M = 30 g = 0.03 kg, the mass of the bullet
v = 500 m/s, the velocity of the bullet
By definition, the KE (kinetic energy) of the bullet is
KE = (1/2)*m*v²
= 0.5*(0.03 kg)*(500 m/s)² = 3750 J
Because the bullet comes to rest, the change in mechanical energy is 3750 J.
The work done by the wall to stop the bullet in 12 cm is
W = (1/2)*(F N)*(0.12 m) = 0.06F J
If energy losses in the form of heat or sound waves are ignored, then
W = KE.
That is,
0.06F = 3750
F = 62500 N = 62.5 kN
Answer:
(a) 3750 J
(b) 62.5 kN
Answer:
Explanation:
a )
Energy stored by left spring when compressed = 1/2 k x²
= .5 x 10 x .02² = .002 J .
Let compression in right spring = y
energy stored to right spring = 1/2 k y²
1/2 k y² = 0.002
.5 x 20 x y² = 0.002
y = .01414 m
= 1.4 cm
Explanation:
Given that,
Angle by the normal to the slip α= 60°
Angle by the slip direction with the tensile axis β= 35°
Shear stress = 6.2 MPa
Applied stress = 12 MPa
We need to calculate the shear stress applied at the slip plane
Using formula of shear stress

Put the value into the formula


Since, the shear stress applied at the slip plane is less than the critical resolved shear stress
So, The crystal will not yield.
Now, We need to calculate the applied stress necessary for the crystal to yield
Using formula of stress

Put the value into the formula


Hence, This is the required solution.
Answer:
B can take 0.64 sec for the longest nap .
Explanation:
Given that,
Total distance = 350 m
Acceleration of A = 1.6 m/s²
Distance = 30 m
Acceleration of B = 2.0 m/s²
We need to calculate the time for A
Using equation of motion

Put the value in the equation



We need to calculate the time for B
Using equation of motion
Put the value in the equation



We need to calculate the time for longest nap
Using formula for difference of time



Hence, B can take 0.64 sec for the longest nap .