Water, of density 1000 kg/m3, is flowing in a drainage channel of rectangular cross-section. The width of the channel is 15 m, t
1 answer:
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1) 0.77 m
2) 0.23 m
Explanation:
1)
Here we want to find the time elapsed for crouching in order to jump and reach a height of 2.0 m above the floor, starting from 1.0 m above the floor.
First of all, we start by calculating the speed required to jump up to a height of 2.0 m. Since the total energy is conserved, the initial kinetic energy is converted into gravitational potential energy, so:
where
m is the mass of the man
v is the speed after jumping
is the acceleration due to gravity
h = 2.0 - 1.0 = 1.0 m is the change in height
Solving for v,
In the acceleration phase, we know that the initial velocity is
And the force exerted on the floor is 2.3 times the gravitational force, so
This means the net force on you is
because we have to consider the force of gravity acting downward.
So the acceleration of the man is
Now we can use the following suvat equation to find the displacement in the acceleration phase, which is how low the man has to crouch in order to jump:
where s is the quantity we want to find. Solving for s,
2)
At the beginning, we are told that the height of the center of mass above the floor is
h = 1.0 m
During the acceleration phase and the crouch, the height of the center of mass of the body decreases by
This means that the lowest point reached by the center of mass above the floor during the crouch is
This value seems unpractical, since it is not really easy to crouch until having the center of mass 0.23 m above the ground.
Answer:
The fraction of mass that was thrown out is calculated by the following Formula:
M - m = (3a/2)/(g²- (a²/2) - (ag/2))
Explanation:
We know that Force on a moving object is equal to the product of its mass and acceleration given as:
F = ma
And there is gravitational force always acting on an object in the downward direction which is equal to g = 9.8 ms⁻²
Here as a convention we will use positive sign with acceleration to represent downward acceleration and negative sign with acceleration represent upward acceleration.
Case 1:
Hot balloon of mass = M
acceleration = a
Upward force due to hot air = F = constant
Gravitational force downwards = Mg
Net force on balloon is given as:
Ma = Gravitational force - Upward Force
Ma = Mg - F (balloon is moving downwards so Mg > F)
F = Mg - Ma
F = M (g-a)
M = F/(g-a)
Case 2:
After the ballast has thrown out,the new mass is m. The new acceleration is -a/2 in the upward direction:
Net Force is given as:
-m(a/2) = mg - F (Balloon is moving upwards so F > mg)
F = mg + m(a/2)
F = m(g + (a/2))
m = F/(g + (a/2))
Calculating the fraction of the initial mass dropped: