Respuesta :
Answer:
θ = 12.95º
Explanation:
For this exercise it is best to separate the process into two parts, one where they collide and another where the system moves altar the maximum height
Let's start by finding the speed of the bar plus clay ball system, using amount of momentum
The mass of the bar (M = 0.080 kg) and the mass of the clay ball (m = 0.015 kg) with speed (v₀ = 2.0 m / s)
Initial before the crash
p₀ = m v₀
Final after the crash before starting the movement
[tex]p_{f}[/tex] = (m + M) v
p₀ = [tex]p_{f}[/tex]
m v₀ = (m + M) v
v = v₀ m / (m + M)
v = 2.0 0.015 / (0.015 +0.080)
v = 0.316 m / s
With this speed the clay plus bar system comes out, let's use the concept of conservation of mechanical energy
Lower
Em₀ = K = ½ (m + M) v²
Higher
[tex]E_{mf}[/tex] = U = (m + M) g y
Em₀ = [tex]E_{mf}[/tex]
½ (m + M) v² = (m + M) g y
y = ½ v² / g
y = ½ 0.316² / 9.8
y = 0.00509 m
Let's look for the angle the height from the pivot point is
L = 0.40 / 2 = 0.20 cm
The distance that went up is
y = L - L cos θ
cos θ = (L-y) / L
θ = cos⁻¹ (L-y) / L
θ = cos⁻¹-1 ((0.20 - 0.00509) /0.20)
θ = 12.95º
The maximum angle, measured from vertical that the rod rotates is equal to 50.34°.
Given the following data:
Mass of rod = 80 g to kg = 0.08 kg.
Length of rod = 40 cm to m = 0.4 m.
Mass of ball = 15 g to kg = 0.015 kg.
Speed of ball = 2.0 m/s.
How to determine maximum angle.
First of all, we would derive an equation for the height of the ball in motion as follows:
[tex]h=L-Lcos \theta \\\\h=L(1-cos \theta)[/tex]
Next, we would determine the velocity of the ball by applying the law of conservation of energy:
[tex]PE=KE\\\\mgh=\frac{1}{2}mv^2\\\\V=\sqrt{2gh}\\\\V=\sqrt{2g(L(1-cos\theta)}[/tex]
Since the collision is perfectly inelastic, we have:
[tex]\sqrt{2gL(1-cos\theta)} = \frac{M_bU}{M_b+M_r} \\\\\sqrt{2 \times 9.8 \times 0.4 \times (1-cos\theta)} = \frac{0.08 \times 2}{0.08+0.015}\\\\\sqrt{7.84 (1-cos\theta)} = 1.6842\\\\7.84 (1-cos\theta)=2.8365\\\\7.84-7.84cos\theta =2.8365\\\\7.84cos\theta =7.84-2.8365\\\\7.84cos\theta = 5.0035\\\\\theta = cos^{-1}(\frac{5.0035}{7.84} )\\\\\theta = cos^{-1}(0.6382)\\\\[/tex]
Maximum angle = 50.34°.
Read more on kinetic energy here: brainly.com/question/1242059
