A spherical hot-air balloon is initially filled with air at 120 kPa and 20°C with an initial diameter of 5 m. Air enters this ba
1 answer:
Answer:
The duration is 17.43 minutes.
Explanation:
Based on the provided information, the initial diameter is 5 m
the velocity is 3 m/s
and the final diameter is 17 m.
To find the solution, we will use the volume change equation expressed as
ΔV = .............1
where ΔV represents the change in volume, rf is the final radius, and ri is the initial radius.
Calculating ΔV yields
ΔV =
ΔV = 2507 m³.
Thus,
Q = velocity × Area
Q = 3 × π ×(0.5)² = 2.356 m³/s.
Next, the change in time can be expressed as
Δt =
Δt =
Δt = 1046 seconds.
Therefore, the total change in time amounts to 17.43 minutes.
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Answer:
a) v₂ = 26.6 ft/s
b) v₂ = 31.9 ft/s
Explanation:
a) Applying the principle of energy conservation for the soccer arm from the point of impact to its lowest point:
The ball's velocity in the tangential direction is given by:
v₂*sinθ = v₁*sin30
With the values:
if v₁ = 0
θ = 0º
The restitution coefficient is:
where O=θ
The aggregate momentum equation is:
, where O = θ
When we incorporate gravitational acceleration:
Isolating v₂ results in:
v₂ = 26.6 ft/s
b) To find the ball's velocity, we utilize:
v₂ * sinθ = v₁ * sin30
if v₁ = 10 ft/s
then v₂ * sinθ = 10 * sin30
thus sinθ = 5/v₂
The restitution coefficient remains:
where O = θ
Solving for v₂ yields:
v₂ = 31.9 ft/s
Answer:
153.2 J
Explanation:
Let’s first identify our known variables:
mass (m) of the block = 10 kg
distance slid down (i.e., displacement) = 2 m
coefficient of kinetic friction (μk) = 0.2
In the following diagram, if we analyze the force component directed along the displacement, we find
Fcos 40°
100 (cos 40°)
76.60 N
The work done by the frictional force is then calculated as:
W = × displacement
W = 76.60 × 2
W = 153.2 J
Therefore, the work done by the frictional force equals 153.2 J
