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Answer:
a) The work done by the force is 136.400 joules.
b) The speed of the mass at the end of the 3.5 meters is approximately 11.679 meters per second.
Explanation:
The correct statement is shown below:
<em>A 2-kg mass is initially at reat on a frictionless surface. A 45 N force acts at an angle of 30º to the horizontal for a distance of 3.5 meters:</em>
<em>a)</em><em> Find the work done by the force.</em>
<em>b)</em><em> Find the speed of the mass at the end of the 3.5 meters.</em>
a) Given that a external constant force is acting on the mass on a frictionless surface, the work done by the force (), measured in joules, is:
(1)
Where:
- External constant force exerted on the mass, measured in newtons.
- Horizontal travelled distance, measured in meters.
- Direction of the external force regarding the horizontal, measured in sexagesimal degrees.
If we know that ,
and
, then the work done by the force is:
The work done by the force is 136.400 joules.
b) The final speed of the mass at the end ot the 3.5 meter is calculated by means of the Work-Energy Theorem, which means that the work done on the mass is transformed into a translational kinetic energy. That is:
(2)
Where:
- Mass, measured in kilograms.
,
- Initial and final speeds of the mass, measured in meters per second.
If we know that ,
and
, then the final speed of the mass is:
The speed of the mass at the end of the 3.5 meters is approximately 11.679 meters per second.