Respuesta :
The work that Sam should do in order to stop is the boat is the same as that of the kinetic energy of the object in order to counter its motion. Kinetic energy is calculated through the equation,
KE = 0.5mv²
where KE is kinetic energy, m is mass, and v is the velocity.
Substituting,
KE = 0.5(1200kg)(1.2 m/s)²
KE = 864 J
KE = 0.5mv²
where KE is kinetic energy, m is mass, and v is the velocity.
Substituting,
KE = 0.5(1200kg)(1.2 m/s)²
KE = 864 J
The amount of work done by Sam to stop the boat is [tex]\boxed{864\,{\text{J}}}[/tex] .
Further Explanation:
Given:
The mass of the boat with all the riders is [tex]1200\,{\text{kg}}[/tex] .
The speed of the boat is [tex]1.2\,{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{\text{s}}}} \right\kern-\nulldelimiterspace}{\text{s}}}[/tex] .
Concept:
Since the boat is drifting with some speed at some point of time, the complete energy of the boat is considered to be stored in the form of its kinetic energy. Therefore, Sam needs to put in work equal to the amount of the kinetic energy of the boat to bring it to rest.
The kinetic energy of a body is the amount of energy stored in the body by virtue of its motion. Mathematically it is shown as:
[tex]KE=\frac{1}{2}m{v^2}[/tex]
Here, [tex]KE[/tex] is the kinetic energy stored in the boat, [tex]m[/tex] is the mass of the boat and [tex]v[/tex] is the speed of the boat.
Substitute the values of [tex]m[/tex] and [tex]v[/tex] in above expression.
[tex]\begin{aligned}KE&=\frac{1}{2}\times1200\times{\left( {1.2}\right)^2}\\&=\frac{{1728}}{2}\,{\text{J}}\\&=8{\text{64}}\,{\text{J}}\\\end{aligned}[/tex]
Now, the amount of work required to stop the boat is equal to the kinetic energy of the boat.
[tex]\begin{aligned}W&=KE\\&=864\,{\text{J}}\\\end{aligned}[/tex]
Thus, the amount of work done to bring the boat to rest is [tex]\boxed{864\,{\text{J}}}[/tex] .
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Answer Details:
Grade: High School
Subject: Physics
Chapter: Conservation of Energy
Keywords:
Boat, Sam, mass of boat, all riders, 1200 kg, kinetic energy of boat, 1.2m/s, work done, 864 J, stop, amusement park, slow down.
