# Gravitational Potential Energy Lab Report

Superior Essays
Conservation of Mechanical Energy
Anupama Cemballi
Department of Physics, Case Western Reserve University
Cleveland, OH 44106-7079
Abstract:

Gravitation Potential Energy:
Introduction and Theory:
Gravitational potential energy is the potential energy an elevated object has due to the force of gravity. Potential energy is the stored energy an object has dependent upon its position. Near the surface of the Earth, the gravitational acceleration of an object is 9.8m/s^2. There is no uncertainty associated with this value since it has been measured countless times. The factors that affect the gravitational potential energy include m, mass, and the height of the object to an end point. The work done on an object due to the gravitational force is
I weighed the cart and the mass by placing it on the balance; its mass was 997 grams. The uncertainty was estimated to be ±1 gram. The balance measures to the one’s place; therefore the most the measurement could be off is one gram. I tied a string to the cart and placed it over the wheel and attached the string to the counterweight, which included a weight hanger and weights. I then determined the hanging mass required to make cart move at constant velocity to determine the friction force on the system. I added paper clips to the counterweight and then pushed the cart towards the pulley, during which the photogate measured the speed. I continued to add paper clips until the speed measured was constant on Logger Pro, which recorded the speed of the cart as it was pulled along the track by the falling weight (the counterweight). The mass to balance the friction force was two grams (seven paperclips) with an uncertainty of 1.5 grams. The uncertainty is so large because the mass of the paper clips is so low, and the balance only measures to the one’s place. I then added an additional mass of about 30 grams. The Logger Pro program recorded the motion of the cart after I released it from …show more content…
The graph of energies versus distance (position) is attached. In the graph, the kinetic energy and the potential energy were calculated with grams instead of kilograms, so the values of slope and standard error must be divided by 1000. The best-fit line for total energy, E, is drawn on the graph. Its slope is -0.28263489 J/m with a standard error of 0.00208773 J/m. The uncertainty of ∆E/∆y can be calculated in quadrature using the following equation: δ ∆E/∆y=√((δ_(∆E/(∆y, slope))^2+δ_(∆E/(∆y, m))^2)) (6)
This value is 0.00208773 J/m, or 0.002 J/m, which is the same as the value calculated on Origin. So ∆E/∆y is -0.283±0.002J/m.

Spring Potential Energy:
Introduction and Theory:
Spring potential energy (aka elastic potential energy) is the stored potential energy of a stretched spring. Hooke’s Law states that the displacement of the spring when a force is acting upon it is directly proportional to that force that makes it compressed or extended. The equation below is Hooke’s Law,
F= -kx (7) where F is the force, k is the constant, x is the position. We can substitute in
F=mg (8) where m is mass and g is gravity, into Hooke’s Law, which gives us kx=mg (9)
Equation number (9) can be rewritten as

x=mg/k (10) which gives us the position as a function of the hanging mass. The the slope of the position versus mass graph is g/k,

## Related Documents

• Great Essays

So we can write dU= -F_s.dx Integrating from position 1 to 2 ∫_1^2▒dU=-∫_(x_1)^(x_2)▒〖F_s dx〗 We know that for a liner spring Fs = kx. Now we have U_(1→2)=-∫_(x_1)^(x_2)▒kxdx=-k/2(x_2^2-x_1^2) U_(1→2)=k/2(x_1^2-x_2^2) Eq. 2.4 Where, k = Spring constant (N/m) x1 = deformation of the spring measured from its undeformed length at initial position x2 = deformation of the spring measured from its actual length at final…

• 1828 Words
• 8 Pages
Great Essays
• Great Essays

Substituting in the values, acceleration roughly equals 4.6259 m/s^2. With the acceleration, the force of the falling object is calculable using the formula f = ma, or force is equal to the mass times the acceleration. When the values are substituted in, the formula determines the force to be 5.3105…

• 1212 Words
• 5 Pages
Great Essays
• Superior Essays

The net force here is inclusive of all external forces (Moore). This law of motion is the basis for the entire experiment. Kinematic Chain According to the kinematic chain, if you integrate acceleration, a constant, your result will be a linear function describing velocity. A integreated= aldjf;aijd;flnsd;ifjj If you integrate the velocity function, your result will be a quadratic function describing position. V integalkd;fasdifjaoijfiajweoir;j Experimental…

