Answer:
Volume of given mass of gas is inversely proportional to pressure of gas
Explanation:
Boyle's law: It states that the volume of given mass of gas is inversely proportional to the pressure of gas at constant temperature.
Mathematical representation:
Suppose, a gas of mass m
T=Constant temperature
V=Volume of gas
P=Pressure of gas
Then, 
The equation for electrical power is<span>P=VI</span>where V is the voltage and I is the current. This can be rearranged to solve for I in 6(a).
6(b) can be solved with Ohm's Law<span>V=IR</span>or if you'd like, from power, after substituting Ohm's law in for I<span>P=<span><span>V2</span>R</span></span>
For 7, realize that because they are in parallel, their voltages are the same.
We can find the resistance of each lamp from<span>P=<span><span>V2</span>R</span></span>Then the equivalent resistance as<span><span>1<span>R∗</span></span>=<span>1<span>R1</span></span>+<span>1<span>R2</span></span></span>Then the total power as<span><span>Pt</span>=<span><span>V2</span><span>R∗</span></span></span>However, this will reveal that (with a bit of algebra)<span><span>Pt</span>=<span>P1</span>+<span>P2</span></span>
For 8, again the resistance can be found as<span>P=<span><span>V2</span>R</span></span>The energy usage is simply<span><span>E=P⋅t</span></span>
Answer
given,
mass of the person, m = 50 Kg
length of scaffold = 6 m
mass of scaffold, M= 70 Kg
distance of person standing from one end = 1.5 m
Tension in the vertical rope = ?
now equating all the vertical forces acting in the system.
T₁ + T₂ = m g + M g
T₁ + T₂ = 50 x 9.8 + 70 x 9.8
T₁ + T₂ = 1176...........(1)
system is equilibrium so, the moment along the system will also be zero.
taking moment about rope with tension T₂.
now,
T₁ x 6 - mg x (6-1.5) - M g x 3 = 0
'3 m' is used because the weight of the scaffold pass through center of gravity.
6 T₁ = 50 x 9.8 x 4.5 + 70 x 9.8 x 3
6 T₁ = 4263
T₁ = 710.5 N
from equation (1)
T₂ = 1176 - 710.5
T₂ = 465.5 N
hence, T₁ = 710.5 N and T₂ = 465.5 N
Refer to the diagram shown below.
From the geometry, obtain
x = 2.5 - 0.55 = 1.95 m
cos θ = 1.95/2.5 = 0.78
θ = cos⁻¹ 0.78 = 38.74°
From the free body diagram, the tension in the chain is 450 N.
F is the centripetal force,
W is Dee's weight.
The components of the tension are
Horizontal component = 450 sin(38.74°) = 281.6 N, acting left.
Vertical component = 450 cos(38.74°) = 351.0 N, acting upward.
Answers:
Horizontal: 281.6, acting left.
Vertical: 351.0 N, acting upward.
Answer: 0 (zero)
Explanation:
The formula for torque = force × perpendicular distance between force and point of rotation.
Where force = 6.3 N, distance between force and point of rotation = 2.1m
It has been stated from the question that the force is applied in such a way that it is parallel to the position vector.
If we take the magnitude of this position vector, it will give the distance between the force and the point of rotation which still shows that the force is parallel to the rotation point which does not satisfy the condition for torque to occur hence torque is zero.
