Explanation:
If a question says "at what point does the ball stop?", it means we need to find the position of the ball when its final velocity is equal to 0. It can be calculated using the equation of kinematics as follows :
d = ut + (1/2) at²
and
v²-u²=2ad
Where, u is initial velocity, v is final velocity, a is acceleration, t is time and d is displacement.
Answer:
1.31498 kg
0.72050 s
0.72050 s
Explanation:
m = Mass of block
g = Acceleration due to gravity = 9.81 m/s²
k = Spring constant = 100 N/M
x = Displacement = 0.129 m
The force balance is

The mass of the block is 1.31498 kg
Time period is given by

The period of oscillations is 0.72050 s
The time period does not depend on the acceleration due to gravity. It varies with the mass and the spring constant.
Hence, the time period would be the same
Since you already gave us the weight of the 2.5-kg box,
we don't even need to know what the distance is, just
as long as it doesn't change.
Look at the formula for the gravitational force:
F = G m₁ m₂ / R² .
If 'G', 'm₁' (mass of the Earth), and 'R' (distance from the Earth's center)
don't change, then the Force is proportional to m₂ ... mass of the box,
and you can write a simple proportion:
(6.1 N) / (2.5 kg) = (F) / (1 kg)
Cross-multiply: (6.1 N) (1 kg) = (F) (2.5 kg)
Divide each side by (2.5 kg): F = (6.1N) x (1 kg) / (2.5 kg) = 2.44 N .