Question

Calculate the ratio of the total energy at B to the total energy at A and also the ratio from C to B and from D to C. What do these ratios tell you about the conservation of energy?

(TMEB/TMEA) = 1.00408163265
(TMEC/TMEB) = 1.01473577236
(TMEC/TMED) = 1.02846441948
QUESTIONS THAT NEED TO BE ASNWERED:
Is the total mechanical energy conserved between A and B? Explain

Is the total mechanical energy conserved between B and C? Explain

Is the total mechanical energy conserved between Cand D? Explain

Answer 1

The total mechanical energy is conserved between A and B and between B and C. There is a small increase in the total mechanical energy between C and D.

Step-by-step explanation:

The ratio of the total energy at B to the total energy at A is 1.00408163265, the ratio from C to B is 1.01473577236, and the ratio from D to C is 1.02846441948.

These ratios tell us that the total mechanical energy is conserved between A and B, as the ratio is very close to 1. This means that there is no significant change in the total mechanical energy between these two points.

Similarly, the ratio from B to C is also close to 1, indicating that the total mechanical energy is conserved between B and C.

Lastly, the ratio from C to D is slightly greater than 1, suggesting that there is a small increase in the total mechanical energy between these two points. This indicates that some external force is doing work on the system, adding energy to it.

Answer 2

Step-by-step explanation:

The chart of details is given to us.

We have three energies. Potential is due to the position of the body , kinetic due to the motion of the body and mechanical is due to both the sum of potential and kinetic energy.

Now the law of conservation of energy states that when a body moves from one position to another it's total energy is conserved or remains constant.

Same is the case here we see that at different points, A, B, C and D the energy changes forms but the total energy remains the same which is the mechanical energy and thus we get the ratio as 1.00, 1.01, 1.02 ≅ 1.00

The potential energy is calculated using the formula PE= mgh

The kinetic energy is calculated using the form KE= 1/2mv²

The mechanical energy = Kinetic energy + Potential energy

Now at Point A height is 8 m which is maximum and the speed is zero which is the minimum .So the total energy = potential energy

ME= 3136+ 0 = 3136 J

We get the mass from PE

PE= mgh

3136 = m *9.8 *8

3136/627.2=m

m= 49.64 kg

Now at Point B height is 3.9 m which has reduced and so the potential energy reduces and the speed becomes 9 m/s which is the maximum and the kinetic energy at this point is also is maximum. So the total energy = potential energy + kinetic energy

ME= PE+ KE

ME= 1528.8+ 1620 = 3148.8 J

Now at Point C height is 4.2 m which has increased and so the potential energy increases and the speed becomes 8.8 m/s which has reduced and the kinetic energy at this point also reduces. So the total energy = potential energy + kinetic energy

ME= PE+ KE

ME= 1646.4+ 1548.8 = 3195.2 J

Now at point D height is 2 m which is minimum and the speed is 11m/s which is the maximum .So the total energy = potential energy + kinetic energy

ME= PE +KE

ME = 784 + 2420= 3204 J

If we calculate the individual KE and PE at points A,B, C, D using m= 49.64kg we will get different answers to the ones given in the chart. That is because some gradient of the kinetic energy is lost as the frictional force or as limiting friction only a part of the PE or kinetic remains which gives the total mechanical energy.