035 (part 1 of 3) 10.0 points A block of mass 531 g is pushed against the spring

Question

035 (part 1 of 3) 10.0 points A block of mass 531 g is pushed against the spring (located on the left-hand side of the track) and compresses the spring a distance 5 cm from its equilibrium position (as shown in the figure below). The block starts from rest, is accelerated by the compressed spring and slides (as shown in the figure below). It leaves the track horizontally, flies through the air, and subsequently strikes the ground across a frictionless horizontal track The acceleration of gravity is 9.81 m/s 531 g - 5 cm 4.8 m What is the spring constant? Answer in units of N/m. 036 (part 2 of 3) 10.0 points What is the speed v of the block when it leaves the track? Answer in units of m/s. 037 (part 3 of 3) 10.0 points What is the total speed of the block when it hits the ground?

Explanation / Answer

in vertical, after leaving the surface,
  
v0y = 0 and ay = - 9.81 m/s^2

y = v0y t + ay t^2 / 2

- 2 = 0 - 9.81 t^2 /2

t = 0.64 sec

v = 4.8/ t = 7.52 m/s

Applying energy conservation,

k x^2 /2 = m v^2 /2

k (0.05^2) = 0.532 x 7.52^2

k = 12000 N/m

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v = 7.52 m/s

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7.52^2 /2 + (9.8 x 2) = vf^2 /2

vf = 9.8 m/s

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