To solve this problem we apply the thermodynamic equations of linear expansion in bodies.
Mathematically the change in the length of a body is subject to the mathematical expression
Where,
Initial Length
Thermal expansion coefficient
Change in temperature
Since we have values in different units we proceed to transform the temperature to degrees Celsius so
The coefficient of thermal expansion given is
The initial length would be,
Replacing we have to,
This means that the building will be 35.5cm taller
r = radius of the circle traveled by the particle = 76 cm = 0.76 m
T = time period of revolution for the particle = 4.5 s
w = angular velocity of the particle
angular velocity of the particle is given as
w = 2π/T
inserting the values
w = 2 (3.14)/4.5
w = 1.4 rad/s
a = centripetal acceleration of the particle in the circle
centripetal acceleration is given as
a = r w²
inserting the values
a = (0.76) (1.4)²
a = 1.5 m/s²
Let the rise in temperature be 
The expansion in length due to change in temperature is given by the expression lαΔt , where l is the length, α is the coefficient of linear expansion, Δt is the change in temperature.
Here l = 93 m, α = 
, and Δt =
So expansion in length = 93**5 = 0.007905 m = 
So order of magnitude in change in length = -3
Answer:
v₀ = 280.6 m / s
Explanation:
we have the shock between the bullet and the block that we can work with at the moment and another part where the assembly (bullet + block) compresses a spring, which we can work with mechanical energy,
We write the mechanical energy when the shock has passed the bodies
Em₀ = K = ½ (m + M) v²
We write the mechanical energy when the spring is in maximum compression
½ (m + M) v² = ½ k x²
Let's calculate the system speed
v = √ [k x² / (m + M)]
v = √[152 ×0.78² / (0.012 +0.109) ]
v = 27.65 m / s
This is the speed of the bullet + Block system
Now let's use the moment to solve the shock
Before the crash
p₀ = m v₀
After the crash
The system is formed by the bullet and block assembly, so the forces during the crash are internal and the moment is preserved
m v₀ = (m + M) v
v₀ = v (m + M) / m
let's calculate
v₀ = 27.83 (0.012 +0.109) /0.012
v₀ = 280.6 m / s
