Answer:
x(t) = - 6 cos 2t
Explanation:
Force of spring = - kx
k= spring constant
x= distance traveled by compressing
But force = mass × acceleration
==> Force = m × d²x/dt²
===> md²x/dt² = -kx
==> md²x/dt² + kx=0 ------------------------(1)
Now Again, by Hook's law
Force = -kx
==> 960=-k × 400
==> -k =960 /4 =240 N/m
ignoring -ve sign k= 240 N/m
Put given data in eq (1)
We get
60d²x/dt² + 240x=0
==> d²x/dt² + 4x=0
General solution for this differential eq is;
x(t) = A cos 2t + B sin 2t ------------------------(2)
Now initially
position of mass spring
at time = 0 sec
x (0) = 0 m
initial velocity v= = dx/dt= 6m/s
from (2) we have;
dx/dt= -2Asin 2t +2B cost 2t = v(t) --- (3)
put t =0 and dx/dt = v(0) = -6 we get;
-2A sin 2(0)+2Bcos(0) =-6
==> 2B = -6
B= -3
Putting B = 3 in eq (2) and ignoring first term (because it is not possible to find value of A with given initial conditions) - we get
x(t) = - 6 cos 2t
==>
Answer:4. Two charged objects have a repulsive force of 0.080 N. If the distance separating the objects is tripled, then what is the new force? Explanation: The electrostatic force is inversely related to the square of the separation distance.
Explanation:
Answer:
-120000 W
Explanation:
Power = change in energy / time
P = ΔE / t
P = (½ mv₂² − ½ mv₁²) / t
P = m (v₂² − v₁²) / (2t)
Given m = 1.5 t = 1500 kg, v₂ = 10 m/s, v₁ = 30 m/s, and t = 5 s:
P = (1500 kg) ((10 m/s)² − (30 m/s)²) / (2 × 5 s)
P = -120000 W
True, they had a hole in their hip socket that allowed them to run faster than other reptiles of their size at the time. As well as most reptiles besides reptiles had legs to the side, rather than under them like dinosaurs did.
Hope this helps!
Answer:
B) PbI2 + 2 KCl
Explanation:
To keep the the law of conservation of matter, the equation given above must be balanced i.e the total element in the reactant must be equal to the total elements in the product.
Given the equation
PbCl2 (aq) + 2 KI (aq) →
At the reactant shown, there are one mole of lead Pb, 2 moles of chlorine Cl, 2moles of Potassium K and 2 moles of Iodine.
During reaction, the Chlorine atom will react with the potassium atom K and the lead atom Pb will react with the iodine atom.
The resulting product that will balance the chemical equation is
PbI2 + 2 KCl
The equation will then become
PbCl2 (aq) + 2 KI (aq) → PbI2 + 2 KCl
If we look at both sides of the equation, we will see that all the elements have the same number of atoms.
