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The surface is tilted to an angle of 37 degrees from the horizontal, as shown above in Figure 3. The blocks are each given a push so that at the instant shown, they are moving toward each other. ii. At the instant shown in Figure 3, the blocks are moving toward each other with the same speed of 0.35m/s . The blocks collide 0.50 seconds later. What is the speed of the two-block system’s center of mass just before the blocks collide?

Respuesta :

Answer:

Incomplete question: "Each block has a mass of 0.2 kg"

The speed of the two-block system's center of mass just before the blocks collide is 2.9489 m/s

Explanation:

Given data:

θ = angle of the surface = 37°

m = mass of each block = 0.2 kg

v = speed = 0.35 m/s

t = time to collision = 0.5 s

Question: What is the speed of the two-block system's center of mass just before the blocks collide, vf = ?

Change in momentum:

[tex]delta(P)=F*delta(t)[/tex]

[tex]P_{f} -P_{i}=F*delta(t)[/tex]

[tex]2m(v_{f} -v_{i})=F*delta(t)[/tex]

[tex]v_{i} =0.35-0.35=0[/tex]

It is neccesary calculate the force:

[tex]F=(m+m)*g*sin\theta[/tex]

Here, g = gravity = 9.8 m/s²

[tex]F=(0.2+0.2)*9.8*sin37=2.3591N[/tex]

[tex]v_{f} =\frac{F*delta(t)}{2m} =\frac{2.3591*0.5}{2*0.2} =2.9489m/s[/tex]

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