The motion is continued until friction comes in contact and slows it down. Some of the physical independent variables of the simple pendulum are the length from the point it pivots, the angular displacement, two different masses of the bob, which is the time it takes the pendulum to complete the vibration. Formulas F = -mgsinθ, This formula explains the Force being up on the oscillating pendulum. The mass times the gravitational pull times the angle at which the pendulum starts at rest. It can be expressed as F= -mgθ because sinθ and θ are very close together in terms of radians.
The second block was tested on an inclined plane, and the angle was found at which the block would move at a constant velocity. The angle found was 230. Using the equation μk=tan θk we found the friction to be 0.42. The friction was different because there was more force required to keep the block sliding down the plane at a constant velocity. Introduction Frictional forces are universal, in which they are found between two solid surfaces in parallel contact.
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.
For most purposes Newton's laws of gravity apply, with minor modifications to take the general theory of relativity into account. 2. Inertia - A property of matter by which it continues in its existing state of rest or uniform motion in a straight line, unless that state is changed by an external force. 3. Potential Energy - Is the energy stored in an object due to its position in a force field or in a system due to its configuration.
The jogger’s head just moves up and down, forcing the ponytail to do so also. We show in two ways that this vertical motion is unstable to lateral perturbations. First we treat the ponytail as a rigid pendulum, and then we treat it as a ﬂexible string; in each case, it is hanging from a support which is moving up and down periodically, and we solve the linear equation for small lateral oscillation. The angular displacement of the pendulum and the amplitude of each mode of the string satisfy Hill’s equation. This equation has solutions which grow exponentially in time when the natural frequency of the pendulum, or that of a mode of the string, is close to an integer multiple of half the frequency of oscillation of the support.
Centripetal Force is the radial force which acts ON a rotating mass and Centrifugal Force is the radial force which is exerted BY a rotating mass. (1b) Centripetal Acceleration is the inwards acceleration necessary to maintain circular motion. If a point moves at uniform speed in a circular path, its direction is continually changing and, therefore, though its speed is constant its velocity is changing. Acceleration is defined as “rate of change of velocity with respect to time” Centripetal Acceleration (a) = v² (Linear Velocity) r Centripetal Acceleration (a) = w²r (Angular Velocity) (2)a Mass 1000kg (m) Radius of Curve 45m (r) Coefficient Friction 0.7 (u) Track of Vehicle 1.5m (d) Centre of Gravity 0.68m (h) Acceleration (force of gravity) 9.81 m/s² (g) Without skidding outwards, Centrifugal force = Frictional resistance to skidding = m v² = u m g r Max Speed v = √u g r =√ 0.7 x 9.81 x 45 =√ 309.015 = 17.5788 m/s Convert to km/h = (17.5788m/s x 3.6) = 63.3 km/h Without overturning, Overturning moment = Righting moment = m v²h = m g d r 2 Max Speed V = √g r d 2 h =√ 9.81 x 45 x 1.5 2 x 0.68 =√ 225.1395 = 15.0046 m/s Convert to km/h = (15.0046m/s x 3.6) = 54 km/h (2)b Rotating Bobs 250g (each) Spring Strength 8 kN/m Centre Mass of Bob 160mm radius (resting) Balance of forces = F + R = Mw²r At Engagement, F = Stiffness x Extension = 8 x 1000 x
[pic] As he tried his approach with inclined planes of different angles, he discovered that the acceleration changed. He asserted that as the angle of the inclined plane approached 90°, the acceleration approached our current value of g. Thus, he related acceleration due to gravity with the sin of the angle of the plane. a = g sin θ More importantly, he found that all bodies, regardless of weight, fall with the same uniform acceleration. The Experiment: [pic] Determining g on an Incline Purpose To use a motion detector to obtain the speed and acceleration of a cart rolling down an incline. To determine the free-fall acceleration g from a graph of acceleration vs. sine of track angle.
The further an object is from its axis of rotation, the further its linear speed. If the center of your back is the axis of rotation, the further your hold your stick out and whip it forward will cause the release of the ball to travel faster. The arms with the stick in hand act as a series of levers which propels the ball forward. Your feet causing friction with the ground allows you to twist your body and transfer the energy from linear momentum to rotational momentum. This allows your body to coil and transfer more kinetic energy into the shot.
Lab #2 Acceleration Mikaila Richards Lab partner: Christina Langone October 17th, 20th, 22nd, 2014 I. Introduction: The purpose of this lab was to design and perform an experiment that proves the hypothesis: An object in free fall moves with constant acceleration. Then determine a value of the acceleration in m/s⌃2. II. Equipment and Materials: * Gravity drop apparatus * Metal ball * Micrometer with the uncertainty of ± 0.1mm * Infrared light timers with an uncertainty of ± 0.0001s III.