University physics experiment course design experiment report
Northern University for Nationalities
University physics experiment
experimental report
Instructor: Wang Jianming
Name: Zhang Guosheng
Student number: XX0233
Academy: School of Information and Computing Science
Class: 05 credits 2 classes
Determination of gravity acceleration
First, the experimental task
Accurate measurement of gravity acceleration in Yinchuan area
Second, the experimental requirements
The relative uncertainty of the measurement results does not exceed 5%
Third, the establishment and comparison of physical models
It is initially determined that there are six model schemes:
Method one, measuring with a dot timer
The instruments used are: dot timers, rulers, iron frames with wallets, paper tapes, clips, heavy objects, student power supplies, etc.
Use the principle of free fall to make the heavy object move freely. Select the ideal paper tape, find the starting point 0, count the p point of time t, and measure the distance of op with the meter ruler as h, where t=0.02 second× The number of two-point interval. From the formula h=gt2/2, g=2h/t2, and the measured substitution can be obtained.
Method 2, measuring the gravity acceleration by dripping method
Adjust the faucet valve to make the water drop drop at the same time. Use the stopwatch to measure the time t for the n water drops. Then the interval between each two water drops is t'=t/n, and the distance drop h of the water drop is measured by the meter rule, by the formula h= Gt'2/2 can get g=2hn2/t2.
Method 3, taking a glass with radius r, containing a suitable liquid, fixed on the rotating table. The rotating table rotates at an angular speed ω around its axis of symmetry, and the shape of the liquid relative to the glass is a rotating paraboloid.
The formula for calculating the gravitational acceleration is derived as follows:
Take any liquid element a on the liquid surface, it is x from the rotation axis, the mass is m, subject to gravity mg, elastic force n.
Ncosα-mg=0
Nsinα=mω2x
Compared with the two equations, tgα=ω2x/g, and tgα=dy/dx, ∴dy=ω2xdx/g,
∴y/x=ω2x/2g. ∴ g=ω2x2/2y.
The coordinates x, y of a point in the Cartesian coordinate system perpendicular to the symmetry axis and the lowest point of the symmetry axis are measured, and the turntable rotation speed ω is substituted to obtain g.
Method 4, photoelectric control timing method
Adjust the faucet valve to make the water drop drop at the same time. Use the stopwatch to measure the time t for the n water drops. Then the interval between each two water drops is t'=t/n, and the distance drop h of the water drop is measured by the meter rule, by the formula h= Gt'2/2 can get g=2hn2/t2.
Method 5, using a cone pendulum measurement
The instruments used are: meter ruler, stopwatch, single pendulum.
Make the pendulum of the pendulum move in a uniform circular motion in the leveling surface, measure the h with a ruler, and measure the time t used for the n-turn of the pendulum cone with a stopwatch, then the angular velocity of the pendulum cone ω=2πn/t
The pendulum cone makes a centripetal force f=mgtgθ for uniform circular motion, and tgθ=r/h, so mgtgθ=mω2r is obtained by the above formula:
g=4π2n2h/t2.
Substituting the measured n, t, h into the g value can be obtained.
Method six, single pendulum method to measure gravity acceleration
When the swing angle is small, the swing period is:
then
By comparing the above six methods, I would like to try to use the photoelectric control timing method to measure, but because the laboratory equipment is not complete, the method can not be carried out; for several other methods, the gravity acceleration principle is measured by the single pendulum method. The method is relatively simple and familiar, and the instrument is also very complete in the laboratory, so the method is used to measure the most smoothly, so that more accurate values can be obtained.
4. Using model six to measure gravity acceleration using a single pendulum method
Summary:
Gravity acceleration is an important parameter in physics. The value of gravitational acceleration in various regions of the Earth varies slightly with the geographic latitude of the area and the height of the relative sea level. Generally speaking, the value of gravity acceleration is the smallest near the equator. The closer to the north and south poles, the larger the value of gravity acceleration is, and the difference between the maximum value and the minimum value is about 1/300. Studying the distribution of gravity acceleration is of great significance in geophysics. Using special instruments, carefully survey the distribution of gravity acceleration in various regions, and also detect underground resources.
