Whether or not an object (such as a plate, glass, or bone) breaks upon impact depends on the average force exerted on that object by the surface. When a 3.8 kg glass figure hits the floor, it will break if it experiences an average force of 712 N. When it hits a tile floor, the glass comes to a stop in 0.014 s. From what minimum height (in m) must the glass fall to experience sufficient force to break?
m
electron1
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Let’s use the following equation to determine the acceleration of the glass figure.
F = m * a
-712 = 3.8 * a
a = -712 ÷ 3.8
This is approximately -187 m/s^2. Let’s use the following equation to determine the velocity of the glass figure just before the force was applied,
vf = vi + a * t
0 = vi + (-712 ÷ 3.8) * 0.014
vi = (712 ÷ 3.8) * 0.014
This is approximately 2.62 m/s. Let’s use the following equation to determine the distance the glass figure must fall to have this velocity.
vf^2 = vi^2 + 2 * g * d, vi = 0 m/s
[(712 ÷ 3.8) * 0.014]^2 = 2 * 9.8 * d
d = [(712 ÷ 3.8) * 0.014]^2 ÷ 19.6
This is approximately 0.35 meter. I hope this is helpful for you.
Anonymous
Use impulse (Ft) equals change of momentum (Δmv = mΔv) to find velocity which causes breakage.
712*0.014 = 3.8(v – 0)
v = 2.62m/s
Then use v ² = 2as to find height (s)
s = 2.62²/(2*9.8) = 0.35m