A catcher arranges to catch a baseball dropped from a height 50 m above his glove. However, his friends substitute a soft 250 g red grapefruit, so that it will smash apart when he catches it. His glove stops the grapefruit in 0.010 s. What force does the glove exert on the grapefruit?
A) 0.078 3 N
B) 783 N
C) 2 450 N
D) 24 500 N
E) 78 300 N

Question

Quizplus · Accepted Answer

To find the force exerted on the grapefruit by the glove, we first need to calculate the acceleration of the grapefruit as it stops and then use Newton's second law (F = ma) to find the force. The grapefruit falls under the influence of gravity, so its initial velocity just before the catch can be found using the equation for an object in free fall: $v^2 = u^2 + 2gh$, where $v$ is the final velocity, $u$ is the initial velocity (0 m/s, since it's dropped), $g$ is the acceleration due to gravity (approximately 9.8 m/s$^2$), and $h$ is the height (50 m). This gives $v = \sqrt{2 \times 9.8 \times 50}$. The change in velocity ($\Delta v$) is this final velocity to 0 m/s (since it stops), over the time interval ($\Delta t$) of 0.010 s, giving an acceleration ($a$) using $a = \Delta v / \Delta t$. Finally, the mass ($m$) of the grapefruit is 0.250 kg (250 g), so the force ($F$) can be calculated with $F = ma$.Let's calculate the final velocity ($v$) first: $v = \sqrt{2 \times 9.8 \times 50} \approx 31.3$ m/s. The acceleration ($a$) as it stops is then $a = \Delta v / \Delta t = 31.3 / 0.010 = 3130$ m/s$^2$. The force is $F = ma = 0.250 \times 3130 = 782.5$ N, which rounds to 783 N, making choice B correct.

A Catcher Arranges to Catch a Baseball Dropped from a Height