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
<span>I think that the coefficient of cubical expansion of a substance depends on THE CHANGE IN VOLUME.
Cubical expansion, also known as, volumetric expansion has the following formula:
</span>Δ V = β V₁ ΔT
V₁ = initial volume of the body
ΔT = change in temperature of the body
β = coefficient of volumetric expansion.
β is defined as the <span>increase in volume per unit original volume per Kelvin rise in temperature.
</span>
With the above definition, it is safe to assume that the <span>coefficient of cubical expansion of a substance depends on the change in volume, which also changes in response to the change in temperature. </span>
To solve this problem we will apply the concepts related to energy conservation. From this conservation we will find the magnitude of the amplitude. Later for the second part, we will need to find the period, from which it will be possible to obtain the speed of the body.
A) Conservation of Energy,
Here,
m = Mass
v = Velocity
k = Spring constant
A = Amplitude
Rearranging to find the Amplitude we have,
Replacing,
(B) For this part we will begin by applying the concept of Period, this in order to find the speed defined in the mass-spring systems.
The Period is defined as
Replacing,
Now the velocity is described as,
We have all the values, then replacing,
The functions of angles are used to find unknown lengths or angles that can't be measured, in terms of known quantities. The trig functions of angles are ratios of lengths, so they're bare naked numbers without units.
