Conservation of Energy Lab
Purpose:
To explore what happens to the gravitational potential energy, kinetic energy, and total mechanical energy of a cart as it rolls down a ramp.

Hypothesis:
As a cart rolls down a ramp, then its kinetic energy increases because the cart gains speed. As a cart rolls down a ramp, then its gravitational potential energy decreases, because it gets closer to earths surface. As a cart rolls down a ramp, then its mechanical energy is constant, because the increase of kinetic energy and decrease of gravitational energy cancels each other out.

Materials and apparatus: * Eye protection * Ramp * 3-4 textbooks or wood blocks * Meter stick * Motion sensor * Laboratory cart

Procedure: 1) Propped up one end of a ramp using textbooks or wood blocks. Used a meter stick to measure the length of the ramp (L) and the height of the ramp (H). 2) Placed the motion sensor at the top of the ramp, directed toward the bottom. Released the cart from a position near the motion sensor. Obtained the position time graph of the cart as it rolled down the ramp away from the motion sensor. 3) Chose one point on the position-time graph near the end of the run. The position coordinate for this point represented the final position d2 and the reference point that was used to determine the height of the cart. This point did not change throughout the experiment. 4) The ramp itself formed a larger triangle and the displacement of the cart down the ramp formed a smaller, similar triangle.
Using the similar triangles, a formula is formed: (to calculate the height, h, of the cart on the ramp)

5) Determined the speed (v) at any point on the position time graph, by using the slope tool in the program for the motion sensor.

Observations:
Mass of cart- 0.8455 kg
Height of ramp (H)- 0.1745 m
Length of ramp (L)- 0.7545 m Initial position | Variable | | d2 (m) | d1 (m) | △d=d2-d1(m) | h(m) | v(m/s) | Eg(J) | Ek(J) | Em(J) | 1 (accepted) | 0.289 | 0.127 | 0.162 | 0.037 | 0.682 | 0.31 | 0.197 | 0.51 | 2 (measured | 0.289 | 0.153 | 0.136 | 0.031 | 0.736 | 0.26 | 0.229 | 0.49 | 3 (measured) | 0.289 | 0.187 | 0.102 | 0.024 | 0.776 | 0.20 | 0.255 | 0.46 | 4 (measured) | 0.289 | 0.237 | 0.052 | 0.012 | 0.923 | 0.10 | 0.360 | 0.46 |

Discussion: a) The measured values include the height and length of the ramp, the mass of the ramp, d2, d1, v. The manipulated values include: △d, h, Eg, Ek, Em. The relationship between Gravitational potential energy and position, Kinetic energy and position, and total mechanical energy and position were tested and calculated. b)

c) As d1 increases, the gravitational potential energy decreases. Therefore, as the height of the cart decreased, the gravitational potential energy decreased as well, as hypothesized above. As d1 increases, the velocity increases as well. Therefore, the kinetic energy increases as height decreases and as d1 and d2 move closer together. As d1 changes, there’s no effect on the mechanical energy (stays within a small margin of error). d) Gravitational potential energy is not affected by friction, because friction does not affect gravity. However, friction does affect kinetic energy, because friction acts on the wheels of the cart against the ramp and therefore affects the velocity. Total mechanical energy is affected by friction, since both gravitational potential energy and kinetic energy are involved in the total mechanical energy.

f) The hypothesis is correct. Kinetic energy does increase as the cart moves further down the ramp. The gravitation potential energy decreases as the cart moves further down the ramp. The mechanical energy is constant within a margin of error.

g) Kinetic energy increases, gravitational potential energy decreases, and mechanical energy is constant as the cart moves down the ramp. There’s a change in both kinetic and gravitational potential energy. Some of the gravitational energy is changed into kinetic energy. The mechanical energy proves that there’s no energy lost, as it stays constant within a small margin of error. h) The final position must stay fixed so that our calculations have a baseline value. The fixed final position means that our velocity calculations have a constant value (final position), which gives the calculations consistency when calculated later. Each starting position in the experiment gives an instantaneous velocity at that point, which allows us to prove our hypothesis. i) The formula for height is . Distance is determined through the y- axis on the position- time graph. The height and length of the ramp is measured. Therefore, the height of the cart above the final position can be calculated. j) The gravitational potential energy of the cart at the bottom of the ramp will be low, and it will increase as the cart moves up the ramp. The kinetic energy of the cart at the bottom of the ramp will be high, and it will decrease as the cart moves up the ramp. The mechanical energy will remain constant. Therefore, the initial velocity of the cart going up the ramp will be approximately equal to the final velocity of the cart in the original experiment.

Conclusion:
The experiment began with setting up the various apparatus to perform and calculate the recorded values. The experiment involved setting up a static final position, with 4 different starting positions, and releasing a cart down a ramp. The outcome of the experiment gave the gravitational potential energy, kinetic energy, and total mechanical energy at the different start positions.

As the cart moved down the ramp, the kinetic energy increased, the gravitational potential energy decreased, and the mechanical energy stayed constant within a small margin of error. The kinetic energy increased because the velocity increased due to acceleration. The gravitational potential energy decreased because the height decreased due to the distance decreasing from the surface of Earth. The mechanical energy remains constant because the kinetic energy and gravitational potential energy are added together to determine the total mechanical energy. As the height decreases, the gravitational potential energy is converted to kinetic energy, so that the total mechanical energy will be constant.

Source of Error:
Possible sources of error include: air resistance, and friction.
Sources of human error include: applying an external force to the cart, measurements that are not exact, disrupting the motion sensor.

The effect on the experiment of applying an external for to the cart is that it may result in an increased velocity. The effect on the experiment of air resistance and friction is that they both act against the cart, and decrease its velocity. The effect on the experiment of measurements are not measured exact would be that all other calculations would contain a margin of error. The effect on the experiment if the motion sensor is disrupted would result in inaccuracies in the graph.

Prelab:

Conservation of Energy Lab- Pre-lab

Purpose:
To explore what happens to the gravitational potential energy, kinetic energy, and total mechanical energy of a cart as it rolls down a ramp.

Hypothesis:
As a cart rolls down a ramp, then its kinetic energy increases because the cart gains speed. As a cart rolls down a ramp, then its gravitational potential energy decreases, because it gets closer to earths surface. As a cart rolls down a ramp, then its mechanical energy is constant, because the increase of kinetic energy and decrease of gravitational energy cancels each other out.

Materials and apparatus: * Eye protection * Ramp * 3-4 textbooks or wood blocks * meter stick * motion sensor * laboratory cart

Procedure: 6) Propped up one end of a ramp using textbooks or wood blocks. Used a meter stick to measure the length of the ramp (L) and the height of the ramp (H). 7) Placed the motion sensor at the top of the ramp, directed toward the bottom. Released the cart from a position near the motion sensor. Obtained the position time graph of the cart as it rolled down the ramp away from the motion sensor. 8) Chose one point on the position-time graph near the end of the run. The position coordinate for this point represented the final position d2 and the reference point that was used to determine the height of the cart. This point did not change throughout the experiment. 9) The ramp itself formed a larger triangle and the displacement of the cart down the ramp formed a smaller, similar triangle.
Using the similar triangles, a formula is formed: (to calculate the height, h, of the cart on the ramp)

10) Determined the speed (v) at any point on the position time graph, by using the slope tool in the program for the motion sensor.