The purpose of this experiment is to find this acceleration for a puck moving on an inclined air table.

Transcription

1 Experiment : Motion in an Inclined Plane PURPOSE The purpose of this experiment is to find this acceleration for a puck moving on an inclined air table. GENERAL In Experiment-1 you were concerned with the motion in which a puck on an air table was moving along the x-axis with a constant velocity and you found a linear relationship between the displacement and the time for this motion. In this experiment we will consider the motion of a puck moving in a straight line in such a way that its velocity changes uniformly (at the same rate). Consider an air table whose backside is raised so as to form a smooth (frictionless) inclined plane, as shown in Fig.3-1a. If we put a puck at the top of the incline and allow it to move down, we observe that the puck still moves in a straight path, but the dots produced on the data sheet are no longer evenly spaced, as shown in Fig.3-1b. This means that, the puck s velocity increases as it goes down the incline. If the velocity of the puck changes with time, we say that it has acceleration. Just as the velocity is the rate of change of position, acceleration is the rate of change of the velocity. Experiment Paper Puck Air table (inclined) x (angle of inclination) 5 x (a) (b) FIGURE -1. (a) The set up for a puck moving down an inclined air table. (b) The dots produced by the puck on the data sheet.

2 Note that, the positive x-axis is taken to be in the direction of the puck s motion. The type of motion that you have observed is straight-line motion with constant acceleration. Suppose that at time t 1 the puck is at point A and has velocity v 1 and that at a later time t it is at point B and has velocity v. The average acceleration of the puck in the interval t is defined as: a v v v av t t t 1 1 (-1) Similar to the definition of the instantaneous velocity, the instantaneous acceleration (or simply the acceleration) of the puck in the x-direction is: a lim t 0 v t dv dt (-) The acceleration is also a vector quantity and is always in the direction of v. It may or may not be in the direction of motion. (In the above equation, the vector sign was suppressed, however, since we have one-dimensional motion, the positive x-axis was taken to be along the direction of motion.) Suppose that at the time t 1 =0, the puck is at position x 0 and has velocity v 0, and that at a later time t =t it is at position x and has velocity v. If the acceleration of the puck is constant, the average acceleration and the instantaneous acceleration are equal to each other, and therefore we find a v v 0 t 0 (-3) or, v v0 at (-4)

3 The expression for the position x of the puck as a function of time can be written as 1 x x0 v 0 t at (-5) where x 0=x(t=0) is the position of the puck at t=0. This equation may easily be checked by taking the derivative dx dt equation for the velocity v (Eq.(-4)). and comparing it with the If the puck starts from rest (v 0 =0), then its position at any instant of time is given as 1 x x0 at (-6) Therefore if the graph of x versus t is plotted, we obtain a straight line that has a slope 1 a and intercept x 0. If, in addition, x 0=0, then this straight line will pass through the origin. EQUIPMENT An air table, a puck shooter, wooden blocks (to tilt the air table to the desired angle of inclination), a ruler, millimetric graph paper. PROCEDURE 1. Put the puck at the top of the inclined plane of the air table. Activate only the (P) switch. Check that the puck falls freely down the plane. Set the sparktimer frequency to 0 Hz. (If the dots you get with f=0 Hz. turn out to be inconvenient for analysis, you can switch to 10 Hz.). Put the puck at the top of the inclined plane. Put the (P) and (S) switches on top of each other and activate them simultaneously. Take your foot off the switches when the puck reaches the bottom of the inclined plane.

4 . Remove the data sheet from the air table and examine the dots produced on it. Have your data approved by your instructor. Take the trajectory of the puck as the positive x- axis. Number the data points starting from the first dot as 0,1,,...,5. Take x=0 and t=0 at the first dot, and measure the distance of the remaining four dots from the dot 0. Also determine the time t for each of these dots. Fill in your data in Table -1 below along with their corresponding measurement errors. 3. Using the data in Table -1, plot x versus t graph on a linear graph paper. Draw best and worst lines, and find the acceleration a a of the puck. 4. Using the data in Table -1, plot log(x) versus log(t) graph on a linear graph paper. Draw graph line, and calculate the slope of the graph line and find the acceleration of the puck. Write the mathematical expression between x and t. DATA & RESULTS 1. How do the dots you got in this experiment differ from those you got in Experiment 1? What type of motion did you have in each of these experiments?. Fill in your data in the table below. Report your measurements with the correct number of significant figures and include the errors.

5 Dot number x x (cm) Log(x) t t (sec.) Log(t) t t (sec ) Table In the space provided below show how to find the error (t ) in t for only one data point.

6 In the space provided below report the slopes of the best and worst lines of the x-t graph with the correct number of significant figures. m b = cm/sec m w = cm/sec 5. Find the acceleration of the puck along with its error from the slopes above and record it with the correct number of significant figures. a a = cm/sec Comments and Discussion: Write down any comments related to the experiment, and/or elaborate on and discuss any points (if there are any):

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