shortest stopping time- physics question. please help :)

Question

A 0.066 kg egg is thrown at a sheet with a velocity of 20.9 m/s. The maximum force that the egg can experience without breaking is 22.4 N. What is the shortest stopping time the sheet can impart to the egg without exceeding this force?

Give your answer with three decimals.

 

thank you :)

Answer 1

Hi Lauren!

 

Another way of framing this problem is with the impulse-momentum theorem:

 

Δp = FΔt

 

where

 

Δp = change in momentum

F = (average) force applied

Δt = time over with the force is applied

 

The egg experiences a change in momentum of:

 

Δp = (p_f - p_o)

 

where

 

p_f = 0 (egg ends at rest)

p_o = mv_o = (0.066 kg)(20.9 m/s)

 

Δp = (0 - 1.38 kg·m/s) = -1.38 kg· m/s

 

[NOTE: The negative just means that, if we assume the egg to be traveling in the positive direction, then the force that stops it must point in the negative direction]

 

The stopping force we are considering will be -22.4 N, to keep the egg from breaking.

 

Then

 

Δp = FΔt --> -1.38 kg·m/s = (-22.4 N)Δt -->  Δt = (-1.38)(-22.4) = 0.062 s

 

This is not a different solution from using kinematics and Newton's laws (in fact, between Mark's and my solutions, you can see the similarities).  It is just another way of framing the problem, which may have its advantages in other circumstances.

I hope this helps!  If you have any questions about this, just let me know.

Answer 2

Hi Lauren,

 

For the shortest stopping time, we would imagine the entire 22.4 N force as opposing the egg to stop it. We use a kinematics equation to calculate the stopping time:

 

v_f = v_i + at

 

where v_f is the final velocity, v_i is the initial velocity, a is the acceleration, and t is the time.

 

We can express the acceleration in terms of Newton's Second Law: F = ma, where F is the force and m is the mass of the egg.

 

Subsituting Newton's Second Law into the kinematics equation gives:

 

v_f = v_i + (F/m)t

 

Solving for the time t, we have

 

t = (m/F)(v_f - v_i)

 

Let's now put in the values.

 

m = 0.066 kg

v_i = 20.9 m/s

v_f = 0, since the egg will come to rest

F = -22.4 N

 

t = [(0.066 kg)/(-22.4 N)](0 - 20.9 m/s)

 

t = 0.062s