Question

In the given roller coaster, the car is at rest at P and posses maximum Potential Energy of 5000 J a. What will be its Kinetic Energy at Q? b. When the Potential Energy at R is 2400 J, what will be its Kinetic Energy at R c. At S, when Kinetic Energy is 3200 J, what will be the Potential energy at S? d. What is the total ME at P, Q, R and S? *Please Answer Fast* Only correct answer will get the marks So, please answer me ​

Answer 1

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$1.5 \: kj$

Answer 2

Answer:

The kinetic energy at Q is 5000 J and at point R is 2600J.

The potential energy at S is 1800J.

The total energy at every point remains constant.

Explanation:

Given the potential energy at P is the maximum, $P.E = 5000 J$

a) The point Q is the ground level, therefore the potential energy at this point is zero.

Following the principle of conservation of energy, the energy at point Q will be the kinetic energy.

If $P.E = 5000 J$, then $K.E=5000 J$

b) The potential energy at point R is 2400 J

The change in the potential energy from point P to R is

$\triangle PE=2400-5000=-2600J$

By conservation of energy, change in the potential energy is equal to change in the kinetic energy.

Therefore, $\triangle PE=\triangle KE=-2600J$

Since the initial kinetic energy is zero, therefore the kinetic energy at point R is

$0-(-2600)=2600 J$

The loss in potential energy is the gain in kinetic energy.

c) At S, given the kinetic energy is 3200 J

Maximum kinetic energy is at point Q.

The change in the kinetic energy from point Q to S is

$\triangle KE=3200-2600=600J$

By conservation of energy, change in the kinetic energy is equal to change in the potential energy.

Therefore, $\triangle KE=\triangle PE=600J$

$\triangle PE=PE_R-PE_S=600J$

$\implies 2400-PE_S=600\implies PE_S=2400-600=1800J$

Therefore the potential energy at point S is 1800 J.          

d) The total mechanical energy at a point is the sum  of potential energy and kinetic energy at that point.

The total mechanical energy at point P is only due to potential energy is 5000 J.

The total mechanical energy at Q is only due to kinetic energy is 5000 J.

The total mechanical energy at R is sum of potential energy and kinetic energy, $2400+2600= 5000 J$.

The total mechanical energy at S is sum of potential energy and kinetic energy, $1800+3200= 5000 J$.

The total energy at any point is 5000J.

Therefore, the total energy at every point remains constant.

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