & Energy For one-dimensional motion, W = F Δx In two- or threedimensions, you must take the vector nature of the force and displacement into account: W = F (Δr)cos θ θ is the angle between the force and the displacement Section 6.1 Work Done by a Constant Force A person pulling a crate along the floor. The work done by the force F is W = Fd cos θ, where d is the displacement. where θ: angle between the force and the displacement vectors More About Work Units Newton x meter = Joule N. m = J Work is a scalar Although the force and displacement are both vectors Work can be positive or negative These are not directions Section 6.1

6 Work!! W = F Δr cosθ# A force does no work (W=0) on the object if the force does not move (Δr=0) through a displacement The work done by a force on a moving object is zero when the force applied is perpendicular to the displacement (cos90 0 =0) of its point of application F θ# F r Δr Work Example The normal force (n) and the gravitational force (mg) do no work on the object cosθ = cos 90 = 0 The force F does work on the object. W = F Δr cosθ# Work Done by a Constant Force In the SI system, the units of work are joules: As long as this person does not lift or lower the bag of groceries, he is doing no work on it. The force he exerts has no component in the direction of motion. Example: Work done on a crate. A person pulls a 50-kg crate 40 m along a horizontal floor by a constant force F P = 100 N, which acts at a 37 angle as shown. The floor is smooth and exerts no friction force. Determine (a) the work done by each force acting on the crate, and (b) the net work done on the crate. The person does no work on the bag of groceries since F P is perpendicular to the displacement d.

7 Example: Work on a backpack. (a) Determine the work a hiker must do on a 15.0-kg backpack to carry it up a hill of height h = 10.0 m (b) Determine also (b) the work done by gravity on the backpack, and (c) the net work done on the backpack. For simplicity, assume the motion is smooth and at constant velocity (i.e., acceleration is zero).