Begin by drawing a picture, showing the spring and block. Indicate the stretch of the spring.
Figure: A block hanging in equilibrium from a spring.
(a) Apply the momentum principle and note that the block's momentum is not changing (after all, it's at rest). This is what it means to be in equilibrium.
Sketch a freebody diagram showing the forces acting on the block.
Figure: A freebody diagram for the block.
Since the block is in equilibrium, the net force on the block is zero. Now, apply the definition of net force as the sum of the forces acting on the block to calculate the net force. Use Hooke's law for the spring force.
Write the above equation in component form for the ycomponent, and solve for the distance stretched.
The spring stretches 0.16 m (16 cm) from its relaxed length. If you've done experiments in the classroom with typical springs used for Hooke's law experiments, then you'll recognize that this distance is reasonable.
(b) Now, you push up on the block with your hand. The spring is stretched 5 cm. Draw a picture of the situation.
Figure: Your hand pushes up on the block.
Draw a freebody diagram for the block. The sum of the upward forces must be equal in magnitude to the downward force since the net force on the block is zero (because it is in equilibrium and its momentum is constant, i.e. it is at rest).
Figure: A freebody diagram for the block when partially supported by your hand.
Again, apply the definition of net force by summing the forces. Note that because of the momentum principle, the net force is zero. Solve for the force by the hand on the block.
Check the direction. It is upward, in agreement with the freebody diagram. It is also less than the gravitational force on the block (2.45 N), as expected. And since the spring is stretched less than half its original distance of 0.16 m, one would expect the force by the hand on the block (1.7 N) to be greater than the force by the spring on the block (0.75 N) which it is. You can therefore be confident that the answer is correct.
