Objective: To study the relationships between position, velocity, and time, with acceleration held constant, of an object moving in one-dimensional motion with minimum friction. A motion sensor will be used to measure various aspects of vector quantities. Description: An Air Track is positioned along the edge of the table. It is a long straight metal beam with many small holes that are roughly each mm in diameter. It is positioned at an angle to allow the gliders to glide down the slope.
A blower pump is placed under the table, and it is connected to the beam, which allows air to blow out from he holes to reduce the friction of a moving object on top of it. At the end of the Air Track there is a Motion Sensor to record the position, velocity, and acceleration of the moving object. There are also two different sized wooden block and two gliders. One of the gliders is gold and the other is red. A meter stick is also provided to record height and length of the given objects. Theory: Velocity is the derivative of a position graph, and acceleration is the derivative of a velocity graph.
When the expression a = dot = DXL/dot is integrated twice with acceleration held constant, it yields two integrations: = ox+vote+l /data v = iv+at These two expressions show the relationship between position, velocity, and acceleration at a given time. Newton’s 2nd law states that the acceleration of an object depends on the net force acting upon the object and the mass of the object. If there were no friction in this experiment, then the acceleration of the glider would be equal to acceleration of gravity multiplied by the angle between the air track and the horizontal table (g x sin Procedure: (3. ) The air track was leveled by placing a glider on the track and adjusting the knob t the end of the air track until the glider did not move. A motion sensor is placed at the end of the raised air track and the grill looks down the track. An index card is stuck at the top of the glider to allow the motion sensor to detect it. Once all of these steps have been completed, the air blower is turned on and the glider is placed on top of the air track 0. Mm from the sensor. Once the glider was released, the Start button on Data Studio was pressed to record the data.
The stop button was pressed just before the glider hit the bottom of the air track. This was done until the points (3. 2) To measure the mass and angle dependence on the glider, the acceleration was measured for a glider of different mass for the same angle (A block was placed underneath the lifted end of the air track). The angle was then changed by another block and was repeated with the other two gliders. (3. 3) To study the relationships between position, velocity, and acceleration closely, we repeated the previous procedure but let the glider hit the end of the track 3 times before clicking the stop button.
Data and Calculations: Length of air track: 126. 5 CM Thickness of block 1: mm Thickness of block 2: mm Angle between air track and the horizontal table: With block 1: sin B = opposite/hypotenuse = 3/126. 5 B = 0. 02372 radians With Block 2: sin B = opposite/hypotenuse = 2/126. 5 B = 0. 01581 radians Mass of glider 1: 271. G Mass of glider 2: 300. G Error Analysis: Our data is affected by the accuracy of the motion sensor and the air track. Some factors that might have affected our data from the motion sensor are temperature, humidity, air circulation of the room, and background noise.
The lab environment where we tested our experiments might not have been an ideal environment. Other factors that could have affected our data are from the uncertainties from the air track and the gliders. Damage to the air track or the gliders might have slowed down the gliders as it went down the ramp. There could have been a problem with the air blower in which it did not blow enough area for the gliders to slide down smoothly with little resistance from friction. Conclusions: We studied the relationship between position, velocity, and acceleration with respect to time.
The experiment showed that the velocity curve is nosier than the position curve, and the acceleration curve is nosier than the velocity curve because the velocity is the derivative of position and acceleration is the derivative of velocity. This results in acceleration to be more sensitive than velocity and velocity to be more sensitive than position graph. As the object moves along the ramp and bounces back as it hits the bottom of the ramp, position is simply calculated by the glider’s distance away from the motion sensor.
However, velocity takes into account the more insensitive factors such as when the glider speeds down or slows down the ramp due to friction and tension. The acceleration is the derivative of the velocity graph so that The slope of a velocity graph gives the acceleration because acceleration is the change in velocity with respect to time. F = ma; m=mass, a-?acceleration As the mass of an object increases, the force of the object also increases. The heavier glider sped down the ramp because of its greater mass; the object has more force going down the ramp. F=MGM*sin B ; g=force of gravity
When the angle of the ramp was increased, this resulted in the gliders to roll down the ramps faster. This is because as the angle increases, the force of the object going down the ramp also increases. As the force of the object going downhill increase, the momentum increases and the In the last experiment where we allowed the gliders to bounce three times before we hit the stop button, we noticed that the velocity curve crossed the axis when the glider hit the end of the ramp and bounced up. This is due to the reason that when the glider bounced back, it moved in the negative direction.