Question:
An athlete throws the shot-put of mass $ 4\,kg $ with initial speed of $ 2.2\,ms^{-1} $ at $ 41^{\circ} $ from a height of $ 1.3\,m $ from the ground. What is the KE of the shot-put when it reaches the ground? (Ignoring the air resistance and gravity $ g=9.8 \, m/s^{-2} $ )
An athlete throws the shot-put of mass $ 4\,kg $ with initial speed of $ 2.2\,ms^{-1} $ at $ 41^{\circ} $ from a height of $ 1.3\,m $ from the ground. What is the KE of the shot-put when it reaches the ground? (Ignoring the air resistance and gravity $ g=9.8 \, m/s^{-2} $ )
Updated On: Jun 6, 2024
- $ 42.84\,J $
- $ 52.84\,J $
- $ 62.84\,J $
- $ 72.84\,J $
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The Correct Option is C
Solution and Explanation
As there is no air resistance and gravitational force is a conservative force, we can apply mechanical energy conservation.
$\Rightarrow(K E)_{f}=(K E)_{i}+\text { Change in PE } $
$=\frac{1}{2} m V^{2}+m g h$
$=\frac{1}{2} \times 4 \times(2.2)^{2}+4 \times(9.8) \times(1.3)$
$=9.68+50.96 $
$=60.64 \approx 62.84 \,J$
$\Rightarrow(K E)_{f}=(K E)_{i}+\text { Change in PE } $
$=\frac{1}{2} m V^{2}+m g h$
$=\frac{1}{2} \times 4 \times(2.2)^{2}+4 \times(9.8) \times(1.3)$
$=9.68+50.96 $
$=60.64 \approx 62.84 \,J$
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Concepts Used:
Work, Energy and Power
Work:
- Work is correlated to force and the displacement over which it acts. When an object is replaced parallel to the force's line of action, it is thought to be doing work. It is a force-driven action that includes movement in the force's direction.
- The work done by the force is described to be the product of the elements of the force in the direction of the displacement and the magnitude of this displacement.
Energy:
- A body's energy is its potential to do tasks. Anything that has the capability to work is said to have energy. The unit of energy is the same as the unit of work, i.e., the Joule.
- There are two types of mechanical energy such as; Kinetic and potential energy.
Read More: Work and Energy
Power:
- Power is the rate at which energy is transferred, conveyed, or converted or the rate of doing work. Technologically, it is the amount of work done per unit of time. The SI unit of power is Watt (W) which is joules per second (J/s). Sometimes the power of motor vehicles and other machines is demonstrated in terms of Horsepower (hp), which is roughly equal to 745.7 watts.
- Power is a scalar quantity, which gives us a quantity or amount of energy consumed per unit of time but with no manifestation of direction.