Galileo observes the slow swing of a holy lamp in the Cathedral of Pisa, and uses his pulse-pulse action to calculate the time of the holy light swing for the timer. He finds that the continuous swinging holy light has the same interval of each swing, and the holy The amplitude of the lamp swing has nothing to do, and the results of the observation are further confirmed by experiments, which lays a foundation for the single pendulum as a timing device. This is the isochronism principle of a single pendulum.
It is simple and convenient to use a single pendulum to measure the acceleration of gravity, because the vibration period of a pendulum is determined by the nature of the vibration system itself, that is, determined by the gravitational acceleration g and the pendulum length l. It is only necessary to measure the pendulum length and measure the period of the oscillation. The g value can be calculated.
experiment equipment:
Single pendulum device, steel tape measure, vernier caliper, computer universal counter, photoelectric door, single cycloid
Experimental principle:
The pendulum is composed of a lightweight thin wire that cannot be stretched and a heavy ball suspended at the lower end of the wire. Under the condition that the length of the pendulum is larger than the diameter of the ball and the mass of the pendulum cone is much larger than the mass of the wire, the suspended ball is pulled to the side from the equilibrium position, and then released, and the pendulum cone is periodically reciprocated at the equilibrium position, such as Figure 2-1 shows.
f =p sinθ
f
θ
t=p cosθ
p = mg
l
Figure 2-1 Schematic diagram of the pendulum
The force f of the pendulum is the resultant force of gravity and rope tension, and f points to the equilibrium position. When the swing angle is small, the arc can be approximated as a straight line, and f can also be approximated as being along this line. Set the pendulum length to l, the ball displacement to x, and the mass to m.
Sinθ=
f=psinθ=-mg =-m x
From f=ma, we know that a=- x
The negative sign in the formula indicates that f is opposite to the direction of displacement x.
The motion of a single pendulum with a small swing angle can be approximated as a simple harmonic motion, and the harmonic vibration formula is compared: a= =-ω2x
Available ω=
So the single pendulum motion cycle is:
t=2π/ω=2π
T2= l
Or g=4π2
When using the single pendulum experiment to measure the gravitational acceleration, a fixed pendulum length l is generally used. After repeatedly measuring the period t of the pendulum, the local gravitational acceleration g can be obtained by substituting the type.
It can be seen from the formula that there is a linear relationship between t2 and l, and its slope. If the respective periods are measured for different pendulum lengths, the gravitational acceleration g can be obtained by using the slope of the t2-l line.
Test conditions and error analysis:
The above formula for measuring the g of the pendulum is based on the formula. The establishment of this formula is conditional, otherwise the measurement will produce the following systematic errors:
1. The relationship between the swing period of the pendulum and the swing angle can be compared by measuring the period values of the two different swing angles θ1 and θ2 when θ<5°. Within the measurement accuracy range of this experiment, it is verified that t of the single pendulum is independent of θ.
In fact, the period t of the pendulum increases as the swing angle θ increases. According to the vibration theory, the period is not only related to the pendulum length l, but also related to the angular amplitude of the oscillation. The formula is:
t=t0[1+2sin2 +2sin2 +...]
Where t0 is the period when θ is close to 0o, that is, t0=2π
2. The mass of the suspension wire m0 should be much smaller than the mass m of the pendulum cone. The radius r of the pendulum cone should be much smaller than the pendulum length l. In fact, any single pendulum is not ideal. It can be proved by theory that considering the influence of the above factors, The swing period is:
3. If considering the buoyancy of the air, the period should be:
Where t0 is the swing period of the same single pendulum in vacuum, ρ air is the density of air, and ρ pendulum cone is the density of the pendulum cone. It can be seen from the above formula that the pendulum cycle is not independent of the pendulum cone material, when the pendulum cone density is very small. Greater impact.
4. The viscous resistance of the air and the friction caused by other factors are ignored. In fact, when the pendulum swings, due to the existence of these frictional resistances, the pendulum is not simply harmonically vibrated but damped to increase the period.
