4. Newton's Second Law An object's acceleration is directly proportional to the net force on it, and inversely proportional to its mass. 200 + 10 + 10 = Total Mass of Syshen Apparatus Air track, gliders; photocell timer; slot weights; hanging weights; balance; meter stick. Physical Principles The object of this lab is to compare the acceleration of a system of two bodies determined in two different ways. In one method, we will measure velocities and calculate the acceleration using a kinematics equation (i.e., no mention of force). The other method determines the acceleration using Newton's second law of motion. We will call the acceleration value determined exclusively from the motion (kinematics) the experimental value, aE. The acceleration value determined from Newton's Law will be considered a theoretical value, aT. Newton's Second Law of Motion states that when a net force acts on a body, the acceleration of that body is directly proportional to this force and inversely proportional to the mass of the body. Thus, stated mathematically, %3D ат т where, at is the theoretical acceleration, F is the net force, and m is the mass which is doing the accelerating. In this experiment we use a system of two bodies, an air track glider and a hanging weight. They are connected by a string which is draped over a low friction pulley at the end of the air track. The glider rides on a level air track, which is approximately a friction free surface. Your instructor will acquaint you with the use of the air track. In this lab, since both masses undergo the same acceleration, the "m" in Eq. (1) equals the total mass of the system. Knowing the masses and the net force (the weight of the hanging weight) we can calculate aT, the theoretical acceleration of the system. The kinematics equation for uniformly accelerated motion which expresses the acceleration of the system in terms of the initial and final velocities of the objects and the distance traveled is: (v-v.) aE 2x where ag is the acceleration, vo is the initial velocity, vr is the final velocity, and x is the distance traveled. The initial velocity is chosen to be zero (the system starts from rest). The final velocity can be determined by measuring the length of the glider "L" and measuring the time necessary for the glider to pass through the photogate-timer "t" when there is no further force acting upon the system (i.e., after the hanging weight has struck the floor and the string has slack). gone L. L can be measured directly on the metric scale which is attached to the air track. Set x equal to 80.0 cm by releasing the glider with the hanging weight exactly that far above the floor. The acceleration as determined by Newton's second law will probably not precisely agree with the acceleration determined by the kinematics equation. As usual, the percent discrepancy (error) is determined by the following relationship: lar-aE % error = x100 4. ат In each of the two cases you will examine, two masses, the glider and the hanging mass, will be accelerating. Thus, the "m" in Eq. (1) represents the sum of their respective masses. In order to keep this total mass the same for the two cases, you will arrange case I by using 10 grams for the hanging weight and tape a 10 gram flat weight to the top of the glider, while for case ILyou will use 20 grams for the hanging weight and remove the 10 gram flat weight from the top of the glider. By setting up the experiment this way, in each of the two cases the same total amount of mass will be accelerated, but in the first case 10 grams will be hanging and the rest gliding, while in the second case 20 grams will be hanging and the rest gliding. Thus, the only difference between the two cases will be the accelerating force which acts on the two-mass system. The accelerating force (the weight of what is hanging) in case II will be twice the accelerating force in case I. NET NET