Particle Kinematics Homework

Transcription

1 Chapter I Particle Kinematics Homework Freeform c 2016 I-1

2 I-2 Freeform c 2016

3 article Kinematics Homework Problems ME 274 roblem I/1 Homework 1. ( ) = 2 4x , where article P moves Given: within the Particle x-y plane P moves on a within path described the x-y plane by y on x a path described by y (x) = 2 4x where oth x and y are both given x in and feet. y are given in feet. etermine the acceleration Find: Determine of P. Write the acceleration your answer of P. as Write a vector your in answer terms of asits a vector x-y in terms of its x-y components. omponents. y path of P P x se the following Use parameters the following in your parameters analysis: in x your = 6 ft analysis:,!x =!2 x ft = / 2 sec ft, and ẋ = -10 ft/s and ẍ = 0.! =!3 ft / sec 2. Freeform c 2016 I-3

4 Homework 1.B Particle Kinematics Homework Problems ME 274 Given: n automobile is traveling on a circular path centered at O and having a radius of R. The automobile has a speed of v and is changing this speed at a rate of v. Problem I/2 n automobile Find: is traveling For this problem: on a circular path centered at O and having a radius of R. The automobile has a speed of v, and is changing this speed at a rate of!v. (a) Determine the acceleration of. Write this as a vector in terms of its x-y components. a) Determine the acceleration of. Write this as a vector in terms of its x-y components. (b) Make a sketch of the acceleration vector for. b) Make a (c) sketch Determine of the acceleration the magnitude vector of the for acceleration. of in terms of the number of g s experienced by a passenger in the automobile. c) Determine the magnitude of the acceleration of in terms of the number of g s experienced by a passenger in the automobile. y v O R! x Use the following Use the parameters followingin parameters your analysis: in your R = analysis: 150 m,! R = = m,, θ v = 20m 135,/ v s = and 10 m/s and v = -6 m/s 2.!v =!2m / s 2. I-4 Freeform c 2016

5 Homework 1.C Given: skier is moving down a slope. long the straight slope from to B, her speed is changing at a constant rate of v B. From B to C, the slope is curved with a radius of curvature of ρ. t point C, her speed is changing at a rate of v C. The skier s speed at points, B and C are v, v B and v C, respectively. Find: For this problem: (a) Sketch the tangent and normal unit vectors at points, B and C. (b) Calculate the acceleration vectors at points, B and C. (c) Sketch the acceleration vectors at points, B and C. B C Use the following parameters in your analysis: v B = 5 m/s 2, v C = -1.5 m/s 2, ρ = 175 m, v = 20 m/s, v B = 30 m/s and v C = 40 m/s. Freeform c 2016 I-5

6 Homework 1.D Given: particle P moves within a plane with a path given in terms of the polar coordinates: R = 2θ 2 where R and θ are as defined below in the figure, and with R and θ given in meters and in radians, respectively. mework Problems ME 274 s within a plane Find: with For a path thisgiven problem: in terms of the polar coordinates of: (a) Determine the velocity and acceleration vectors of P in terms of their polar coordinates. e as defined below (b) Make in the afigure sketchand of with the velocity R and! and given acceleration in meters vectors and in for P. ely. the velocity and acceleration vectors of P in eir polar coordinates. etch of the velocity and acceleration vectors the rate of change of speed of P. f P increasing or decreasing at this instant? e! e R R P! O Use the following parameters in your analysis: θ = π/2 rad, θ = -3 rad/s and θ = -2 rad/s 2. parameters in your analysis:! = " radians,!! = " 1.5 rad / sec and I-6 Freeform c 2016

7 Homework 1.E Given: particle P moves in three-dimensional space on a surface given by z = x 2 y, where x = t 2 /2 and y = 3 cos 2πt. Find: For time t = 1 s, determine the velocity and acceleration vectors of P in terms of their Cartesian coordinates. Freeform c 2016 I-7