The errors caused by the above four factors are systematic errors, and the conditions required by the theoretical formula are not well satisfied in the experiment, so they belong to the theoretical method error. In addition, the instruments used are such as thousands
University physics experiment
experimental report
Instructor: Wang Jianming
Name: Zhang Guosheng
Student number: XX0233
Academy: School of Information and Computing Science
Class: 05 credits 2 classes
Determination of gravity acceleration
First, the experimental task
Accurate measurement of gravity acceleration in Yinchuan area
Second, the experimental requirements
The relative uncertainty of the measurement results does not exceed 5%
Third, the establishment and comparison of physical models
It is initially determined that there are six model schemes:
Method one, measuring with a dot timer
The instruments used are: dot timers, rulers, iron frames with wallets, paper tapes, clips, heavy objects, student power supplies, etc.
Use the principle of free fall to make the heavy object move freely. Select the ideal paper tape, find the starting point 0, count the p point of time t, and measure the distance of op with the meter ruler as h, where t=0.02 second× The number of two-point interval. From the formula h=gt2/2, g=2h/t2, and the measured substitution can be obtained.
Method 2, measuring the gravity acceleration by dripping method
Adjust the faucet valve to make the water drop drop at the same time. Use the stopwatch to measure the time t for the n water drops. Then the interval between each two water drops is t'=t/n, and the distance drop h of the water drop is measured by the meter rule, by the formula h= Gt'2/2 can get g=2hn2/t2.
Method 3, taking a glass with radius r, containing a suitable liquid, fixed on the rotating table. The rotating table rotates at an angular speed ω around its axis of symmetry, and the shape of the liquid relative to the glass is a rotating paraboloid.
The formula for calculating the gravitational acceleration is derived as follows:
Take any liquid element a on the liquid surface, it is x from the rotation axis, the mass is m, subject to gravity mg, elastic force n.
Ncosα-mg=0
Nsinα=mω2x
Compared with the two equations, tgα=ω2x/g, and tgα=dy/dx, ∴dy=ω2xdx/g,
∴y/x=ω2x/2g. ∴ g=ω2x2/2y.
The coordinates x, y of a point in the Cartesian coordinate system perpendicular to the symmetry axis and the lowest point of the symmetry axis are measured, and the turntable rotation speed ω is substituted to obtain g.
Method 4, photoelectric control timing method
Adjust the faucet valve to make the water drop drop at the same time. Use the stopwatch to measure the time t for the n water drops. Then the interval between each two water drops is t'=t/n, and the distance drop h of the water drop is measured by the meter rule, by the formula h= Gt'2/2 can get g=2hn2/t2.
Method 5, using a cone pendulum measurement
The instruments used are: meter ruler, stopwatch, single pendulum.
Make the pendulum of the pendulum move in a uniform circular motion in the leveling surface, measure the h with a ruler, and measure the time t used for the n-turn of the pendulum cone with a stopwatch, then the angular velocity of the pendulum cone ω=2πn/t
The pendulum cone makes a centripetal force f=mgtgθ for uniform circular motion, and tgθ=r/h, so mgtgθ=mω2r is obtained by the above formula:
g=4π2n2h/t2.
Substituting the measured n, t, h into the g value can be obtained.
Method six, single pendulum method to measure gravity acceleration
When the swing angle is small, the swing period is:
then
By comparing the above six methods, I would like to try to use the photoelectric control timing method to measure, but because the laboratory equipment is not complete, the method can not be carried out; for several other methods, the gravity acceleration principle is measured by the single pendulum method. The method is relatively simple and familiar, and the instrument is also very complete in the laboratory, so the method is used to measure the most smoothly, so that more accurate values can be obtained.
4. Using model six to measure gravity acceleration using a single pendulum method
Summary:
Gravity acceleration is an important parameter in physics. The value of gravitational acceleration in various regions of the Earth varies slightly with the geographic latitude of the area and the height of the relative sea level. Generally speaking, the value of gravity acceleration is the smallest near the equator. The closer to the north and south poles, the larger the value of gravity acceleration is, and the difference between the maximum value and the minimum value is about 1/300. Studying the distribution of gravity acceleration is of great significance in geophysics. Using special instruments, carefully survey the distribution of gravity acceleration in various regions, and also detect underground resources.
