To determine whether the student's claim is correct, we can use the principle of conservation of energy. When an object is dropped, its potential energy (PE) is converted to kinetic energy (KE) just before it hits the ground. The potential energy at a height is given by the formula:
\[ PE = mgh \]
where:
- \( m \) is the mass of the object (in kilograms),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)),
- \( h \) is the height from which it is dropped (in meters).
Step 1: Calculate the Potential Energy
For a ball dropped from a height of 3.0 meters, its potential energy just before it hits the ground can be calculated as:
\[ PE = m \cdot g \cdot h = m \cdot (9.81 , \text{m/s}^2) \cdot (3.0 , \text{m}) \]
\[ PE = m \cdot 29.43 , \text{J} \]
Step 2: Set Up the Inequality
The student claims that the kinetic energy (KE) upon hitting the ground is less than 96 joules. Since all the potential energy converts to kinetic energy (assuming no energy losses due to air resistance or other factors), we can set up the inequality:
\[ m \cdot 29.43 < 96 \]
Step 3: Solve for Mass
Now we can solve for \( m \):
\[ m < \frac{96}{29.43} \approx 3.26 , \text{kg} \]
Conclusion
This result means that if the mass of the ball is less than approximately 3.26 kg, the kinetic energy would indeed be less than 96 joules. If the ball has a mass greater than or equal to 3.26 kg, the kinetic energy would be 96 joules or more.
Therefore, whether the student's claim is correct depends on the mass of the ball. If the mass of the ball is less than 3.26 kg, then she is correct; if it is 3.26 kg or more, she is incorrect. Without knowing the mass of the ball, we cannot definitively say if her claim is correct.
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