A block is pushed against the spring with spring constant 6.6 kN/m (located on t

Question

A block is pushed against the spring with spring constant 6.6 kN/m (located on the left- hand side of the track) and compresses the spring a distance 4.7 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 fric- tionless 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 9.81 m/s2 .

A. What is the speed v of the block when it leaves the track? Answer in units of m/s.

B. What is the horizontal distance x the block travels in the air? Answer in units of m.

C. What is the total speed of the block when it hits the ground? Answer in units of m/s.

Explanation / Answer

(A) applying energy conservation,

k x^2 /2 = mv^2 /2

6600 (0.047^2) = m v^2

v = sqrt(14.6 / m )

put m in kg and get v in m/s.

(b) height of track is h (in meter ), then in vertical,

h = 0 + g t^2 /2

t = sqrt(2 h / g )

x = v t = sqrt(29.2 h / m g )

(C) energy conservation,

m v^2 /2 + m g h = m vf^2 /2 + 0

vf^2 = (14.6 / m) + (2 g h )

vf = sqrt[ (14.6 / m) + (2 g h )]

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