From the information given in the drawing, it's not possible
to tell whether the displacements are equal, because we
don't know what the vectors represent.
If the vectors are distances, then the displacements are not
equal, because the distance between the start and end points
are not equal.
If the vectors are speeds, then they don't tell us anything about
the distance between the start and end points, so we can't calculate
the displacements.
Answer:
2.61 J
Explanation:
Since potential energy U = mgy where m = mass of object, g = acceleration due to gravity = 9.8 m/s² and y = height of object above the ground.
Now for the coffee mug, m= 0.422 kg and it is 0.63 m on a table, so it is 0.63 m above the ground. Thus, y = 0.63 m.
We compute U
U = mgy
= 0.422 kg × 9.8 m/s² × 0.63 m
= 2.605 J
≅ 2.61 J
So, the potential energy of the mug with respect to the floor is 2.61 J
Answer: the constant angular velocity of the arms is 86.1883 rad/sec
Explanation:
First we calculate the linear velocity of the single sprinkler;
Area of the nozzle = π/4 × d²
given that d = 8mm = 8 × 10⁻³
Area of the nozzle = π/4 × (8 × 10⁻³)²
A = 5.024 × 10⁻⁵ m²
Now total discharge is dived into 4 jets so discharge for single jet will be;
Q_single = Q / n = 0.006 / 4 = 1.5 × 10⁻³ m³/sec
So using continuity equation ;
Q_single = A × V_single
V_single = Q_single/A
we substitute
V_single = (1.5 × 10⁻³) / (5.024 × 10⁻⁵)
V_single = 29.8566 m/s
Now resolving the forces as shown in the second image,
Vt = Vcos30°
Vt = 29.8566 × cos30°
Vt = 25.8565 m/s
Finally we calculate the angular velocity;
Vt = rω
ω_single = Vt / r
from the given diagram, radius is 300mm = 0.3m
so we substitute
ω_single = 25.8565 / 0.3
ω_single = 86.1883 rad/sec
Therefore the constant angular velocity of the arms is 86.1883 rad/sec
Answer:
i) 0.9504
ii) 0.0452
Explanation:
Given data: reliability of hydraulic brakes= 0.96
reliability of mechanical brakes = 0.99
So the probability of stopping the truck = 0.96×0.99= 0.9504
At low speed
case: A works and B does not
= 0.96×(1-0.99) = 0.0096
case2 : B works and A does not
= 0.99×(1-0.96) = 0.0396
Therefore, probality of stopping = 0.0096+0.0396 = 0.0492
