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

To calculate the mechanical energy of the system at point O, we need to consider both the kinetic energy and the gravitational potential energy.

a) Kinetic Energy at O:
The kinetic energy (KE) is given by the equation KE = 1/2 * mass * velocity^2. Since particle B has a mass of 10g (which is equivalent to 0.01 kg) and a velocity of 10 m/s, we can plug these values into the equation to find the kinetic energy:
KE = 1/2 * 0.01 kg * (10 m/s)^2 = 0.5 J

b) Gravitational Potential Energy at O:
In this case, since the reference level of gravitational potential energy is the horizontal plane containing point O, the gravitational potential energy (PE) at point O is zero. This is because the height from the reference level to point O is zero.

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

To calculate the mechanical energy at the highest point A, we need to consider that at the highest point, the velocity will be zero and the only form of energy present will be the gravitational potential energy.

b) Gravitational Potential Energy at A:
The gravitational potential energy at point A can be determined using the equation PE = mass * gravity * height. Since at the highest point, the height (h) will be the maximum, we can input the known values:
PE = 0.01 kg * 9.8 m/s^2 * h, where h is the height from the reference level to point A.

Now, let's interpret the results:
a) At point O, the mechanical energy of the system is 0.5 J. This means that there is some energy present due to the particle's velocity. The gravitational potential energy is zero since it is measured with respect to the reference level. Therefore, the total mechanical energy is determined solely by the kinetic energy of the particle.

b) At the highest point A, the mechanical energy of the system will be purely gravitational potential energy. This is due to the fact that the particle has come to a stop, and there is no kinetic energy present. The height (h) from the reference level to point A will determine the amount of gravitational potential energy.

Overall, this problem illustrates the conservation of mechanical energy in a vertical motion. Starting at point O, the mechanical energy is a combination of kinetic and potential energy. At the highest point, the mechanical energy is entirely gravitational potential energy.