A particle B of mass 10g is shot vertically upward from a point O with velocity 10m/s. The horizontal plane containing O is the reference level of the gravitational potential energy .Neglect all air effects.

a) Calculate the mechanical energy of the system at O.
b) Calculate the mechanical energy of the system at the highest point A.
Interpret the result

1)0.5

2)0.5

To answer this question, we need to understand the concept of mechanical energy. Mechanical energy is the sum of the kinetic energy (KE) and the gravitational potential energy (PE) of a system.

a) To calculate the mechanical energy at point O, we need to find both the kinetic energy and the gravitational potential energy.

The kinetic energy (KE) is given by the formula KE = (1/2)mv^2, where m is the mass of the particle and v is its velocity. In this case, the mass of particle B is given as 10 g, which is equal to 0.01 kg, and the velocity is 10 m/s. Plugging these values into the formula, we have KE = (1/2)(0.01 kg)(10 m/s)^2 = 0.5 J.

The gravitational potential energy (PE) is given by the formula PE = mgh, where m is the mass of the particle, g is the acceleration due to gravity (which is approximately 9.8 m/s^2), and h is the height from the reference level. At point O, the height is zero, so the gravitational potential energy is also zero.

Therefore, the mechanical energy (ME) at point O is the sum of kinetic and potential energy, which is ME = KE + PE = 0.5 J + 0 J = 0.5 J.

b) To calculate the mechanical energy at the highest point A, we only need to consider the gravitational potential energy because the velocity of the particle becomes zero at the highest point. At the highest point, the particle has reached its maximum height, so the gravitational potential energy is at its maximum.

The gravitational potential energy is given by PE = mgh, where m is the mass of the particle, g is the acceleration due to gravity, and h is the height from the reference level. At the highest point, the height is the maximum height reached by the particle. Since we are given that the particle was shot vertically upward, the maximum height reached is when the particle momentarily comes to rest before reversing its direction.

Using the equation v^2 = u^2 + 2gh, where v is the final velocity (0 m/s), u is the initial velocity (10 m/s), and h is the maximum height, we can solve for h. Rearranging the equation, h = (v^2 - u^2) / (2g). Plugging in the values, we have h = (0^2 - 10^2) / (2 * 9.8) = -101 J.

Since the reference level is a horizontal plane, which means the height is measured from the ground, the height is negative. Thus, the gravitational potential energy at the highest point is -101 J.

Therefore, the mechanical energy at the highest point A is the gravitational potential energy, which is ME = PE = -101 J.

Interpretation:
The negative value of the gravitational potential energy at the highest point indicates a decrease in the potential energy of the system compared to the reference level. This is because the potential energy is zero at point O, and it decreases as the particle moves upward. At the highest point, the particle has lost all its initial kinetic energy and the potential energy is at its lowest point, thus explaining the negative value.