Explain how the energy (total, kinetic, or potential) will change when you let an object free-fall from the top of a building.
An object at the top of a building has a given height (h) above the ground. As such, it has initial potential energy (PE i ) with respect to its mass (m), gravity (g), and initial height (h). This is expressed as PE i =mgh. However, kinetic energy (KE i ) at this initial point is zero since the object is not moving (Kurtus, 2018). Thus the initial total energy (TE i ) is the sum of PE i and KE i , that is;
Delegate your assignment to our experts and they will do the rest.
TE i =PE i +KE i
=mgh+0
=mgh
However, when you release the object, it accelerates downwards, leading to an increase in the velocity (v) (Kurtus, 2018). The kinetic energy increases with the free-fall while the potential energy decreases (Kurtus, 2018). Thus, the final Kinetic Energy (KE f ) is given by mv 2 /2. When it hits the ground, the height (h) becomes zero. Therefore, the final potential energy (PE f ) is zero. The final total energy (TE f ) for falling becomes;
TE f = PE f + KE f
=0+mv 2 /2
=mv 2 /2
Nonetheless, due to the conservation of energy law, when you drop an object, the initial and final total energy is the same: mgh= mv 2 /2.
Explain why a bullet with a mass of 15 grams and a velocity of 400 m/s has more momentum than you at rest. Calculate the momentum for both.
Each object has mass, and thus, if it is in motion, it has momentum ( ). As such, momentum ( ) is defined as the mass in motion. It is a vector obtained by getting the product of an object's mass (m) and velocity (v) (Naskar, 2018). It is expressed as;
Momentum=mass × velocity
=m × v
Therefore, the momentum of the bullet is given by;
bullet =m bullet × v bullet
=15/1000 kg ×400 m/s
=6 kgm/s
On the other hand, since I am at rest, velocity=0. Thus, my momentum is given by;
=m × v
= 65 kg × 0 m/s
=0 kgm/s
As such, an individual at rest has no momentum, whereas the bullet in motion has momentum. This is because momentum is dependent on both the mass of an object as well as its velocity. Thus, since the bullet is moving, it has more momentum than my body, which is at rest.
References
Kurtus, R. (2018, March 16). Energy from gravity of falling objects by Ron Kurtus - Physics lessons: School for champions. Retrieved November 7, 2020, from https://www.school-for-champions.com/science/gravity_energy_falling.htm#.X6aTdGgzbIU
Naskar, A. (2018). Impulse and momentum - Thoughtful physics . Quantemporary.
