Arizona State University| PHY 121: Univ Physics I: Mechanics|Homework 1-1| Problem 5| Curved Motion Diagram

The motion diagram shown in the figure represents a pendulum released from rest at an angle of  45^{\circ} from the vertical. The dots in the motion diagram (Figure 1) represent the positions of the pendulum bob at eleven moments separated by equal time intervals. The green arrows represent the average velocity between adjacent dots. Also given is a “compass rose” in which directions are labeled with the letters of the alphabet.

A) What is the direction of the acceleration of the object at moment 5?
B) What is the direction of the acceleration of the object at moments 0 and 10?

The figure shows two illustrations. The first illustration shows 11 dots, labeled from 0 to 10, corresponding to 11 positions of a pendulum bob. Ten vectors extend from 0 to 1, from 1 to 2, from 2 to 3, from 3 to 4, from 4 to 5, from 5 to 6, from 6 to 7, from 7 to 8, from 8 to 9, and from 9 to 10. The line obtained from these vectors extends downward and to the right from point 0 to point 5 and then upward, and to the right to point 10. Magnitudes of vectors are increasing from point 0 to point 5 and decreasing from point 5 to point 10. The second illustration shows eight vectors of the same length, labeled from A to H, starting at the same point. Each following vector makes an angle of 45 degrees clockwise from the previous vector. Vector A is directed upward.

Figure 1



Answer: A

The acceleration of the object at moment 5 is the acceleration found from the change in velocity between moments 4 and 5 and moments 5 and 6. 

Acceleration is defined as the change in velocity per unit time. Mathematically,

\vec{a}=\frac{\vec{\Delta v}}{\Delta t}

Since velocity is a vector, acceleration is a vector that points in the direction of the change in the velocity.

Part B:

Answer: D,F