Uniformly Accelerated Movement Abstract Acceleration is defined as the rate of change of velocity with respect to time in a given direction. Uniformly accelerated movement is movement that always has the same acceleration, meaning that it is a constant force; the force of gravity is the classic example. We will prove that acceleration with a constant force of gravity can help determine velocity and distance at a certain time using derived basic equations. The data collected determines a 3.78% of error that proves the equations are correct, and that its value could have been affected by errors in the process. 1 Introduction Acceleration is defined as the rate of change of velocity with respect to time in a given direction.
Running Lady Experiment Aim: To investigate and observe the differences between constant velocity and increasing and decreasing velocity, by carrying out the Running Lady Experiment. Hypothesis: | Constant Velocity | Increasing Velocity | Decreasing Velocity | Displacement v Time | Displacement Time | Time Displacement | Time Displacement | Velocity v Time | Velocity Velocity Time | Time | Time Velocity | Graph 1: That a constant velocity will equate to a constant increase when graphed as Displacement v Time. That the slope of the graph will remain constant throughout, indicating a steady or constant velocity. Graph 2: That an increased velocity will show a slight curve on a positive slope as the displacement gets slightly increased whilst time is constant, demonstrating increasing velocity situations. Graph 3: That a decrease in velocity will show a slight downward slope toward the middle of the line as displacement decreases as time remains constant.
The direction of acceleration is the same as the direction of the net force. The acceleration of the body is also directly proportional to the net force but inversely proportional to its mass. Newton defined momentum P as the product of mass and velocity. The change in momentum, symbolized by ∆P, is brought about by the impulse acting on the body, F_net ∆t=∆P As ∆t approaches zero, the instantaneous rate of change of momentum is, F_net=lim┬(∆t→0)〖∆P/∆t〗=dP/dt=(d(mv))/dt Since for most object, mass is constant, F_net=m dv/dt Newton’s second law of motion is mathematically expressed as F_net=ma From Newton’s second law T=m_1 a The hanging mass m_1 is also accelerating with the same acceleration due to the net force m_2 a on it. m_2 a=m_2 g-T T=m_2 g-m_2 a Equating the tensions m_1 a=m_2 g-m_2 a m_1 a+m_2 a=m_2 g (m_1+m_2 )a=m_2 g a=(m_2 g)/(m_1+m_2 ) The acceleration is the same acceleration described in the kinematics equation a=2s/t^2 For a body starting from rest, s is the distance traveled by the cart and t is the time of travel.
When an object demonstrates a constant acceleration, the velocity of the object will change either increasing or decreasing with the same rate while traveling in the same direction. During this experiment, we used the equationH=12gt2 . From this equation, h denotes height, g represents acceleration due to gravity (9.8 m/s2), and t stands for time. The variables in this equation are all accounted for with the exception of g. The height is the distance from the bottom of the ball to the top of the pad (measured in meters). The time (t) corresponds to how long it took the ball to travel after being released from the clip to the pad
Because the length of a pendulum L, and the square of the period of the pendulum T2 are directly proportional, we were able to determine g by calculating the slope of the T2 vs L graph. From our calculations, this value turned out to be 10.3m/s2, while the accepted value for the acceleration is 9.8m/s2. Percentage Difference = 10.3−9.8 9.8 = 5.10 % There are a few reasons for the small error in our estimation: 1. There was some uncertainty in measuring the length of the pendulum L.
Because ‘F’ and ‘x’ are directly proportional, a graph of ‘F’ vs ‘x’ is a line with slope ‘k’ A mass on a spring is a simple harmonic oscillator which is an object that oscillates the equilibrium point and experiences a restoring force proportional to the object’s displacement. The time it takes for a spring to complete an oscillation is called the period of oscillation, ‘T’. The period of oscillation of a simple harmonic oscillator that is described by Hooke’s Law is: T=2π√(m/k). This formula shows that as the mass, ‘m’, increases and the spring
Theory Overview In theory, y=yo-1/2gt^2, where y equals height in the vertical direction.Time, symbolized by t, would be the amount of seconds it took an object to fall this vertical distance, and g being the gravitational force of 9.8 acting on it before it hit the ground.Time can be found more directly by using the equation=2yo/g . Y symbolizes the initial velocity in the y or vertical direction. If the ball were traveling along the x-axis or in a horizontal direction, the equation would be x=vt. In the horizontal direction, the force of gravity is not significant factor because the object is already on the ground. However, if an object were shot out of a gun for example , in a horizontal direction , then the force of gravity would directly act upon the object on its descent .
The velocity can be obtained by finding the slope of the graph of position as a function of time. The acceleration can be obtained by finding the slope of the graph of velocity as a function of time. The critical concepts are contained in the equations for motion with constant acceleration in one dimension, as follows: x=x0+vxot+1/2axt2 Equation 1 vx=vx0+axt Equation 2 In these equations, x is the position at time t andx0 is the position at time t=0 of the object; vxis the velocity of the object along the direction of motion, x, at time t, and is the velocity of the object along the direction of motion, x, at time t=0 ; and ax is the acceleration of the object along the direction of motion, x. Uniformly accelerated linear motion is all around us. Architects often consider the safety of the slides by simulating and calculating the acceleration of a child slides down.
For instance, if the velocity of an object were said to be 25 m/s, then the description of the object's velocity is incomplete; the object could be moving 25 m/s south, or 25 m/s north or 25 m/s southeast. To fully describe the object's velocity, both magnitude (25 m/s) and direction (e.g., south) must be told. According to Newton's second law of motion, a body undergoes an acceleration that is directly proportional to the net force exerted on it. Since both these quantities are vectors, this means that the net force and acceleration are in the same direction and their magnitudes are directly proportional to each other. In static equilibrium, a body is not moving.
Newton’s Second Law and the Work-Kinetic Energy Theorem October 13, 2010 Abstract This experiment utilizes an air track first as an inclined plane with the slider accelerating due to gravity and second as a level surface with the slider accelerating due to the pull of an attached free-falling object of known mass. In both cases, the Work performed is calculated based on formulas for mechanical work and for kinetic energy. The two results are compared. The first part yielded an average acceleration of 0.715 m/s2 (a 1.58% error) and the average result for the Work performed was 0.0204 N*m with only a 0.9% difference. The second part suffered critical errors due to improper data and the results are not significant or useful.