Speed is distance over time, learn that formula and look at the image
Answer:
ω = 12.023 rad/s
α = 222.61 rad/s²
Explanation:
We are given;
ω0 = 2.37 rad/s, t = 0 sec
ω =?, t = 0.22 sec
α =?
θ = 57°
From formulas,
Tangential acceleration; a_t = rα
Normal acceleration; a_n = rω²
tan θ = a_t/a_n
Thus; tan θ = rα/rω² = α/ω²
tan θ = α/ω²
α = ω²tan θ
Now, α = dω/dt
So; dω/dt = ω²tan θ
Rearranging, we have;
dω/ω² = dt × tan θ
Integrating both sides, we have;
(ω, ω0)∫dω/ω² = (t, 0)∫dt × tan θ
This gives;
-1[(1/ω_o) - (1/ω)] = t(tan θ)
Thus;
ω = ω_o/(1 - (ω_o × t × tan θ))
While;
α = dω/dt = ((ω_o)²×tan θ)/(1 - (ω_o × t × tan θ))²
Thus, plugging in the relevant values;
ω = 2.37/(1 - (2.37 × 0.22 × tan 57))
ω = 12.023 rad/s
Also;
α = (2.37² × tan 57)/(1 - (2.37 × 0.22 × tan 57))²
α = 8.64926751525/0.03885408979 = 222.61 rad/s²
True : <span>There are numerous third-class </span>levers<span> in the human </span>body<span>; one example can be illustrated in the elbow joint</span>
Answer:
block velocity v = 0.09186 = 9.18 10⁻² m/s and speed bollet v₀ = 11.5 m / s
Explanation:
We will solve this problem using the concepts of the moment, let's try a system formed by the two bodies, the bullet and the block; In this system all scaffolds during the crash are internal, consequently, the moment is preserved.
Let's write the moment in two moments before the crash and after the crash, let's call the mass of the bullet (m) and the mass of the Block (M)
Before the crash
p₀ = m v₀ + 0
After the crash
= (m + M) v
p₀ = 
m v₀ = (m + M) v (1)
Now let's lock after the two bodies are joined, in this case the mechanical energy is conserved, write it in two moments after the crash and when you have the maximum compression of the spring
Initial
Em₀ = K = ½ m v2
Final
E
= Ke = ½ k x2
Emo = E
½ m v² = ½ k x²
v² = k/m x²
Let's look for the spring constant (k), with Hook's law
F = -k x
k = -F / x
k = - 0.75 / -0.25
k = 3 N / m
Let's calculate the speed
v = √(k/m) x
v = √ (3/8.00) 0.15
v = 0.09186 = 9.18 10⁻² m/s
This is the spped of the block plus bullet rsystem right after the crash
We substitute calculate in equation (1)
m v₀ = (m + M) v
v₀ = v (m + M) / m
v₀ = 0.09186 (0.008 + 0.992) /0.008
v₀ = 11.5 m / s