In this lab you will measure one-dimensional motion of an object and determine t

Question

In this lab you will measure one-dimensional motion of an object and determine the relationships that displacement, velocity and acceleration have with time. Apparatus: DataStudio interface, motion sensor, dynamic track with one end bumper and two legs, dynamic cart, 500-g black bar mass, and a 2-inch riser block (pink). Background: An object moving with constant acceleration can be described by the four, one-dimensional kinematic equations: nu = nu_o + at x = 1/2 (nu + nu_o) x = 1/2 at^2 + nu_o t nu^2 = nu_o^2 + 2ax From equation (1 c) it can be seen that if a plot were made of displacement versus time, during constant acceleration, a parabolic curve would result. Velocity (at any point in time) can be measured as the slope of this line. Equation (1a) predicts a linear relationship between velocity and time, as seen below on the velocity/time graph. Acceleration can be determined by measuring the line's slope on a velocity versus time plot. In this lab you will measure the velocity and acceleration of a moving object by measuring the slopes of these two types of plots. In this experiment, what device are you going to use to measure the cart's position and velocity as it moves? From the graph on page one, what is the most useful type of plot to use if you are attempting to measure an object's acceleration? How would you determine acceleration from that graph? If a cart with low friction wheels is given a push on a horizontal track in the (+) direction, what can you say about the cart's acceleration after the push is completed?

Explanation / Answer

3. Device used to measure the cart's position: Motion sensor, Data studio interface

  Device used to measure the cart's velocity: Motion sensor, Dynamic track with one end bumper and two legs, Data studio interface, Dynamic cart, 500g black bar mass.

   Data studio interface is used to collect data on the position of the cart (its distance from the motion detector) at regularly spaced instants in time as the cart moves with the low-friction wheels. From this set of distance-versus-time data, data studio interface will calculate approximate values for the velocity and the acceleration at each sampled time and will plot the velocity and the acceleration of the cart as functions of time.

4. The most useful type of plot used to measure an object's acceleration is the second graph, i.e.,

Velocity versus Time graph.

   Here the acceleration can be determined by measuring the linear straight line's slope as shown in the

   Velocity versus Time graph. Determine the average acceleration by dividing the change in velocity by the

change in time.

5. There appears to be a linear relationship between the acceleration and the applied force. The cart will accelerate in the direction of the net force acting on it. So if the cart moves in a direction we call "forward", then a net force in the positive direction ("forward") will cause it to accelerate in the positive direction (forward).

Please note that the cart is moving with low friction wheels. So, the frictional force has no major impact on acceleration.

During the initial push of the cart, the cart is speeding up. The sign of acceleration will be the same as the sign of velocity. Velocity is positive because the cart is pushed on a horizontal track in positive direction. Therefore, the acceleration is positive. After the push is removed, the cart remains at constant acceleration unless it is blocked by any other object or no other forces are acting on it.

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