Conservation of Energy

1. Target

To find the kinetic friction constant μ according to the conservation of energy principle.

1. Theory

The conservation of energy experiment states that the total energy of an isolated system cannot change—it is said to be conserved over time. Energy can be neither created nor destroyed, but can change form.

Formula: Ek=Ug, W=Fd cos θ=ΔEk

1. Experimental process

The known scalars are the mass of blocks M and m, and the M can be dragged to the left by the block m. However, the only tool we could use is ruler. So we need to calculate the relevant variables to get the expression of the μ.

Step 1: First of all, let the two blocks at rest.

Step 2: Release the m block, when the m block reaches the ground instantly, the first course ends and the M slides distance of h.

Step 3: Then the M still slides length of l to left and stops, this process is considered as the next course.

Step 4: During the two courses, using the law of conservation of energy or work-energy principle, we could get two equations to induce the μ.

1. Data
 M/kg m/kg h/m l/m Theoretical μ Average μ Error/% 1 0.198 0.2925 0.38 0.638 0.3165 0.2947 7.42% 2 0.198 0.2925 0.38 0.674 0.2946 0.2947 -0.01% 3 0.198 0.2925 0.38 0.670 0.2969 0.2947 0.77% 4 0.198 0.2925 0.38 0.673 0.2952 0.2947 0.19% 5 0.198 0.3225 0.38 0.642 0.2906 0.2947 -1.38% 6 0.198 0.3225 0.38 0.602 0.3160 0.2947 7.24% 7 0.198 0.3225 0.38 0.648 0.2871 0.2947 -2.56% 8 0.198 0.3225 0.38 0.646 0.2883 0.2947 -2.17% 9 0.198 0.3225 0.38 0.642 0.2906 0.2947 -1.38% 10 0.198 0.3925 0.38 0.564 0.2919 0.2947 -0.95% 11 0.198 0.3925 0.38 0.573 0.2860 0.2947 -2.95% 12 0.198 0.3925 0.38 0.572 0.2866 0.2947 -2.74% 13 0.198 0.3435 0.38 0.626 0.2853 0.2947 -3.18% 14 0.198 0.3435 0.38 0.606 0.2975 0.2947 0.96% 15 0.198 0.3435 0.38 0.607 0.2969 0.2947 0.75%

1. Result

Assume that the ground UG=0, according to the law of energy conservation, during the first course, we could get:

mgh-μMgh=0.5Mv2

Therefore, μ=(mgh-0.5Mv2)/Mgh

During the second course, according to the work-energy principle, we could get:

μMgl=0.5Mv2

After that it is time for us to figure out the l.

Because μMgl=0.5Mv2,we just change the order of this formula, that is, l=(0.5Mv2)/μMg

1. Error Analysis

During this experiment, there may be some errors occur inevitably. Here are some reasons.

First of all, it is not so appropriate for us to use ruler to measure the displacement driven by M, using ordinary timer can also cause some mistakes.

Secondly, to calculate the kinetic friction constant, we ignore the mass of the cord, and the friction between the cord and the pulley. This error is not so serious, but in a way, it should be put into one of the reasons.

To reduce the errors, I think the best way is to use some instruments that can measure the variables more accurately.