![]() ![]() 15N and the mean period was found to be 1.375 seconds. The measured minimum value for force was found to be. The period and force were measured from 0-26 seconds, as shown in graph 2, to obtain the minimum value of force and be assured that the period was constant over the course of the trial. The measurements taken from Test 2 were recorded and placed onto graph 2. Percent error between the two values is exceptionally close to 0, thus proving that the fore of tension is equal to the force of gravity added to the force due to centripetal acceleration. The mean value for velocity will be used in equation (8) to calculate the force of tension that should be exhibited by the string. 31 m/s and the mean value for force is 1.91N. Graph 1 shows the data for Force/Time on top and Velocity/Time on the bottom from 16-25 seconds, the time over which the mean values for velocity and force were calculated using the data acquisition software. ![]() The velocity and force were measured from 16-25 seconds, as shown in graph 1, to obtain the mean values. The measurements taken from Test 1 were recorded and placed onto graph 1. Since the centripetal force is mass times velocity squared over the radius of the circle the two formulae, (5) and (9), can be combined: Linear velocity is kept constant in order to maintain a similarly constant angular velocity and can be written in terms of radians where T is the period: When the force of gravity is counteracted, possibly by a horizontal spinning table, then the force of tension on the string is only due to the centripetal force and the second term is equal to 0. The formula for tension is found by isolating it to one side of the equation presented earlier: The only two external forces on the mass are the force due to gravity, – mg, and the force of tension on the string. The two triangles are similar in that (Δ r) (Δ v) and therefore it is also true thatĪ mass, m, attached to a string and set into motion by pulling to angle Θ creates the experimental conditions for a simple pendulum, as shown in Figure II. and, with them being equal in magnitude, and placing the tail of to the head of to get the change in velocity, Δ. radii and are separated by angle Θ and in the limit as Using velocities from figure Ib. Triangles a and b are similar in that they create isosceles triangles with angle Θ, and have equal side lengths. įigure I: Showing the similar triangles made by the velocities of equal magnitude compared to the triangle made by radii separated by angle Θ. Applying this force constantly to the direction of motion will cause the body to remain moving in a uniform circular motion. Thusly, if a force is kept constant perpendicular to the direction of motion then uniform motion along an arc with radius r is achieved. On the contrary, a force applied perpendicular to the direction of motion will only cause a change in the direction, not magnitude. Acceleration, being a quantity calculated by how fast the velocity is changing per unit time, can be expressed as the derivative of velocity giving the equation:Īpplying a force parallel to the direction of motion will cause the velocity to either increase or decrease in magnitude, whereas a force applied to any angle will cause a change in magnitude and direction. The second law states that a body’s force is equal to its mass times its acceleration. The first law states that a body remains in constant uniform motion, or at rest, unless a net force acts upon it. Newton’s laws are used to describe patterns of motion on masses. The large percent difference in the second experiment is due to an error in the experimental procedure. The results of the experiment confirm that the tension caused on the string of the pendulum is the centripetal force in addition to the force due to gravity. 5% whereas the difference in the calculated centripetal force was 18% different. The percentage difference for the calculated tension of the pendulum string and the actual tension is. Tension of the pendulum and centripetal force on the rotating table were calculated using formulae derived from Newton’s first and second law, angular acceleration and angular velocity. The data was then analyzed graphically and mathematical calculations were performed on the graphical data. To acquire data regarding force, period, and velocity of the experimental setups a force sensor and photogate motion sensor were employed. Two experimental conditions were measured using 1) a simple pendulum and 2) a rotating table. In this experiment Newton’s first and second laws of motion were used to study and verify the expression for the force, F, to be provided to mass, m, to execute circular motion. ![]()
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