007 (part 1 of 3) 10.0 points A block is pushed against the spring with spring c

Question

007 (part 1 of 3) 10.0 points A block is pushed against the spring with spring constant 6.5 kN/m (located on the left- hand side of the track) and compresses the spring a distance 4.9 cm from its equilibrium position (as shown in the figure below). The block starts at rest, is accelerated by the compressed spring, and slides across a frictionless track except for a small rough area on a horizontal section of the track (as shown in the figure below). It leaves the track horizontally, flies through the air, and subsequently strikes the ground. The acceleration of gravity is 9.8 m/s 6.5 kN/m 476 g --Vz p00999.. 4.9 cm 1.1 m What is the speed v of the block when it O leaves the track?

Explanation / Answer

a)

using conservation of energy

spring potential energy = work done by friction + kinetic energy

(0.5) k x2 = uk mg d + (0.5) m v2

(0.5) (6500) (0.049)2 = (0.3) (0.476) (9.8) (1.1) + (0.5) (0.476) v2

v = 5.13 m/s

b)

consider the motion along the Y-direction

Voy = initial velocity = 0 m/s

a = acceleration = 9.8

Y = displacement = height = 1.9 m

t = time taken

using the equation

Y = Voy t + (0.5) a t2

1.9 = 0 t + (0.5) (9.8) t2

t = 0.62 sec

consider the motion along the horizontal direction

X = v t = 5.13 x 0.62 = 3.2 m

c)

v' = speed as it hits the ground

using conservation of energy

kinetic energy at the top + potential energy at top = kinetic energy at the bottom

(0.5) m v2 + mgh = (0.5) m v'2

(0.5) (5.13)2 + (9.8 x 1.9) = (0.5) v'2

v' = 7.97 m/s

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