Answer:
1.28 m
Explanation:
Generally, pressure of fluid is given by
where g is acceleration due to gravity, h is the height and 
is the density
Considering that the pressure for mercury is same as for blood only that the height and density of fluid are different then
Since g is constant, then
Making 
the subject of the formula then
Where subscripts m and b denote mercury and blood respectively
Assuming density of blood is 1060 Kg/m3, density of mercury as 13600 Kg/m3 and substituting height of mercury for 0.1 m then
Answer:
v_f = 1.05 m/s
Explanation:
From conservation of energy;
E_f = E_i
Thus,
(1/2)m(v_f)² + (1/2)I(ω_f)² + m•g•h_f + (1/2)k•(x_f)² = (1/2)m(v_i)² + (1/2)I(ω_i)² + m•g•h_i + (1/2)k•(x_i)²
This reduces to;
(1/2)m(v_f)² + (1/2)Ik(x_f)² = (1/2)k•(x_i)²
Making v_f the subject, we have;
v_f = [√(k/m)] * [√((x_i)² - (x_f)²)]
We know that ω = √(k/m)
Thus,
v_f = ω[√((x_i)² - (x_f)²)]
Plugging in the relevant values to obtain;
v_f = 17.8[√((0.068)² - (0.034)²)]
v_f = 17.8[0.059] = 1.05 m/s
If we neglect frictional force, the total mechanical energy of the ball is conserved.
The total mechanical energy of the ball is the sum of its kinetic energy K and its potential energy U:
where the kinetic energy depends on the speed v of the ball:
while the potential energy depends on the height h at which the ball is:
As the ball travels along the roller coaster, there is a continuous conversion between kinetic and potential energy, because the total mechanical energy E has always the same value. Therefore, when the ball goes on top of a hill, its height h increases and its potential energy U increases as well, while the speed v decreases and K decreases. Vice-versa, when the ball reaches the bottom of a hill, its height h decreases and therefore the potential energy U decreases, while the speed v increases and therefore the kinetic energy K of the ball increases as well.
