Careful measurements made during the impact of the 145-g metal cylinder with the spring-loaded plate reveal asemielliptical relation between the contact force Fand the time t of impact as shown. Determine the reboundvelocity v of the cylinder if it strikes the plate with a velocity of 5.3 m/s.5.3 m/s145 gU210.07Time t, sAnswer: vm/sForce F. N

Question
Asked Jun 22, 2019
Careful measurements made during the impact of the 145-g metal cylinder with the spring-loaded plate reveal a
semielliptical relation between the contact force Fand the time t of impact as shown. Determine the rebound
velocity v of the cylinder if it strikes the plate with a velocity of 5.3 m/s.
5.3 m/s
145 g
U
21
0.07
Time t, s
Answer: v
m/s
Force F. N
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Careful measurements made during the impact of the 145-g metal cylinder with the spring-loaded plate reveal a semielliptical relation between the contact force Fand the time t of impact as shown. Determine the rebound velocity v of the cylinder if it strikes the plate with a velocity of 5.3 m/s. 5.3 m/s 145 g U 21 0.07 Time t, s Answer: v m/s Force F. N

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Expert Answer

Step 1

Write the expression for the area under the semi ellipse curve.

 

1
A= - παb
2
1
A= π (21 Ν) (0.035 s)
2
=1.1545
-Ιο
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1 A= - παb 2 1 A= π (21 Ν) (0.035 s) 2 =1.1545 -Ιο

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Step 2

The area under the curve is equal to force acting the plate.

 

A = Fdt 1.1545
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A = Fdt 1.1545

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Step 3

Apply the impulse mome...

ΣFat -mΔνβ
ΣFa=m (% -y)
0
1 kg
1.1545 14510'g2-(-5.3m/s))
2 7.962 -5.3
ν,-2.662 m/s
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ΣFat -mΔνβ ΣFa=m (% -y) 0 1 kg 1.1545 14510'g2-(-5.3m/s)) 2 7.962 -5.3 ν,-2.662 m/s

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