Week 3 Recitation Problems PDF

Preview

Summary

Download Week 3 Recitation Problems PDF

Description

33-141 Recitation

Week 3

Problem X.3.1) A particle is moving around a circular track. (a) Sketch the trajectory of the particle on a full sheet of paper. Choose an origin for a xy coordinate system. Select two locations for the particle, approximately one eight of the circle apart, and label them A and B. (b) Draw the two position vectors for A and B, and draw the displacement vector indicating motion from A to B. (c) How would you use the displacement vector to determine the average velocity of the particle between A and B? Draw this velocity vector. Choose a point on the circle between A and B. Label this B’. (d) If you were to move B’ closer and closer to A, how would the direction of the average velocity between A and B’ change? (e) Describe the direction of the instantaneous velocity at point A. Does your answer depend on whether or not the particle is speeding up, slowing down, or moving at constant speed? (f) If you had chosen a different origin for your coordinate system, which of the vectors would change? Problem X.3.2) A particle is moving around a circular track, at constant speed. (a) Sketch the trajectory of the particle on a full sheet of paper. Select two locations for the particle, approximately one eight of the circle apart, and label them A and B. Draw (large) vectors representing the velocity at the two points. (b) Copy these vectors to a separate sheet of paper, and graphically determine ∆𝑣 (c) Is the angle between 𝑣𝐴 and ∆𝑣 greater than, less than, or equal to 90°? (d) If you were to move point B closer to point A, would this angle increase, decrease, or remain the same? (e) Does the angle approach a limiting value? If so, what is it? (f) Describe how you would use ∆𝑣 to determine the average acceleration. (g) What is the angle between the instantaneous velocity and the instantaneous acceleration for a particle moving round the track at constant speed?

Problem X.3.3) A particle is moving around a circular track, speeding up at a constant rate. (a) Sketch the trajectory of the particle on a full sheet of paper. Select two locations for the particle, approximately one eighth of the circle apart, and label them A and B. Draw (large) vectors representing the velocity at the two points. (b) Copy these vectors to a separate sheet of paper, and graphically determine ∆𝑣 (c) Is the angle between 𝑣𝐴 and ∆𝑣 greater than, less than, or equal to 90°? (d) Consider how this angle would change if you were to move point B closer to point A. What range of values is possible for this angle? (e) What can you say about the angle between the instantaneous velocity and the instantaneous acceleration for a particle speeding up as it moves round the track? (f) What can you say about the angle between the instantaneous velocity and the instantaneous acceleration for a particle slowing down as it moves round the track?

Problems from: University Physics, 13th edition, by H. D. Young & R. A. Freedman, Pearson Addison Wesley, 2012. Problem 9.8) A wheel is rotating about an axis that is in the z-direction. The angular velocity ωz is -6 rad/s at t = 0 increases linearly with time, and is +8 rad/s at t = 7 s We have taken counterclockwise rotation to be positive. (a) Is the angular acceleration during this time interval positive or negative? (b) During what time interval is the speed of the wheel increasing? Decreasing? (c) What is the angular displacement of the wheel at t = 7 s?

Problem 9.11) The rotating blade of a blender turns with constant angular acceleration α (a) How much time does it take to reach an angular velocity of ωf starting from rest? (b) Through how many revolutions does the blade turn in this time interval?

Problem 3.6) A dog running in an open field has components of velocity vx = 2.6 m/s and vy = -1.8 m/s at t1=10 s. For the time interval from t1 = 10 s to t2 = 20 s the average acceleration of the dog has magnitude 0.45 m/s2 and direction 31° measured from the +x-axis toward the +y-axis. At t2 = 20 s, (a) what are the x- and y-components of the dog’s velocity? (b) What are the magnitude and direction of the dog’s velocity? (c) Sketch the velocity vectors at t1 and t2. How do these two vectors differ?

X.3.4. In this problem, try to make use of the relative velocity equations: 𝑣𝐴|𝐵 = 𝑣𝐴|𝐶 + 𝑣𝐶|𝐵

𝑣𝐴|𝐵 = −𝑣𝐵|𝐴

even if you can find the answer using intuition and mental arithmetic! George is in a train moving eastward at 50 m/s. Henry, standing beside the tracks, throws a ball at 30 m/s eastward. (a) What is the velocity of the train relative to George? (b) What is the velocity of the train relative to Henry? (c) What is the velocity of Henry relative to George? (d) What is the velocity of George relative to Henry? (e) What is the velocity of the ball relative to George? (f) What is the velocity of the ball relative to Henry?

Carnegie Mellon University 33-141 Recitation

Physics Department Thursday Week 3

Numbered Problems from: University Physics, 13th edition, by H. D. Young & R. A. Freedman, Pearson Addison Wesley, 2012.

Problem X.3.5) Look at this poster for the movie “Skyscraper”. It shows Dwayne ‘The Rock’ Johnson jumping from a crane into an open window. Sketch his trajectory. Given that ‘The Rock’ is about 2m tall, estimate the horizontal range and vertical drop from crane to window. How fast must he have been running along the crane in order to make the jump? Is this plausible? Google the highest recorded human speed and compare.

Problem X.3.6) You are on the target range preparing to shoot a new rifle when it occurs to you that you would like to know how fast the bullet leaves the gun (the muzzle velocity). You bring the rifle up to shoulder level and aim it horizontally at the target center. Carefully you squeeze off the shot at the target which is 100 meters away. When you collect the target you find that your bullet hit 20 centimeters below where you aimed.

Problem 3.10) A daring swimmer (mass m) dives off a cliff with a running horizontal leap, as shown in the figure. What must her minimum speed be just as she leaves the top of the cliff so that she will miss the ledge at the bottom, which is Δx wide and Δy below the top of the cliff?

Problem 3.19) Win the Prize. In a carnival booth, you win a stuffed giraffe if you toss a quarter into a small dish. The dish is on a shelf above the point where the quarter leaves your hand and is a horizontal distance of 2.1 m from this point (Fig. E3.19). If you toss the coin with a velocity of 6.4 m/s at an angle of 60° above the horizontal, the coin lands in the dish. You can ignore air resistance.

(a) What is the height of the shelf above the point where the quarter leaves your hand?

(b) What is the vertical component of the velocity of the quarter just before it lands in the dish?

Problem 3.48) Martian Athletics. In the long jump, an athlete launches herself at an angle above the ground and lands at the same height, trying to travel the greatest horizontal distance. Suppose that on earth she is in the air for time T, reaches a maximum height h, and achieves a horizontal distance D. If she jumped in exactly the same way during a competition on Mars, where gMars is 0.379 of its earth value, find her time in the air, maximum height, and horizontal distance. Express each of these three quantities in terms of its earth value. Air resistance can be neglected on both planets.

Problem 3.60) A water hose is used to fill a large cylindrical storage tank of diameter D and height 2D. The hose shoots the water at 45° above the horizontal from the same level as the base of the tank and is a distance 6D away (Fig. P3.60). For what range of launch speeds (v0) will the water enter the tank? Ignore air resistance, and express your answer in terms of D and g.

Problem 3.71) A boulder of mass m is rolling horizontally at the top of a vertical cliff that is a height h1 above the surface of a lake, as shown in Fig. P3.71. The top of the vertical face of a dam is located a distance d from the foot of the cliff, with the top of the dam level with the surface of the water in the lake. A level plain is a height h2 below the top of the dam.

(a) What must be the minimum speed of the rock just as it leaves the cliff so it will travel to the plain without striking the dam? h1

d

h2

(b) How far from the foot of the dam does the rock hit the plain?...