ame: ID: A (15 points) A body of mass 5.0 kg is suspended by then displaced down

Question

ame: ID: A (15 points) A body of mass 5.0 kg is suspended by then displaced downward an additional 5.0 cm and released. 17. a spring which stretches 10 cm when the mass is attached. It is a) Its position as a function of time is approximately A) y()--o.10 sin (9.90 B) y() = +0.10 cos (99) C) y()--0.05 cos (9.9t+.1) D) y() +0.05 sin (9.91+5) E) y(0)--0.05 cos (9.9) b) What will the velocity of the mass be 1.3 sec after the mass has been put into motion? A) 11.0 cm/s B) 18.2 cm /s C) 33.1 cm/s D) 48.2 cm/s E) 49.5 cm/s e) What is the force that the spring exerts on the mass 1.3 sec after the mass is put into motion? A) 12.4N B) 23.9N C) 28.1 N D) 32.3 N E) 49.0N

Explanation / Answer

17. given, m = 5 kg

d = 10 cm

x = 5 cm

a. hence

psring constat = k

from force balance

mg = kd

hence

k = mg/d

hence

from the given data

amplitudxe, A = x = 5 cm

xo = -0.05 cm

so E) is the answer

y(t) = -0.05cos(9.9t)

b. v(t) = dy/dt = 9.9*(-0.05)*(_1)sin(9.9t)

at t = 1.3 s

hence

v(1.3 s ) = 0.14799784 m/s= 14.799784 cm/s

c. F = m*a = kx

F = mg*x(1.3 s)/d = -23.40316 N

hecne option B)

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