gravity - 22 Experiment II: Determination of g from...

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22 Experiment II: Determination of g from Newton’s Laws Goals Experimentally determine the acceleration ( a ) of a two-body system, and the friction force ( f ) Calculate g , the acceleration due to gravity, from a and f using Newton’s laws of motion Introduction and Background The acceleration due to gravity, g , is an important quantity that is most commonly used to calculate the weight (W) of an object from its mass (m): W = mg. The value of g depends on the location. For example, the g value on the Moon is much smaller than that on Earth. Even on the surface of the Earth g varies slightly from location to location, although it is a good approximation to use g = 9.80 m/s 2 as an average. In this lab, however, we will pretend that we know nothing about the value of g , and we will experimentally determine the value of g by measuring the acceleration of a two-mass system and the friction force associated with the motion. Theory : The set-up for the experiment is shown schematically in Fig. 2-1. Obviously the acceleration of the two masses depends on the weight of the mass m 1 , which in turn depends on the value of g . Mass m 2 is a cart, able to roll on the lab table with a small but finite friction. m 2 is connected to the hanging mass m 1 by a light (negligible mass) string passing over a pulley. When the system is released from rest, m 1 will accelerate downward and m 2 will accelerate forward with an acceleration of the same magnitude since the string is unstretchable. This acceleration can be derived by applying Newton’s second law individually to both masses. The free-body force diagrams for both masses are shown in Figure 2-2. Now derive g using Newton’s second law and the force diagrams and show the derivation in your lab report . You should arrive at the equation: 1 1 2 1 ) ( m f a m m m g + + = (2-1) Therefore, we can determine the value of g if we can experimentally measure a and f since m 1 and m 2 are easily determined. Measuring a : The acceleration of the two-body system can be regarded as constant if the friction is constant. This is one of the assumptions we will make in this experiment. For motion with constant acceleration we have Figure 2.1 – Experimental arrangement.
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gravity - 22 Experiment II: Determination of g from...

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