A definition of the problem and selection of variables
How does the acceleration of an object depend on the mass of it? The independent variable is the total mass of the system and the dependent variable is acceleration. Net force is held constant by keeping the mass of the hanger constant. This means that only mass is added to the cart and there is no added pulling force.
A developed method for the collection of data
Grace plugged a motion sensor into her computer which was linked up with LoggerPro. The motion sensor was put behind the cart so that it sped up in front of the motion sensor and forward motion was detected. This yielded a velocity vs time graph for the cart, the slope of which was the acceleration of the cart. This yielded the dependent variable.
The procedure
A cart on a ramp was attached to a mass hanger via a light cord (everything is assumed to be frictionless), and the cart starts from a resting position far up the table, where the hanger hangs high up. The motion sensor was turned on behind the cart. The cart was released from this position and a separate person caught the cart before it flew off the table. For 10 different trials, varying amounts of mass were added to the cart while the mass on the hanger was held constant, keeping the net force pulling on the cart constant. The acceleration of the cart prior to being caught was recorded via the slope of the LoggerPro graph.
How does the acceleration of an object depend on the mass of it? The independent variable is the total mass of the system and the dependent variable is acceleration. Net force is held constant by keeping the mass of the hanger constant. This means that only mass is added to the cart and there is no added pulling force.
A developed method for the collection of data
Grace plugged a motion sensor into her computer which was linked up with LoggerPro. The motion sensor was put behind the cart so that it sped up in front of the motion sensor and forward motion was detected. This yielded a velocity vs time graph for the cart, the slope of which was the acceleration of the cart. This yielded the dependent variable.
The procedure
A cart on a ramp was attached to a mass hanger via a light cord (everything is assumed to be frictionless), and the cart starts from a resting position far up the table, where the hanger hangs high up. The motion sensor was turned on behind the cart. The cart was released from this position and a separate person caught the cart before it flew off the table. For 10 different trials, varying amounts of mass were added to the cart while the mass on the hanger was held constant, keeping the net force pulling on the cart constant. The acceleration of the cart prior to being caught was recorded via the slope of the LoggerPro graph.
Recorded data
Processed recorded: Net force (N) = Hanger Mass (kg) * Gravitational constant (9.8 m/s/s)
Presented Processed and Interpretation
Acceleration (m/s/s) = A/Total Mass of System (kg)
Hanger Mass was kept constant at 0.05 kg. Thus, net force is held constant at 0.05 kg * 9.8m/s/s = 0.49 N. The A value of the graph, the constant value of the inversely proportional model, was 0.46. This is significantly close to the value of the net force held constant, and thus it can be surmised that the k value of the acceleration vs total mass graph is the net force acting upon the system.
Our results are in line with Newton's 2nd Law of Acceleration, net force, and mass because acceleration is proportional to the net force acting on a system, and inversely related to the total mass of the system. When more mass is added to an object, it becomes more difficult to accelerate at a proportional rate.
The y-intercept is the acceleration when mass = 0. The y-intercept does not exist because no object can have a mass of zero. Objects must have mass and take up space to exist.
Conclusion
Ultimately, when no unbalanced forces are added to an object, the object will not accelerate. When net forces acting on the object are constant, but mass increases, acceleration decreases. Such results could be used for most situations in which motion of objects is involved. If a plane is flying at a constant velocity, it will keep flying at that constant velocity unless another force acts upon it. However, if an enormous gust of wind were to propel the plane forward, the plane would accelerate, but, if hypothetically, 100 extra people appeared in the plane, the rate of acceleration would substantially decrease. Acceleration decreases proportionally to the added mass of those 100 people as is in line with Newton's 2nd Law. Two of the biggest uncertainties had to do with how the A value was not exactly equal to the value of net force (N). What is likely at play for them not being precisely the same is likely errors in the aged sensor detectors and LoggerPro, as both programs can stray away from accuracy at times. Human error in measuring weight, properly dispersing it, and starting and stopping the cart also likely resulted in slightly less precise results. Improving the investigation may involve finding a larger variety of individual weights, so that we could have increased the net force in equal increments, or possibly using a robot to stop the object.
Acceleration (m/s/s) = A/Total Mass of System (kg)
Hanger Mass was kept constant at 0.05 kg. Thus, net force is held constant at 0.05 kg * 9.8m/s/s = 0.49 N. The A value of the graph, the constant value of the inversely proportional model, was 0.46. This is significantly close to the value of the net force held constant, and thus it can be surmised that the k value of the acceleration vs total mass graph is the net force acting upon the system.
Our results are in line with Newton's 2nd Law of Acceleration, net force, and mass because acceleration is proportional to the net force acting on a system, and inversely related to the total mass of the system. When more mass is added to an object, it becomes more difficult to accelerate at a proportional rate.
The y-intercept is the acceleration when mass = 0. The y-intercept does not exist because no object can have a mass of zero. Objects must have mass and take up space to exist.
Conclusion
Ultimately, when no unbalanced forces are added to an object, the object will not accelerate. When net forces acting on the object are constant, but mass increases, acceleration decreases. Such results could be used for most situations in which motion of objects is involved. If a plane is flying at a constant velocity, it will keep flying at that constant velocity unless another force acts upon it. However, if an enormous gust of wind were to propel the plane forward, the plane would accelerate, but, if hypothetically, 100 extra people appeared in the plane, the rate of acceleration would substantially decrease. Acceleration decreases proportionally to the added mass of those 100 people as is in line with Newton's 2nd Law. Two of the biggest uncertainties had to do with how the A value was not exactly equal to the value of net force (N). What is likely at play for them not being precisely the same is likely errors in the aged sensor detectors and LoggerPro, as both programs can stray away from accuracy at times. Human error in measuring weight, properly dispersing it, and starting and stopping the cart also likely resulted in slightly less precise results. Improving the investigation may involve finding a larger variety of individual weights, so that we could have increased the net force in equal increments, or possibly using a robot to stop the object.