A definition of the problem and selection of variables:
How does the acceleration of an object depend on the net forces acting upon it? The independent variable is net force, the dependent variable is acceleration, and total mass of the system is the primarily controlled variable. Other controlled variables are that this takes place on the same planet with the same cart on the same track
The controlling variables:
The total mass of the system is held constant by transferring the additional black weights that were on the cart to the hanger, keeping the mass within the pulley-system of the cart, hanger, pulley, string, and added mass. This prevents the addition of a confounding variable that might prevent the real cause of the results from coming into fruition.
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
The independent variable was measured before hand by taking the mass of the hanger. This could then be calculated to net force via the equation Force of Gravity = Mass*Gravitational Acceleration Constant, where net force is the force of gravity. 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 taken off the cart and moved to the hanger, keeping the overall mass of the system constant, while changing the net force pulling on the cart. 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 net forces acting upon it? The independent variable is net force, the dependent variable is acceleration, and total mass of the system is the primarily controlled variable. Other controlled variables are that this takes place on the same planet with the same cart on the same track
The controlling variables:
The total mass of the system is held constant by transferring the additional black weights that were on the cart to the hanger, keeping the mass within the pulley-system of the cart, hanger, pulley, string, and added mass. This prevents the addition of a confounding variable that might prevent the real cause of the results from coming into fruition.
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
The independent variable was measured before hand by taking the mass of the hanger. This could then be calculated to net force via the equation Force of Gravity = Mass*Gravitational Acceleration Constant, where net force is the force of gravity. 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 taken off the cart and moved to the hanger, keeping the overall mass of the system constant, while changing the net force pulling on the cart. The acceleration of the cart prior to being caught was recorded via the slope of the LoggerPro graph.
Raw Data: what was initially collected
Processed Raw Data: Net Force = Hanger Mass (kg) * 9.8m/s/s
Presented Processed Data and Interpretation
Acceleration (m/s/s) = A*Net Force (N)
Total Mass was kept constant at 1.18 kg. 1/1.18 = .8474. The slope of the graph was roughly .65 m/s^2/N. These constant values are significantly close, and thus it can be surmised that the slope of the acceleration vs Net Forces graph is the reciprocal of the total mass of the system.
Our results are in line with Newton's 2nd Law of Acceleration, net force, and mass. The slope is acceleration/net force (m/s^2/N) which is 1/mass because acceleration is proportional to the net force acting on a system, and inversely related to the total mass of the system.
The y-intercept is the acceleration when Net Force = 0. The y-intercept is 0 m/s/s because of Newton's law of inertia: objects at a constant velocity (including 0) will stay constant unless an unbalanced force acts upon them. In this case, there is zero unbalanced forces acting upon the cart when Net Force = 0.
Conclusion
Ultimately, when an unbalanced force is added to a object, the object accelerates. More net force leads to a linear increase in acceleration, as shown by the graph with a constant slope. The slope of a graph of acceleration vs net forces is equal to the reciprocal of the total mass of the system. 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. For instance, if an enormous gust of wind were to propel the plane forward, the plane would accelerate. The amount that plane accelerates divided by the net force in newtons acted upon the plane is equal to the reciprocal of the plane's mass as is in line with Newton's 2nd Law. Two of the biggest uncertainties had to do with how the slope of the graph was not equal to the reciprocal of mass. 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
Acceleration (m/s/s) = A*Net Force (N)
Total Mass was kept constant at 1.18 kg. 1/1.18 = .8474. The slope of the graph was roughly .65 m/s^2/N. These constant values are significantly close, and thus it can be surmised that the slope of the acceleration vs Net Forces graph is the reciprocal of the total mass of the system.
Our results are in line with Newton's 2nd Law of Acceleration, net force, and mass. The slope is acceleration/net force (m/s^2/N) which is 1/mass because acceleration is proportional to the net force acting on a system, and inversely related to the total mass of the system.
The y-intercept is the acceleration when Net Force = 0. The y-intercept is 0 m/s/s because of Newton's law of inertia: objects at a constant velocity (including 0) will stay constant unless an unbalanced force acts upon them. In this case, there is zero unbalanced forces acting upon the cart when Net Force = 0.
Conclusion
Ultimately, when an unbalanced force is added to a object, the object accelerates. More net force leads to a linear increase in acceleration, as shown by the graph with a constant slope. The slope of a graph of acceleration vs net forces is equal to the reciprocal of the total mass of the system. 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. For instance, if an enormous gust of wind were to propel the plane forward, the plane would accelerate. The amount that plane accelerates divided by the net force in newtons acted upon the plane is equal to the reciprocal of the plane's mass as is in line with Newton's 2nd Law. Two of the biggest uncertainties had to do with how the slope of the graph was not equal to the reciprocal of mass. 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