Is conservation of mechanical energy likely to hold in this situation? A soccer ball is thrown into the air. (Disregard air resistance.) Explain your reasoning.
What do you think?
Emily passes a soccer ball 9.7 m directly
across the field to Kara, who then kicks the
ball 11.7 m directly down the field to Luisa.
What is the magnitude of the ball’s total
displacement as it travels between Emily and
Luisa?
Answer in units of m
016 (part 2 of 2) 10.0 points
Howmany degrees to the side of straight down
the field is the ball’s total displacement?
Answer in units of ◦
To determine whether the conservation of mechanical energy is likely to hold in this situation, we need to consider the factors involved. The conservation of mechanical energy applies when the total mechanical energy of a system remains constant over time. The mechanical energy of an object includes its kinetic energy (energy due to motion) and potential energy (energy due to its position or height).
In this situation, a soccer ball is thrown into the air without considering air resistance. Since air resistance is disregarded, we can assume that there are no external forces acting on the ball besides the force of gravity. In the absence of external forces, the total mechanical energy of the ball should be conserved.
When the ball is thrown upwards, the initial mechanical energy is in the form of kinetic energy. As the ball rises, it gradually loses kinetic energy due to the force of gravity acting in the opposite direction. However, this loss in kinetic energy is compensated by the increase in potential energy as the ball gains height.
At the highest point of the ball's trajectory, its velocity momentarily becomes zero (reaching its maximum height) and all of its initial kinetic energy has been converted to potential energy. As the ball descends and falls back towards the ground, the process is reversed: it gains kinetic energy while losing potential energy.
In the absence of friction and any other external forces, the loss in kinetic energy during the ball's ascent is equal to the gain in kinetic energy during its descent. Consequently, the total mechanical energy of the ball remains constant throughout its motion.
Therefore, in this scenario where air resistance is disregarded, it is very likely that the conservation of mechanical energy will hold for the soccer ball thrown into the air.