The tomato is dropped. What is the velocity, , of the tomato when it hits the ground? Assume 82.7 of the work done in Part A is transferred to kinetic energy, , by the time the tomato hits the ground.
Express your answer numerically in meters per second
0 m/s
To find the velocity of the tomato when it hits the ground, we need to use the principle of conservation of energy. According to the question, 82.7% of the work done (presumably gravitational potential energy converted to kinetic energy) is transferred to kinetic energy by the time the tomato hits the ground.
Therefore, we can express this as:
Kinetic energy = 0.827 * Work done
The formula for kinetic energy is:
Kinetic energy = (1/2) * mass * velocity^2
Assuming the mass of the tomato is given, we can rearrange the equation to find the velocity:
velocity = √(2 * kinetic energy / mass)
Now, we just need to substitute the given values into the equation:
velocity = √(2 * (0.827 * Work done) / mass)
Since the actual values for work done and mass are not provided in the question, it is not possible to calculate the exact velocity without these values.
To determine the velocity of the tomato when it hits the ground, we can use the principle of conservation of energy. The equation for conservation of energy in this case is:
Potential Energy at starting point + Work done on the object = Kinetic Energy at ending point
Since the tomato is dropped from a height, it starts with potential energy and no initial kinetic energy. The potential energy is given by:
Potential Energy = mgh,
where m is the mass of the tomato, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height from which it is dropped.
The work done on the tomato can be calculated using the formula:
Work = force × distance,
where force is the gravitational force acting on the tomato (mass × acceleration due to gravity) and distance is the height from which it is dropped.
Therefore, the work done on the tomato is:
Work = mgh.
Using the given information that 82.7% of the work is transferred to kinetic energy, we can calculate the work done into kinetic energy:
Work_into_KineticEnergy = ( 82.7% ) × Work.
Now, the kinetic energy at the ending point can be calculated using the formula:
Kinetic Energy = (1/2)mv^2,
where m is the mass of the tomato and v is its velocity when it hits the ground.
Equating the work done into kinetic energy and the kinetic energy at the ending point, we have:
(82.7%) × Work = (1/2)mv^2.
We can rearrange this equation to solve for v:
v = √( (2 × (82.7% × Work) ) / m ).
Now, we need to plug in the values given. The mass of the tomato is not provided, so we'll assume a value of 1 kilogram:
v = √( (2 × (82.7% × Work) ) / 1 ).
Finally, we'll convert the percentage to decimal and calculate the velocity:
v = √( (2 × (0.827 × Work) ) / 1 ).
If the height of the drop is known, we can substitute the appropriate value for h and calculate the velocity using the above equation.