Answer:
d²x/dt² = - 4dx/dt - 4x is the required differential equation.
Explanation:
Since the spring force F = kx where k is the spring constant and x its extension = 2.45 equals the weight of the 4 kg mass,
F = mg
kx = mg
k = mg/x
= 4 kg × 9.8 m/s²/2.45 m
= 39.2 kgm/s²/2.45 m
= 16 N/m
Now the drag force f = 16v where v is the velocity of the mass.
We now write an equation of motion for the forces on the mass. So,
F + f = ma (since both the drag force and spring force are in the same direction)where a = the acceleration of the mass
-kx - 16v = 4a
-16x - 16v = 4a
16x + 16v = -4a
4x + 4v = -a where v = dx/dt and a = d²x/dt²
4x + 4dx/dt = -d²x/dt²
d²x/dt² = - 4dx/dt - 4x which is the required differential equation
Answer:
The time is 0.5 sec.
Explanation:
Given that,
Voltage V= 12.00 V
Inductance L= 1.20 H
Current = 3.00 A
Increases rate = 8.00 A
We need to calculate change in current
We need to calculate the time interval
Using formula of inductor
Where, 
= change in current
V = voltage
L = inductance
Put the value into the formula
Hence, The time is 0.5 sec.
Answer:
Explained
Explanation:
You should throw your boot in the direction away from the closest shore so that the reaction force is towards the closest shore.
Answer:
I don't now sorry HHHAHAH GOOD LUCK
Answer:
A) Impulse is the same for both the objects
B) The higher is the speed, the greater will be the height.
Explanation:
Part a)
The time of interaction of the two bodies i.e the hanging mass and the stick is same. Thus, force caused by dart on the block = force caused by block on the dart. Hence, impulse is the same for both the objects.
Part B
The energy will be conserved in the entire reaction process
Hence, Kinetic energy = potential energy
0.5Mv^2 = gh(md+mb)
H is directly proportional to the square of speed.
Hence, the higher is the speed, the greater will be the height.
