Question

1. A crane released a block of mass ? 5.0 kg from a height ℎ of 2.0 m towards a spring with spring constant ? of 85 N/m as shown in the figure. Air resistance with a magnitude of 30.0 N acts on the block as it moves through the vertical height ℎ.

(a) By how many meters was the spring compressed? (Ans.: 1.68 m)

(b) What is the velocity of the block just as it touches the spring? (Ans.: 3.90 m/s)

Answer 1

a)

let the maximum compression in the spring is x

Using work energy theorem

change in kinetic energy = total work done on the block

0 - 0 = 5 * 9.8 * (2 + x) - 0.50 * 85 * x^2 - 30 * (2)

solving for x

x = 1.68 m

the maximum compression in the spring would be 1.68 m

b) let the speed of block when it touches the spring is v

Using work energy theorem

change in kinetic energy = total work done on the block

0.50 * 5 * v^2 - 0 = 5 * 9.8 * (2 ) - 30 * (2)

solving for v

v = 3.9 m/s

the speed of block when it touches the spring is 3.9 m/s