Imagine a spring balance is dropped from the top of a building along with a stone of mass
1kg.
a)What will ne the reading of the spring balance while falling down? Why?
b) If the stone takes 4s to reach the ground, find out the height of the building?
c)What is the velocity of the stone just before it touches the ground?
Answers
a) Reading in the spring balance will be 0 kg. Why so ?
This is because both (the spring balance and the stone) are under the influence of gravity. Both are falling towards Earth with g m/s². We know that, if two objects are dropped at the same time (let's say from different heights, if the height is also same then the vertical separation between them will be 0 throughout the freefall, trivial case), then the vertical separation between them will remain same throughout the freefall (because both have same initial velocity, here 0 m/s and same acceleration which is g m/s²). Thus, the spring won't expand or compress. So, it's reading will be 0 kg throughout the freefall.
Another approach would be is to draw the FBD of the block. What does a spring balance measure ? It measures the force applied on it. In freefall, the stone won't exert a force on it.
I've shown that, the force applied on the stone by the spring balance is zero. Thus, from Newton's Third Law of motion, force applied on the spring balance by the stone will also be zero. Since there is no force, there won't be any extension in the spring. Hence, reading will be 0kg.
b) Time taken, t = 4s
Since, s = ut + ½at²
=> H = 0 + ½gt²
=> H = ½ × 10 × 16 = 80m
c) Since, v = u + at
=> v = 0 + 10×4 = 40 m/s (downwards)
Taking, g = 10m/s²
Sign Convention used here : Up # -ve, Down # +ve
This is all assuming air resistance is zero, gravity is uniform throughout the motion and other necessary assumptions.
Hope, this helps...
