Homework 2 - Motion In 2D

Problem 2.1

The helicopter view of the figure below shows two people pulling on a stubborn mule. Find:

  1. the single force that is equivalent to the two forces shown. (\(|\vec{F_2}|=80.0~N\) and \(|\vec{F_1}|=120~N\))
  2. the force a third person would have to exert on the mule to make the net force equal to zero. The forces are measured in units of Newtons (\(N\)).

hw2_fig1.png

Problem 2.2

The rectangle shown in the below figure has sides parallel to the x and y axes. The position vectors of two corners are \(\vec{A} = 10.0~m\) at \(50.0^\circ\) and \(\vec{B} = 12.0~m\) at \(30.0^\circ\).

  1. Find the perimeter of the rectangle.
  2. Find the magnitude and direction of the vector from the origin to the upper-right corner of the rectangle.

hw2_fig2.png

Problem 2.3

A soccer player kicks a rock horizontally off a \(40.0~m\) high cliff into a pool of water. If the player hears the sound of the splash \(3.00~s\) later, what was the initial speed given to the rock? Assume the speed of sound in air is \(343~m/s\).

Problem 2.4

To start an avalanche on a mountain slope, an artillery shell is fired with an initial velocity of \(300~m/s\) at \(55.0^\circ\) above the horizontal. It explodes on the mountainside \(42.0~s\) after firing. What are the x and y coordinates of the shell where it explodes, relative to its firing point?

Problem 2.5

  1. Can a particle moving with instantaneous speed \(3.00~m/s\) on a path with radius of curvature \(2.00~m\) have an acceleration of magnitude \(6.00~m/s^2\) ?
  2. Can it have an acceleration of magnitude \(4.00~m/s^2\)? In each case, if the answer is yes, explain how it can happen; if the answer is no, explain why not.

Problem 2.6

An athlete swings a ball, connected to the end of a chain, in a horizontal circle. The athlete is able to rotate the ball at the rate of \(8.00~rev/s\) when the length of the chain is \(0.600~m\). When he increases the length to \(0.900~m\), he is able to rotate the ball only \(6.00~rev/s\).

  1. Which rate of rotation gives the greater speed for the ball?
  2. What is the centripetal acceleration of the ball at \(8.00~rev/s\)?
  3. What is the centripetal acceleration at \(6.00~rev/s\)?