A block is pushed against the spring with spring constant 8.5 kN/m (located on t

Question

A block is pushed against the spring with

spring constant 8.5 kN/m (located on the lefthand side of the track) and compresses the

spring a distance 5.3 cm from its equilibrium

position (as shown in the ?gure below).

The block starts at rest, is accelerated by

the compressed spring, and slides across a frictionless track (as shown in the ?gure below).

It leaves the track horizontally, ?ies through

the air, and subsequently strikes the ground.

The acceleration of gravity is 9.81 m/s^2

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

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

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

A block is pushed against the spring with spring constant 8.5 kN/m (located on the lefthand side of the track) and compresses the spring a distance 5.3 cm from its equilibrium position (as shown in the ?gure below). The block starts at rest, is accelerated by the compressed spring, and slides across a frictionless track (as shown in the ?gure below). It leaves the track horizontally, ?ies through the air, and subsequently strikes the ground. The acceleration of gravity is 9.81 m/s^2 A.What is the speed v of the block when itleaves the track?Answer in units of m/s B.What is the horizontal distance x the blocktravels in the air?Answer in units of m C.What is the total speed of the block when ithits the ground?Answer in units of m/s

Explanation / Answer

A. using energy conservation,

kx2 /2 = mv2 /2

8500 x (0.053)2 = 0.583 x v2

v = 6.40 m/s

B. it have to travel 2.3m vertically,

H = gt2 /2

t = 2.3 x 2/9.81 = 0.685 sec

x = vt = 6.40 x 0.685 = 4.38 m

C. until then it will also aquire vertical velocity compnnet.

vy = u + at = 0 + 9.81 x 0.685 = 6.72 m/s

vx =v = 6.40 m/s

Total speed = 6.722 + 6.402 = 9.29 m/s

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