Galileo observes the slow swing of a holy lamp in the Cathedral of Pisa, and uses his pulse-pulse action to calculate the time of the holy light swing for the timer. He finds that the continuous swinging holy light has the same interval of each swing, and the holy The amplitude of the lamp swing has nothing to do, and the results of the observation are further confirmed by experiments, which lays a foundation for the single pendulum as a timing device. This is the isochronism principle of a single pendulum.
It is simple and convenient to use a single pendulum to measure the acceleration of gravity, because the vibration period of a pendulum is determined by the nature of the vibration system itself, that is, determined by the gravitational acceleration g and the pendulum length l. It is only necessary to measure the pendulum length and measure the period of the oscillation. The g value can be calculated.
experiment equipment:
Single pendulum device, steel tape measure, vernier caliper, computer universal counter, photoelectric door, single cycloid
Experimental principle:
The pendulum is composed of a lightweight thin wire that cannot be stretched and a heavy ball suspended at the lower end of the wire. Under the condition that the length of the pendulum is larger than the diameter of the ball and the mass of the pendulum cone is much larger than the mass of the wire, the suspended ball is pulled to the side from the equilibrium position, and then released, and the pendulum cone is periodically reciprocated at the equilibrium position, such as Figure 2-1 shows.
f =p sinθ
f
θ
t=p cosθ
p = mg
l
Figure 2-1 Schematic diagram of the pendulum
The force f of the pendulum is the resultant force of gravity and rope tension, and f points to the equilibrium position. When the swing angle is small, the arc can be approximated as a straight line, and f can also be approximated as being along this line. Set the pendulum length to l, the ball displacement to x, and the mass to m.
Sinθ=
f=psinθ=-mg =-m x
From f=ma, we know that a=- x
The negative sign in the formula indicates that f is opposite to the direction of displacement x.
The motion of a single pendulum with a small swing angle can be approximated as a simple harmonic motion, and the harmonic vibration formula is compared: a= =-ω2x
Available ω=
So the single pendulum motion cycle is:
t=2π/ω=2π
T2= l
Or g=4π2
When using the single pendulum experiment to measure the gravitational acceleration, a fixed pendulum length l is generally used. After repeatedly measuring the period t of the pendulum, the local gravitational acceleration g can be obtained by substituting the type.
It can be seen from the formula that there is a linear relationship between t2 and l, and its slope. If the respective periods are measured for different pendulum lengths, the gravitational acceleration g can be obtained by using the slope of the t2-l line.
Test conditions and error analysis:
The above formula for measuring the g of the pendulum is based on the formula. The establishment of this formula is conditional, otherwise the measurement will produce the following systematic errors:
1. The relationship between the swing period of the pendulum and the swing angle can be compared by measuring the period values of the two different swing angles θ1 and θ2 when θ<5°. Within the measurement accuracy range of this experiment, it is verified that t of the single pendulum is independent of θ.
In fact, the period t of the pendulum increases as the swing angle θ increases. According to the vibration theory, the period is not only related to the pendulum length l, but also related to the angular amplitude of the oscillation. The formula is:
t=t0[1+2sin2 +2sin2 +...]
Where t0 is the period when θ is close to 0o, that is, t0=2π
2. The mass of the suspension wire m0 should be much smaller than the mass m of the pendulum cone. The radius r of the pendulum cone should be much smaller than the pendulum length l. In fact, any single pendulum is not ideal. It can be proved by theory that considering the influence of the above factors, The swing period is:
3. If considering the buoyancy of the air, the period should be:
Where t0 is the swing period of the same single pendulum in vacuum, ρ air is the density of air, and ρ pendulum cone is the density of the pendulum cone. It can be seen from the above formula that the pendulum cycle is not independent of the pendulum cone material, when the pendulum cone density is very small. Greater impact.
4. The viscous resistance of the air and the friction caused by other factors are ignored. In fact, when the pendulum swings, due to the existence of these frictional resistances, the pendulum is not simply harmonically vibrated but damped to increase the period.
The errors caused by the above four factors are systematic errors, and the conditions required by the theoretical formula are not well satisfied in the experiment, so they belong to the theoretical method error. In addition, the instruments used are such as thousands
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