Please answer ALL questions as this is very important.

Use the images attached (Titled "Lab: The Pendulum") to answer questions 1-9.

pivot@ - - ------ center of mass small objectpivot@ - - ------ center of mass small objectLAB: THE PENDULUM Purpose: to study what factors inuence oscillations of a simple pendulum Equipment: 3 small, but heavy obj ects (keys, washers, erasers, etc; can be 3 different objects) about 60 cm of sewing thread, dental floss, or a thin string 1 pencil or 1 pepsicle stick 2 pieces of masking tape or Scotch tape (about 2 inches each} 1 ruler with centimeters or a measuring tape a at surface (gig: the top of a dining table or a kitchen counter) Theory: A simple pendulum consists ofa mass (called the bob) suspended from one end of a string (Fig. 1). It is assumed that the whole pendulum's mass is concentrated in its bob and that the string cannot be stretched. When Mthe bob rests at point B, directly below the pivot (see Fig. 1). This position is called the equilibrium. The bob can be made to swing in an arc if it is displaced from the equilibrium and let go. pivot FTGStOT' mg Figure 1 As shown in Fig. 1, two forces act on the bob at each point of its motion: the force of gravity, m, and the tension ofthe string, r. The force ofgravity always points downward. The force of tension points along the string and varies at each point of the pendulum's motion. When the bob is displaced from point B, the total force on it is equal to: Ftotat = mg + FT The total force has two components: a force perpendicular to the path of the bob, called the centripetal force (Fcenw) and a force tangential to the path, called the restoring force (rey). The centripetal force is maximum at the equilibrium, where the bob has the maximum speed. However, this force becomes zero when the bob is the farthest from the equilibrium (point A),_si_nce it momentarily stops there. Lab: The Penduham The restoring force is maximum when the displacement from the equilibrium is maximum (point A in Fig. 1). As the bob moves from its maximum displacement toward point B, the restoring force decreases and reaches zero when the bob is at point B (equilibrium). However, the bob does not stop there and continues to travel because of its inertia. Once the bob reaches the highest point on the other side of the equilibrium (not shown in Fig. 1), the restoring force will again have a maximum value and will accelerate the bob back toward B. The bob's inertia will again cause the bob to pass through B and continue on its circular path, repeating the process. A swing from the highest point on the left to the highest point on its right and back to the highest point on its left is called an oscillation. The time needed for one oscillation is called the period. The quantities listed below are used to describe oscillations of a pendulum. Amplitude: maximum displacement of the bob from its equilibrium Period: time required for one oscillation; symbol T; unit: second Frequency: number of oscillations per second; symbol f; unit: Us = hertz = Hz Pend. Length: measured from the pivot to the middle of the bob; symbol L; unit: meter It can be shown that the theoretical period, Lbs is related to the length of the pendulum, L, and the acceleration due to gravity, g, in the following way: T 2 L E 1 = a- q. g We can see from Eq. 1 that an increase in the length of the pendulum, L, causes a longer period of oscillations. Conversely, if the acceleration due to gravity is smaller (egg: on the Moon rather than on the Earth, or at a high mountain rather than at the sea level) then the period of oscillation will be longer. If the period of a simple pendulum is known, the magnitude of the acceleration due to gravity, g, can be calculated from Eq. 1 to be: _L(2\")2 E 2 g _ T q' Procedure: A) Mass Dependence Table 2 Comparison of Tex for masses: % diff the period with 1 object versus the period with 2 objects the period with 1 object versus the period with 3 objects the period with 2 objects versus the period with 3 objects B) Length Dependence Table 3 Pendulum length, L (m) Time for 20 oscillations (s) Texe (S) Table 4 Comparison of Text for lengths: % diff the period with L=70 cm versus the period with L=50 cm the period with L=70 cm versus the period with L=30 cm the period with L=50 cm versus the period with L=30 cmpencil taped to the table tabletop 7-8 cm string small object side viewpencil taped to the table the object swings left & right front view