Explanation & answer:
Given:
Fuel consumption, C = 22 L/h
Specific gravity = 0.8
output power, P = 55 kW
heating value, H = 44,000 kJ/kg
Solution:
Calculate energy intake
E = C*P*H
= (22 L/h) / (3600 s/h) * (1000 mL/L) * (0.8 g/mL) * (44000 kJ/kg)
= (22/3600)*1000*0.8*44000 j/s
= 215111.1 j/s
Calculate output power
P = 55 kW
= 55000 j/s
Efficiency
= output / input
= P/E
=55000 / 215111.1
= 0.2557
= 25.6% to 1 decimal place.
Answer:
The magnitude of the electric field is 0.1108 N/C
Explanation:
Given;
number of electrons, e = 8.05 x 10⁶
length of the wire, L = 1.03 m
distance of the field from the center of the wire, r = 0.201 m
Charge of the electron;
Q = (1.602 x 10⁻¹⁹ C/e) x (8.05 x 10⁶ e)
Q = 1.2896 x 10⁻¹² C
Linear charge density;
λ = Q / L
λ = (1.2896 x 10⁻¹² C) / (1.03 m)
λ = 1.252 x 10⁻¹² C/m
The magnitude of electric field at r = 0.201 m;

Therefore, the magnitude of the electric field is 0.1108 N/C
Answer:
5m/8
Explanation:
Function T gives the time the Hobbits have to prepare for the attack, T(k), in minutes, as a function of troll's distance, k, in meters.
Function V gives visibility from the watchtower, V(m), in meters, as a function of the height of the watchtower, m, in meters.
Therefore, T(V(m)) will give the time the Hobbits have to prepare for the troll attack as a function of the height, m, of the watchtower.
We can input m into function V to obtain the visibility from watchtower, V(m), in meters. Since visibility indicates the distance you can see, this also gives the distance of the trolls. This can then be input into function T to obtain the time that the Hobbits have to prepare for a troll attack.
Let's find T(V(m)) by substituting the formula for V(m) into function T as shown below.
T(V(M))=T(50m)
=50m/80
We can simplify this as follows:
=50m/80
=5m/8
Answer:
Explanation:
We can use the conservation of the angular momentum.


Now the Inertia is I(professor_stool) plus mR², that is the momentum inertia of a hoop about central axis.
So we will have:

Now, we just need to solve it for ω.

I hope it helps you!
Answer:
maximum amplitude = 0.08 m
Explanation:
Given that
Time period T= 0.58 s
acceleration of gravity g= 9.8 m/s²
We know that time period of simple harmonic motion given as
T = 2π/ω
0.58 = 2π/ω
ω = 10.83rad/s
ω=angular frequency
Lets take amplitude = A
The maximum acceleration given as
a= ω² A
The maximum acceleration should be equal to g ,then block does not separate
a= ω² A
9.8 = 10.83² A
A = 0.08m
maximum amplitude = 0.08 m