Physics 40 HW #1. Chapter 1

Transcription

1 Physics 40 HW # Do these from the Knight but do NOT turn in: Ch : 3 9,, 6; Ch : 4, 6, 0, We will go over the book problems in discussion session so do them neatly to share! The following will be turned in. Please solve them on additional paper. Show all your work clearly and neatly. Box final numerical answers. NEATNESS COUNTS! Chapter.3. Model: We will assume that the term quickly used in the problem statement means a time that is short compared to 30 s. Solve: Assess: Notice that the acceleration vector points in the direction opposite to the velocity vector because the car is decelerating..9. Solve: (a) Let v 0 be the velocity vector between points 0 and and v be the velocity vector between points and. Speed v is greater than speed v 0 because more distance is covered in the same interval of time. (b) Acceleration is found by the method of Tactics Box.3. Assess: The acceleration vector points in the same direction as the velocity vectors, which makes sense because the speed is increasing.

2 car as a particle... Model: Represent the Visualize: The dots are equally spaced until brakes are applied to the car. Equidistant dots on a single line indicate constant average velocity. Upon braking, the dots get closer as the average velocity decreases, and the distance between dots changes by a constant amount because the acceleration is constant..6. Model: Represent the tennis ball as a particle. Visualize: The ball falls freely for three stories. Upon impact, it quickly decelerates to zero velocity while comp-ressing, then accelerates rapidly while re-expanding. As vectors, both the deceleration and acceleration are an upward vector. The downward and upward motions of the ball are shown separately in the figure. The increasing length between the dots during downward motion indicates an increasing average velocity or downward acceleration. On the other hand, the decreasing length between the dots during upward motion indicates acceleration in a direction opposite to the motion, so the average velocity decreases. Assess: For free-fall motion, acceleration due to gravity is always vertically downward. Notice that the acceleration due to the ground is quite large (although not to scale that would take too much space) because in a time interval much shorter than the time interval between the points, the velocity of the ball is essentially completely reversed.

3 Chapter.4. Model: The jogger is a particle. Solve: The slope of the position-versus-time graph at every point gives the velocity at that point. The slope at t 0 s is s 50 m 5 m v.5 m/s 0 s The slope at t 5 s is 50 m 50 m v 0.0 m/s 0 s The slope at t 35 s is 0 m 50 m v 5.0 m/s 0 s.6. Visualize: Please refer to Figure EX.6. The particle starts at x0 0 m at t 0 0. Its velocity is initially in the x direction. The speed decreases as time increases during the first second, is zero at t s, and then increases after the particle reverses direction. Solve: (a) The particle reverses direction at t s, when v x changes sign. (b) Using the equation xf x0 area of the velocity graph between t and t f, x 0 m (area of triangle between 0 s and s) (area of triangle between s and s) x x s 3s 4s 0 m (4 m/s)( s) (4 m/s)( s) 0 m 0 m area of trapazoid between s and 3 s 0 m (4 m/s 8 m/s)(3 s s) 6 m x area between 3 s and 4 s 3s 6 m (8 m/s m/s)( s) 6 m

4 .0. Visualize: The graph is a graph of velocity vs. time, so the acceleration is the slope of the graph. Solve: When the blood is speeding up the acceleration is When the blood is slowing down the acceleration is Assess: 6 m/s is an impressive but reasonable acceleration. a y a y y m/s m/s 0.05s y 0.80 m/s 5.3 m/s 0.5 s.. Solve: (a) At t 0 s, the position of the particle is (b) From the graph itself at t 0 s, v 4 m/s (c) The acceleration is x s.0 m area under velocity graph from t 0 s to t.0 s.0 m (4.0 m/s)(.0 s) 6.0 m vx vfx vix 6 m/s 0 m/s ax m/s 3 s

5 . How many significant figures are in the following numbers? (a) , (b) , (c) , (d) Newton s law of universal gravitation is represented by F GMm r Here F is the gravitational force exerted by one small object on another, M and m are the masses of the objects, and r is a distance. Force has the SI units kg m/s. What are the SI units of the proportionality constant G? 3. Hydraulic engineers in the US often use, as a unit of volume of water, the acre-foot, defined as the volume of water that will cover acre of land to a depth of ft. A severe thunderstorm dumped.0 in. of rain in 30 min. on a town of area 65 km. What volume, in acre-feet, fell on the town? 4. Earth has a mass of 5.98 x 0 4 kg. The average mass of the atoms that make up the Earth is 40.0u where u is an atomic mass unit. How many atoms are there in the Earth? Express your final answer in scientific notation with proper significant figures. 6. An astronomical unit (AU) is the average distance between the Earth and the Sun, approximately.50 x 0 8 km. The speed of light is about 3.0 x 0 8 m/s. Express the speed of light in astronomical units per hour. 7. A student measures the mass of 6 different pennies to be.5g,.4g,.6g..3g,.7g, and.g. Find the average value of the mass of the pennies and the uncertainty of the mass as the average deviation. Show your work and express you answer in standard form. Use the Error analysis handout for information on how to do this. 8. The position of a particle moving along the x axis is given by x 6. 0t. 0t, where x is in meters and t in seconds. a) Sketch the x-t graph., labeling intercepts. b) Find the function for the velocity and sketch the v-t graph, labeling everything. c) Find the acceleration of the particle. 9. A particle moving with a constant acceleration has a velocity of 0 cm/s when its position is x = 0 cm. Its position 7.0 s later is x = 30 cm. What is the acceleration of the particle? Derive the displacement and velocity equations and sketch them, labeling everything.