The oscillating motion of a spring is caused by the stretching or compression of it. As the spring is stretched then released, it will exert a force, pushing back the mass until it reaches its amplitude of its motion. The amplitude can then be used in Hooke’s Law in order to understand the manner in which the spring exerts a force on the mass attached to it which is F=kx; ‘x’ being the equilibrium point, ‘k’ being the spring constant and ‘F’ being the restoring force. Hooke’s law states that the further the spring is stretched from its equilibrium point, the greater the force the spring will exert towards its equilibrium point. 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.
We used a vernier caliper to obtain the diameter of those two and therefore, the radius. When adding all the numbers together, we found that the true radius(r) of the orbit was 0.139 m. To find our tension, we needed to find out how much weight we needed to pull the object towards away from the spring and on the tip of the pointer as shown below. The tension needed to pull the mass on the tip of the pointer 1.05 kg. In theory the force of acceleration needed to pull the mass to same exact spot should equal the force of tension multiplied by the force due to gravity. Using Newton’s second law, F=ma, we know that the
1 Introduction Acceleration is defined as the rate of change of velocity with respect to time in a given direction. It is a vector quantity that is defined as the rate at which an object changes its velocity . An object is accelerating if it is changing its velocity. The next equations describe velocity and acceleration: a = v/s (1) where v = m/ s (2) where m = distance in meters; s = time in seconds. Since acceleration is a vector quantity it has magnitude and direction .
Longitudinal wave The vibrations of the object set particles in the surrounding medium in vibrational motion, thus transporting energy through the medium. For a sound wave traveling through air, the vibrations of the particles are best described as longitudinal. Longitudinal waves are waves in which the motion of the individual particles of the medium is in a direction that is parallel to the direction of energy transport. Sound waves in air (and any fluid medium) are longitudinal waves because particles of the medium through which the sound is transported vibrate parallel to the direction that the sound wave moves. As the vibrating string moves in the forward direction, it begins to push upon surrounding air molecules, moving them to the right towards their nearest neighbor.
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.
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.
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.
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.
The strength, distance, and length of the wind gusts determine how big the ripples become. The crest of a wave is its highest point. Wavelength is the horizontal distance, and wave height is the wave’s vertical distance. The last type of motion is currents. Currents are the ocean’s constant flow of water that is pushed on by either the wind or from tides that are caused by the moon’s gravitational field.