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Waist Level

Waist Level
Waist Level
How do I figure out the force of the ball? Please help!?


You are standing on scales which read weight in Newtons. A 0.50 kg ball is dropped from a height of 1 m into your hands. Your hands drop from chest level to waist level during the catch, a distance of about 25 cm. Your mass is 62 kg. Assuming that you decelerate the ball uniformly during the catch, what would be the maximum reading on the scales? (Hint: The scales read 607.6 N before you caught the ball.)

You want to get the initial velocity when you first start slowing down the ball. To do this, you need to know how long it's been accelerating. Use
x = 0.5gt^2
x is already known to be 1m, if I'm reading your problem right, i.e. that the ball drops 1m before you even touch it. Then it drops an additional 0.25m. Hope I'm reading that right.

Why did you need t? You needed it for this formula:
Of course, v0 is zero, since there was no initial downward motion.

Now to find acceleration during the drop when you're slowing it down. I figure, why not just combine the downward gravitational acceleration and your upward deceleration?
v = v0+(a-g)t
x = v0+0.5(a-g)t^2
You've already found v0. It's not zero this time. It's the velocity at the start of the 0.25m slowdown. v=0 this time, since you're slowing down the ball to a stop. So you know x,v, and v0, but don't know a and t. You have two equations and two unknowns, so you should be able to solve for both.

Now that you know a, the upward acceleration, just use F=ma to get the upward force you exerted to stop the ball. That's the total force you exerted both to oppose gravity and to slow the ball down. After you stop the ball, you're only pushing against gravity, so that's irrelevant to finding the maximum reading, following what the problem requests.

So just add that F to the 607.6, obviously, and you're done.

tia if you select for best

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