Pablo's engineering team has developed a new material that is strong enough to withstand major impacts, including bullets, witho
ut breaking or deforming. He plans to design a new type of motorcycle helmet using the material as its outside covering. A prototype of the helmet is shown below. Pablo knows that other types of motorcycle helmets have outside coverings that bend and deform slightly on impact. So if Pablo's new helmet is going to be as effective at protecting people's heads as existing helmets, he'll need to
A.
slightly reduce the total mass of the new helmet by reducing the amount of internal cushioning.
B.
maximize the total mass of the helmet by adding flexible steel to the outside covering.
C.
increase the amount of cushioning on the inside of the new helmet to help it absorb impacts.
D.
use a thicker outside covering than other helmets to help prevent deformation even further.
A.
slightly reduce the total mass of the new helmet by reducing the amount of internal cushioning.
B.
maximize the total mass of the helmet by adding flexible steel to the outside covering.
C.
increase the amount of cushioning on the inside of the new helmet to help it absorb impacts.
D.
use a thicker outside covering than other helmets to help prevent deformation even further.
1 answer:
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Answer:
The distance the block will slide before it stops is 3.3343 m
Explanation:
Given;
mass of bullet, m₁ = 20-g = 0.02 kg
speed of the bullet, u₁ = 400 m/s
mass of block, m₂ = 2-kg
coefficient of kinetic friction, μk = 0.24
Step 1:
Determine the speed of the bullet-block system:
From the principle of conservation of linear momentum;
m₁u₁ + m₂u₂ = v(m₁ + m₂)
where;
v is the speed of the bullet-block system after collision
(0.02 x 400) + (2 x 0) = v (0.02 + 2)
8 = v (2.02)
v = 8/2.02
v = 3.9604 m/s
Step 2:
Determine the time required for the bullet-block system to stop
Apply the principle of conservation momentum of the system
when the system stops, vf = 0
3.9604 -2.352t = 0
2.352t = 3.9604
t = 3.9604/2.352
t = 1.684 s
Thus, time required for the system to stop is 1.684 s
Finally, determine the distance the block will slide before it stops
From kinematic, distance is the product of speed and time
Now, recall that t = 1.684 s
S = 3.9604(1.684) - 1.176(1.684)²
S = 6.6693 - 3.3350
S = 3.3343 m
Thus, the distance the block will slide before it stops is 3.3343 m