• 1739 Words
• 7 Pages
Superior Essays
• Great Essays

Buoyancy is the upward force of a liquid which counters the weight of an immersed object. The theoretical buoyancy of an object can be calculated by using the formula B=V(1g/mL) and then converting the units to kilograms and multiplying the answer by the force of gravity which is 9.8 N/kg. Description/Method The idea of this experiment is to understand the relationship between mass, density, and buoyancy,…

• 935 Words
• 4 Pages
Great Essays
• Improved Essays

Based on the Force - Time graph generated by slowly pulling the cart with weights, we get measurement of static and kinetic friction to calculate the coefficients of frictions. From the graph, the maximum static force is peak force value before kinetic friction takes place.Then get µs according to equation fsmax = µs N. From the average kinetic friction from the Force -Time graph and equation fk = µk N, calculate its coefficient. This lab leads to a conclusion that the coefficient of static friction is usually larger than that of kinetic friction. Our experimental value of coefficient of static and kinetic friction for plastic cart is ( 0.183 ± 0.003 ) N and ( 0.098 ± 0.001 ) N. For the cork cart is ( 0.250 ± 0.003 ) N and ( 0.217 ± 0.002 ) N. For the felt cork cart is ( 0.203 ± 0.003 ) N and ( 0.165 ± 0.002 )…

• 1118 Words
• 5 Pages
Improved Essays
• Improved Essays

Newton’s second law of motion states that force is proportional to mass and acceleration. Lastly, Newton’s third law of motion is for every action there is an equal and opposite reaction. Newton’s other major contribution to science was his theory of gravity; law of universal gravitation. Newton’s theory of gravity was that the forces between any objects is equal to their product of the masses, every object’s mass attracts to any other object’s mass in the universe, and is equal to the distance between them. This was also part of Henry Cavendish’s contribution to the Universal Law of Gravity.…

• 824 Words
• 4 Pages
Improved Essays
• Improved Essays

More traditional tools for measuring mass are spring scales and triple beam balances. Discuss in terms of forces and torques how each of these tools can be used to determine the unknown mass of an object. Include in your discussion an explanation as to why mass measurements taken by a spring scale are affected by local variations in gravitational field strength, while those taken by a balance are not. The way a triple beam balance works has to do with the idea that equal masses on each side are being pulled downwards by gravity with equivalent forces. As mentioned before, torque can be obtained by multiplying the mass of the weight, times the force of gravity, times the distance from its pivot point or the fulcrum (T=m*g*l).…

• 1296 Words
• 6 Pages
Improved Essays
• Improved Essays

On the other hand, force or flux are examples of vector valued fields. Furthermore, stress is an example of a rank-two tensor field. Material Point notion If we consider a body with volume ”V” which separates parts of a physical space with its surface “A”, the material point “P” is an internal point in this body which has volume ∆V and mass ∆m. Figure 1 depicts part of a body discretized with material points. Figure 1 Discretization in a material point method simulations Physical properties of materials…

• 1025 Words
• 4 Pages
Improved Essays
• Improved Essays

The Freundlich model can be expressed as [8]: .................................................................................................... (6) where qe mass of adsorbate is adsorbed per unit mass of adsorbent (mg/g), Ce is the equilibrium concentration of adsorbate (mg/l), Kf indicates adsorption capacity and n an intensity factor of the adsorption process , which varies with the heterogeneity of the adsorbent. The adsorption is better favorability when 1/n is to be grater. The fractional values of 1/n ranged between 0 and 1. The constants Kf and 1/n were calculated from the intercept and slope of the plot of ln qe versus ln Ce. Fig.10 shows the linear plot of Freundlich isotherm for adsorption of CV and MB onto fennel seeds.…

• 1209 Words
• 5 Pages
Improved Essays
• Improved Essays

Core 1 Quantitative Assignment 1 Background: When wanting to find the mass of a massive object, the following is needed, Newton’s gravitational law (F = ma = mv2/r). Newton’s gravitational law can be used to calculate the mass which is represented by (M). This can be calculated if the velocity represented by (v), at orbital radius represented by (r), is known for the equation. When these two laws are put together they create the formula M = v2 r / G what G represents is the gravitational constant (6.673 X 10 – 11 m3 Kg – 1 s – 2). For a circular orbit, the velocity (v) is determined by its circumference of (2r) this is divided by the time it takes to complete an entire orbit also referred to as a period (P), this is entirely…

• 701 Words
• 3 Pages
Improved Essays