Respuesta :
First let us lay out the formula for Potential and Kinetic Energy:
PE = mgh
KE = (mv^2)/2
where: m=mass, v=velocity, g=gravitational acceleration, h=height
Calculating for mass using the known values of PE:
340J = m (9.81 m/s^2) (50ft) (1m/3.28ft)
m = 2.27 kg
The law of conservation of energy states that energy is neither created nor destroyed. Therefore, the change in Kinetic Energy from 50 ft to 35 ft would be equal to the change in Potential Energy from 50 ft to 35 ft. However it would be opposite in signs since one is losing while other is gaining.
KE(35ft) – KE(50ft) = - [ PE(35ft) – PE(50ft]
KE(50ft) = 0 since the brick is initially at rest
KE(35ft) = 340J - 2.27kg (9.81 m/s^2) (35ft) (1m/3.28 ft)
KE(35ft) = 102.38 J
The brick’s kinetic energy is [tex]\boxed{101.46{\text{ J}}}[/tex] when it is 35 ft above the street level.
Further Explanation:
Energy is the capability to do work. But the presence or availability of energy alone cannot imply that work is always obtainable from it. Energy occurs in various forms, some of which are mentioned below:
Kinetic energy
The energy that is associated with the motion of particles is called kinetic energy. A moving vehicle and a person moving on the road possess kinetic energy due to their motion.
Potential energy
The energy related to the position of an object is potential energy. An apple placed on the table has potential energy due to its position.
Mechanical energy
The sum of the kinetic and potential energy of any particle is known as mechanical energy.
Law of conservation of energy:
According to this law, energy can neither be created nor be destroyed but can only be converted from one form to another.
The formula for total or mechanical energy is as follows:
[tex]{\text{TE}} = {\text{PE}} + {\text{KE}}[/tex] ...... (1)
Here,
TE is the total energy.
PE is the potential energy.
KE is the kinetic energy.
When brick is placed on the edge of roof, its kinetic energy is zero and it possesses only potential energy due to its position.
Substitute 340 J for PE and 0 J for KE in equation (1).
[tex]\begin{aligned}{\text{TE}}&= {\text{340 J}} + {\text{0 J}}\\&= {\text{340 J}}\\\end{aligned}[/tex]
The formula to calculate the potential energy is as follows:
[tex]{\text{PE}} = {\text{mgh}}[/tex] ...... (2)
Here,
m is the mass of object.
g is the acceleration due to gravity.
h is the height of object.
PE is the potential energy.
Rearrange equation (2) to calculate m.
[tex]{\text{m}} = \dfrac{{{\text{PE}}}}{{{\text{gh}}}}[/tex] ...... (3)
The height of roof is 50 ft. This is to be converted into m. The conversion factor for this is,
[tex]1{\text{ ft}} = 0.3048{\text{ m}}[/tex]
Therefore the height of roof can be calculated as follows:
[tex]\begin{aligned}{\text{h}} &= \left( {50{\text{ ft}}} \right)\left( {\frac{{0.3048{\text{ m}}}}{{1{\text{ ft}}}}} \right)\\&= 15.24{\text{ m}}\\\end{aligned}[/tex]
Since 1 Joule equals [tex]1{\text{ kg}} \cdot {{\text{m}}^2} \cdot {{\text{s}}^{ - 2}}[/tex] so 340 J can also be written as [tex]{\text{340 kg}} \cdot {{\text{m}}^2} \cdot {{\text{s}}^{ - 2}}[/tex]. Substitute [tex]{\text{340 kg}} \cdot {{\text{m}}^2} \cdot {{\text{s}}^{ - 2}}[/tex] for PE, 15.24 m for h and [tex]9.8{\text{ m/}}{{\text{s}}^2}[/tex] for g in equation (3).
[tex]\begin{aligned}{\text{m}}&= \frac{{{\text{340 kg}} \cdot {{\text{m}}^2} \cdot {{\text{s}}^{ - 2}}}}{{\left( {9.8{\text{ m/}}{{\text{s}}^2}} \right)\left( {15.24{\text{ m}}} \right)}}\\&= 2.277{\text{ kg}}\\\end{aligned}[/tex]
Rearrange equation (1) for KE.
[tex]{\text{KE}} = {\text{TE}} - {\text{PE}}[/tex] ...... (4)
Now height becomes 35 ft. This is to be converted into m. The conversion factor for this is,
[tex]1{\text{ ft}} = 0.3048{\text{ m}}[/tex]
Therefore the height of roof can be calculated as follows:
[tex]\begin{aligned}{\text{h}}&= \left( {35{\text{ ft}}} \right)\left( {\frac{{0.3048{\text{ m}}}}{{1{\text{ ft}}}}} \right)\\&= 10.69{\text{ m}}\\\end{aligned}[/tex]
Substitute 2.277 kg for m, [tex]9.8{\text{ m/}}{{\text{s}}^2}[/tex] for g and 10.69 m for h in equation (2).
[tex]\begin{aligned}{\text{PE}}&= \left( {2.277{\text{ kg}}} \right)\left( {9.8{\text{ m/}}{{\text{s}}^2}} \right)\left( {10.69{\text{ m}}} \right)\\&= 238.54{\text{ J}}\\\end{aligned}[/tex]
Substitute 340 J for TE and 238.54 J for PE in equation (4).
[tex]\begin{aligned}{\text{KE}}&= {\text{340 J}} - {\text{238}}{\text{.54 J}}\\&= {\text{101}}{\text{.46 J}}\\\end{aligned}[/tex]
Learn more:
- What does conserving mass mean in a chemical reaction? https://brainly.com/question/2093705
- Write the chemical formula of the compound: https://brainly.com/question/10585691
Answer details:
Grade: High School
Chapter: Energy and its forms
Subject: Chemistry
Keywords: kinetic energy, potential energy, 340 J, 101.46 J, 238.54 J, energy, PE, TE, KE, 2.277 kg.
