You will need
- - rangefinder;
- - electronic stopwatch;
If the body falls freely from a height h, measure it with a meter or any other device. Calculate the speed of falling bodies v by finding the square root of the product of the acceleration of free fall at the height of the number 2, v=√(2∙g∙h). If before the beginning of time the body has already had the speed v0, then to the result add to its value v=√(2∙g∙h)+v0.
Example. A body falls freely from a height of 4 m with zero initial velocity. What will be its speed when reaching the earth's surface? Calculate the speed of the falling body formula, given that v0=0. Make the substitution v=√(2∙9,81∙4)≈8,86 m/s.
Measure the time of fall t of a body of the electronic stopwatch in seconds. Find its speed at the end of the period of time that continued movement adding to the initial speed v0 of the product of time and acceleration of free fall v=v0+g∙t.
Example. The stone began to fall with initial speedu 1 m/s. Find its speed after 2 s. Substitute the values of these quantities in the formula v=1+9,81∙2=20,62 m/s.
Calculate the speed of fall of a body thrown horizontally. In this case its movement is the result of two types of motion, in which simultaneously takes part in the body. This uniform motion horizontally and uniformly accelerated vertically. As a result, the body trajectory is a parabola. The speed of the body at any point in time is equal to the vector sum of the horizontal and vertical velocity component. Since the angle between the vectors of these velocities are always direct, to determine the speed of the fall of a body thrown horizontally, use the Pythagorean theorem. The speed of a body is equal to the square root of the sum of the squares of the horizontal and vertical components at this point in time, v=√(v гор2+ v верт2). Vertical component of speed count by the method described in the preceding paragraphs.
Example. A body is thrown horizontally from a height of 6 m with speedu 4 m/s. Determine its speed when hitting the ground. Find the vertical component of velocity when hitting the ground. It will be the same as if the body fall freely from a predetermined height v Vert =√(2∙g∙h). Substitute the value into the formula and get v=√(v гор2+ 2∙g∙h)= √(16+ 2∙9,81∙6)≈11,56 m/s.
Advice 2 : How to find the speed of the fall
The speed of the falling body in the air, unlike the vacuum of space does not only depend on the initial speed, height and free fall acceleration, but air resistance. Because the impact of the latter depends on the shape of the body and difficult mathematical accounting, it is more rational to measure this velocity directly.
You will need
- - a computer with a sound card;
- two solar panels from calculators;
- - the range;
- - building level;
- - lighting fixture.
Connect one of the solar battery from a calculator (the larger can not be used) to the left channel line input of the sound card and the other to the right. Be aware that some sound cards is stereo output only, and input - mono, and, besides, there is power to the microphone. Then connect solar batteries in series, observing correct polarity, a load resistor to 100 ohms and connect to this input via capacitor 0.1 UF - he doesn't miss them a constant component.
Install the computer program Audacity. Position the solar panels at the surface vertically (using a level) at a distance from each other that it is about half the diameter of a falling body. Send them to the illuminator from a distance of about a meter. Run the program. In record mode, make sure that the sudden closing and opening of the solar panels on the waveform there is a significant disturbance.
Turn in Audacity the recording mode. Relieve body down so that it initially blocked one of the solar panels, and then both.
Stop recording. On the waveform (or two waveforms, if your sound card equipped with stereo input) using the built-in program scale, measure the time interval between the peaks of the disturbances. It is expressed in seconds.
A ruler accurately measure the distance between the solar panels. Move it from centimeters to meters. Divide this distance by the time interval, measured using the program Audacity, and you get the falling speed immediately before touch the body surface. It will be expressed in meters per second. If necessary, ensure that it is in other units, such as kilometers per hour (1 km/h = 0,2(7) m/s). Try to compare this rate with the calculated according to the formula V=sqrt(2hg), where V is the velocity, m/s, h - height, m, g - acceleration of free fall, 9,822 m/s2. The smaller will be the measured speed compared to the estimated, the more influence air resistance.
Do not touch both the computer case, the conclusions of radioelements and grounded objects, as well as the housing of the light source.