A 40 − k g boy jumps from a height of 3.0 m , lands on one foot and comes to rest in 0.10 s after he hits the ground. Assume that he comes to rest with a constant deceleration. If the total cross-sectional area of the bones in his legs just above his ankles is 3.0 c m 2 , what is the compression stress in these bones? Leg bones can be fractured when they are subjected to stress greater than 1.7 × 10 8 P a . Is the boy in danger of breaking his leg?
A 40 − k g boy jumps from a height of 3.0 m , lands on one foot and comes to rest in 0.10 s after he hits the ground. Assume that he comes to rest with a constant deceleration. If the total cross-sectional area of the bones in his legs just above his ankles is 3.0 c m 2 , what is the compression stress in these bones? Leg bones can be fractured when they are subjected to stress greater than 1.7 × 10 8 P a . Is the boy in danger of breaking his leg?
A
40
−
k
g
boy jumps from a height of
3.0
m
, lands on one foot and comes to rest in
0.10
s
after he hits the ground. Assume that he comes to rest with a constant deceleration. If the total cross-sectional area of the bones in his legs just above his ankles is
3.0
c
m
2
, what is the compression stress in these bones? Leg bones can be fractured when they are subjected to stress greater than
1.7
×
10
8
P
a
. Is the boy in danger of breaking his leg?
In an isothermal process, you are told that heat is being added to the system. Which of the following is not true? (a) The pressure of the gas is decreasing. (b) Work is being done on the system. (c) The average kinetic energy of the particles is remaining constant. (d) The volume of the gas is increasing. (e) Work is being done by the system.
No chatgpt pls will upvote
8.114 CALC A Variable-Mass Raindrop. In a rocket-propul-
sion problem the mass is variable. Another such problem is a rain-
drop falling through a cloud of small water droplets. Some of these
small droplets adhere to the raindrop, thereby increasing its mass
as it falls. The force on the raindrop is
dp
dv
dm
Fext
=
+
dt
dt
dt
=
Suppose the mass of the raindrop depends on the distance x that it
has fallen. Then m kx, where k is a constant, and dm/dt = kv.
This gives, since Fext
=
mg,
dv
mg = m
+ v(kv)
dt
Or, dividing by k,
dv
xgx
+ v²
dt
This is a differential equation that has a solution of the form
v = at, where a is the acceleration and is constant. Take the initial
velocity of the raindrop to be zero. (a) Using the proposed solution
for v, find the acceleration a. (b) Find the distance the raindrop has
fallen in t = 3.00 s. (c) Given that k = 2.00 g/m, find the mass of
the raindrop at t = 3.00 s. (For many more intriguing aspects of
this problem, see K. S. Krane, American Journal of…
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