Newton's Third Law - Weight on Scale when catching a ball

[Sabellic]

Homework Statement

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.)

Weight of person = 607.6N
Mass of Ball= 0.50 kg
Displacement of ball when dropped = 1.0 metres
Displacement of ball during deceleration = 0.25 metres

Homework Equations

Force = Mass * acceleration

Force (weight) = Mass * 9.81

Velocity (final) ^2= Velocity (initial) ^2 + 2 * acceleration * displacement

Vf^2 = Vi^2 + (2 * a * d)

The Attempt at a Solution

Calculate final velocity of ball after it is first dropped before it is caught:


Vf= x
Vi= 0 m/s
a= 9.81 m/s^2
d= 1.0 metres

Vf^2 = Vi^2 + (2 * a * d)
x^2 = 0^2 + (2*9.81*1)
x^2 = 19.62
x = 4.43 m/s

Calculate acceleration (negative) of ball as it is being caught:

Vf= 0 m/s
Vi= 4.43 m/s
a= x
d= 0.25 metres

Vf^2 = Vi^2 + (2 * a * d)
0^2 = 4.43^2 + (2 * x * 0.25)
0 = 19.62 + (0.50x)
-0.50x = 19.62
x = 39.24

Therefore, the acceleration of the ball as it is being caught is 39.24 metres per second squared downward.


Now, calculate the force of the ball:

F=ma
F=0.5 x 39.24
F=19.62

Now, calculate the maximum weight reading on the scale (which occurs as the ball is being caught):

Weight of man + weight of ball + force of ball during deceleration

607.6 Newtons + (0.5)*(9.81) + 19.62 Newtons
which is...
607.6 Newtons + 4.905 Newtons + 19.62 Newtons=632.125 Newtons

Thus, the maximum scale reading would be 632.125 Newtons.



Am i right?

 

[calef]

Your methodology is right, yeah. Lemme check the math.

Edit: Yep, you're right.

 

[Moetasim]

Yes, your calculations and solution appear to be correct. The maximum reading on the scale would be 632.125 Newtons, which is the weight of the person (607.6 N) plus the weight of the ball (4.905 N) plus the force of the ball during deceleration (19.62 N). This is in accordance with Newton's Third Law, which states that for every action, there is an equal and opposite reaction. In this case, the action is the force of the ball being caught by the person's hands, and the reaction is the force felt by the person and measured by the scale.