Answer:
Given R (t) = 60/(1+t²), ft
/min
To find the amount of air in ft³, during the first min,
R (t) = 60/(1+t²
at t=1min, R is the air amount in ft³/min
Take the integral, and evaluate over [0,1]
Integral Of R (t) = 60/(1+t²) = 60 tan⁻¹(t),
60(Tan⁻¹(1) - Tan⁻¹(0)) = 60(pi/2) = 30 π
Therefore, it means that in the first minute, 30π ft³ of air escaped.
2.88 m/s is the velocity afterward.
Explanation:
By using the law of conservation of momentum
Initial momentum = final momentum





v = is their combined velocity afterwards
Solving equation (1) for v




V = 2.88 m/s
Therefore the velocity afterward is <u>2.88 m/s</u>.
Answer:
Part a)
When rotated about the mid point

Part b)
When rotated about its one end

Explanation:
As we know that the angular acceleration of the rod is rate of change in angular speed
so we will have



Part a)
When rotated about the mid point



now torque is given as


Part b)
When rotated about its one end



now torque is given as


Answer:
The overall thermal efficiency is 30%.
Explanation:
Given;
Output power = 500 kWh
input energy per kg of coal = 6 MJ = 6 x 10⁶ J = 1.66667 kWh
1000 kg of coal will produce 1000 x 1.66667 kWh = 1666.67 kWh
Thus, total input power = 1666.67 kWh
Overall thermal efficiency = Total output power/Total input Power
Overall thermal efficiency = (500/1666.67) *100
Overall thermal efficiency = 0.29999 *100
Overall thermal efficiency = 30%
Therefore, the overall thermal efficiency is 30%.
Answer:
13.23J
Explanation:
PE = m*g*h
PE = (3 kg ) * (9.8 m/s/s) * (0.45 m)