To determine the speed of the box at the highest point, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
Let's break down the steps:
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Calculate the gravitational potential energy gained as the box is lifted: \[ \text{Potential Energy (PE)} = m \cdot g \cdot h \] Where:
- \( m = 50 , \text{kg} \) (mass of the box)
- \( g = 9.81 , \text{m/s}^2 \) (acceleration due to gravity)
- \( h = 0.5 , \text{m} \) (height lifted)
Plugging in the values: \[ \text{PE} = 50 , \text{kg} \cdot 9.81 , \text{m/s}^2 \cdot 0.5 , \text{m} = 245.25 , \text{J} \]
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Determine the net work done on the box. The total work done on the box is given as 300J. The net work done will be the work done minus the potential energy gained: \[ \text{Net Work} = \text{Total Work} - \text{Potential Energy} \] \[ \text{Net Work} = 300 , \text{J} - 245.25 , \text{J} = 54.75 , \text{J} \]
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Use the net work to find the change in kinetic energy: \[ \text{Net Work} = \Delta KE = \frac{1}{2} m v^2 \]
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Set up the equation: \[ 54.75 , \text{J} = \frac{1}{2} \cdot 50 , \text{kg} \cdot v^2 \]
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Solve for \( v^2 \): \[ 54.75 = 25 v^2 \implies v^2 = \frac{54.75}{25} = 2.19 \]
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Take the square root to find \( v \): \[ v = \sqrt{2.19} \approx 1.48 , \text{m/s} \]
Thus, the speed of the box at the highest point is approximately \( 1.48 , \text{m/s} \).
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