A 2 kg object is released from rest from a height of 10 m above the ground. Calculate
1) the initial potential energy at the moment of release;
2) the kinetic energy at the moment it reaches 4 m above the ground
3) After the impact the object just before Impact with the ground
Plz rssponse
To solve these questions, we need to use the concepts of potential energy, kinetic energy, and conservation of energy.
1) The initial potential energy at the moment of release can be calculated using the formula:
Potential Energy = mass * gravitational acceleration * height
Given:
Mass (m) = 2 kg
Height (h) = 10 m
Gravitational acceleration (g) = 9.8 m/s²
Potential Energy = 2 kg * 9.8 m/s² * 10 m
Potential Energy = 196 Joules
Therefore, the initial potential energy at the moment of release is 196 Joules.
2) The kinetic energy at the moment the object reaches 4 m above the ground can be calculated using the conservation of energy. At this point, the potential energy will decrease, and the kinetic energy will increase. The total mechanical energy (sum of potential energy and kinetic energy) remains constant.
Initially, the object has potential energy (P.E) only. At 4 m above the ground, this potential energy is converted into kinetic energy (K.E). So,
Potential Energy at 10 m = Kinetic Energy at 4 m
Using the formula for potential energy:
Potential Energy at 10 m = mass * gravitational acceleration * height
Potential Energy at 10 m = 2 kg * 9.8 m/s² * 10 m
Potential Energy at 10 m = 196 Joules
Therefore, the kinetic energy at 4 m above the ground is also 196 Joules.
3) Just before impact with the ground, the object will have only kinetic energy. All of the object's potential energy will have been converted to kinetic energy. The formula for kinetic energy is:
Kinetic Energy = (1/2) * mass * velocity²
To find the velocity just before impact, we can use the equation for conservation of energy:
Potential Energy at 10 m = Kinetic Energy just before impact
Potential Energy at 10 m = mass * gravitational acceleration * height
196 Joules = 2 kg * 9.8 m/s² * 10 m
Solving for the height, we find:
height = 196 Joules / (2 kg * 9.8 m/s²) = 10 m
So the height just before impact is 10 m, which means the object has no potential energy left. Therefore, all of the initial potential energy has been converted into kinetic energy just before impact.