5.) At rest, Block A compresses a spring (ki-200 N/m) by 0.25 m. One the system

Question

5.) At rest, Block A compresses a spring (ki-200 N/m) by 0.25 m. One the system is released, Block A slides across a surface with a coefficient of kinetic friction of 0.2 and strikes Block B which is sitting, at rest, 3 meters from Block A's starting position. After the impact, Block B slides 1 m until it makes contact with another spring (k280 N/m) and compresses it 0.2 m before Block B comes to a rest. What is the coefficient of restitution of the impact between Block A and Block B? (Block A weighs 3 N, Block B weighs 1.5 N) 5, = 0.25 m k, -200 N/ mA 02 k2 = 80 N/ m 3 m I m 20.2 m

Explanation / Answer

To calculate the coefficient of restitution must know the initial and final velocities of the body

e= - (V2f – V1f) / ( V2i – V1i)

Let's calculate the initial velocity of block A

We use the conservation of mechanical energy to find the initial velocity of block A

Emi = Us = ½ k x2

Eme = K = ½ m Va2

Emi = Eme

½ k x2 = ½ m Va2

Va= sqrt(k/m) X

Va= sqrt (200/(3/9.8) ) 0.25

Va = 6.39 m

Now we calculate the speed just before the crash

fr= m a

N = m a mg = m a

a = g

a = 0.2 9.8 = 1.96 m/s

Vaf2 = Va2 – 2 a x Vaf2= 6.392 - 2 1.96 3 = 29.074 m/s

Vaf = 5.392 m/s

This is the speed just before the crash

Vai = 5.392 m/s

Vbi =0

Now we need the output speed of the block B after the collision

for this we use the conservation of energy in the second block

Emc = ½ m Vc2

Emd = ½ k2 x22

½ mb Vc2 = ½ k2 x22

Vc = sqrt (k2/m.2) x2

Vc = sqrt(80/ (1.5/9.8) ) 0.2

Vc = 4.572 m/s

calculate the acceleration to rubbing

m.2g = m.2 a2

a2 = g = 0.2 9.8 = 1.96 m/s2

Vc2 = Vbf2 – 2 a2 x2

Vbf2 = Vc2 + 2 a2 x2

Vbf2 = 4.5722 + 2 1.96 1

Vbf2 = 24.82 m/s

Vbf = 4.982 m/s

Just after the crash

Vbf = 4.982 m/s

No explicit velocity data block A after the collision occur, so assume the most common situation, the VAF = 0 comes to rest after the impact

with four values that can calculate the coefficient of restitution

e = - (4.982 – 0) / (5.328 – 0)

e = – 0,935

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