8 Homework 1.F Given: particle P moves within a plane with a path given in terms of the polar coordinates of: R = 2θ 2, where R and θ are as defined below in the figure, and with R and θ given in meters and in radians, respectively. mework Problems ME 274 Find: For this problem: (a) Determine the velocity and acceleration vectors of P in terms of their polar coordinates. s within a plane with a path given in terms of the polar coordinates of: (b) Make a sketch of the velocity and acceleration vectors for P. (c) Determine the rate of change of speed of P. e as defined below (d) Is in the speed figure of and P with increasing R and or! given decreasing meters at this and instant? Explain. ely. the velocity and acceleration vectors of P in eir polar coordinates. etch of the velocity and acceleration vectors the rate of change of speed of P. f P increasing or decreasing at this instant? e! e R R P! O Use the following parameters in your analysis: θ = π/2 rad, θ = -3 rad/s and θ = -2 rad/s 2. parameters in your analysis:! = " radians,!! = " 1.5 rad / sec and I-8 Freeform c 2016

9 Homework 1.G Given: utomobile is traveling down a roadway with a speed of v when it encounters a hailstorm. Hailstone P is known to be falling with a speed of v P at an angle of θ forward of the automobile. Particle Kinematics Homework Problems ME 274 Find: For this problem: (a) Write down, as a vector, the velocity of P as seen by a passenger in the automobile. Problem I/5 utomobile (b) is traveling t whatdown anglea with roadway the vertical with a speed is thisof observed v when velocity encounters of P? a hailstorm. Hailstone P is known to be falling with a speed of v P at an angle of! forward of the automobile. a) Write down, as a vector, the velocity of P as seen by a passenger in the automobile. b) t what angle with the vertical is this observed velocity of P? v v P! P Use the following parameters in your analysis: v = 40 m/s, v P = 10 m/s and θ = 20. Use the following parameters in your analysis: v = 20 m / sec, v P = 6 m / sec and! = Freeform c 2016 I-9

10 Particle Kinematics Homework Problems ME 2 Homework 1.H Problem I/14 Two cars are travelling as shown. Car is traveling along a circular path of radius, r, Given: Two cars are travelling as shown. Car is traveling along a circular path of radius, r, with a constant speed, v with. Car a constant B is traveling speed, v with. Car a speed, B is traveling v B, in the with direction a speed, of v Bthe, in positive the positive x axis. Th x-axis. The speed of B isspeed changing of B at is achanging rate of v B at. a rate of v! B. t this instant, find: a) The velocity of as seen by car B. Find: t this instant: b) The acceleration of as seen by car B. (a) Determine the velocity of as seen by car B. Use the following parameters in your analysis: r = 100 m, v = 15 m/s, v B = 20 m/s, (b) Determine the acceleration v! = -2 of m/s 2 as. seen by car B. B B r y x Use the following parameters in your analysis: r = 150 m, v = 20 m/s, v B = 30 m/s and v B = 4 m/s 2. I-10 Freeform c 2016

11 Particle Kinematics Homework Problems ME 274 Homework 1.I Problem I/15 worker is lifting a large crate, P, using a pulley shown in the diagram. He is holding Given: workerthe is lifting rope at a point large crate, and P, is using walking a pulley to the shown right at ina the constant diagram. speed Hev is holding the. What is the speed rope at point and is walking to the right at a constant speed v. of the crate when the worker has walked a distance x? Find: What is the speed of the crate when the worker has walked a distance x? Use the following parameters in your analysis: v = 1.5 m/s, x = 2 m, h = 5 m. O P h P Use the following parameters in your analysis: v = 2 m/s, x = 3 m and h = 8 m. x Freeform c 2016 I-11

12 be small. termine the speed of block B when s = 0. termine the speed of block B when s = 4 m. Chapter I: Particle Kinematics Homework Homework 1.J Given: Blocks and B are connected by the pulley-system shown below. Block moves downward with a constant speed of v on a vertical guide. ssume the radii of the pulleys to be small. Find: For this problem: (a) Determine the speed of block B when s = 0 m. (b) Determine the speed of block B when s = 4 m. 8 m / sec in your analysis. 1.5 m O s s B v B Use the following parameters in your analysis: v = 25 m/s. I-12 Freeform c 2016