Answer:
(a). Energy is 64,680 J
(b) velocity is 51.43m/s
(c) velocity in mph is 115.0mph
Explanation:
(a).
The potential energy 
of the payload of mass 
is at a vertical distance 
is
.
Therefore, for the payload of mass 
at a vertical distance of 
, the potential energy is
(b).
When the payload reaches the bottom of the shaft, all of its potential energy is converted into its kinetic energy; therefore,
(c).
The velocity in mph is
The answer would be D, negative acceleration
In a gear train with two gears, the gear ratio is defined as follows
where
is the angular velocity of the input gear while
is the angular velocity of the output gear.
This can be rewritten as a function of the number of teeth of the gears. In fact, the angular velocity of a gear is inversely proportional to the radius r of the gear:
But the radius is proportional to the number of teeth N of the gear. Therefore we can rewrite the gear ratio also as
r(t) models the water flow rate, so the total amount of water that has flowed out of the tank can be calculated by integrating r(t) with respect to time t on the interval t = [0, 35]min
∫r(t)dt, t = [0, 35]
= ∫(300-6t)dt, t = [0, 35]
= 300t-3t², t = [0, 35]
= 300(35) - 3(35)² - 300(0) + 3(0)²
= 6825 liters
Answer:
41.8m/s^2
Explanation:
Since the dragster starts from rest, initial velocity (u) = 0m/s, final velocity (v) = 25.9m/s, time (t) = 0.62s
From the equations of motion, v = u + at
a = (v - u)/t = (25.9 - 0)/0.62 = 25.9/0.62 = 41.8m/s^2
