What is the similarities of a furnace and the sun?
1 answer:
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Answer:
the work done to lift the bucket = 3491 Joules
Explanation:
Given:
Mass of bucket = 10kg
distance the bucket is lifted = height = 11m
Weight of rope= 0.9kg/m
g= 9.8m/s²
initial mass of water = 33kg
x = height in meters above the ground
Let W = work
Using riemann sum:
the work done to lift the bucket =∑(W done by bucket, W done by rope and W done by water)
=
Work done in lifting the bucket (W) = force × distance
Force (F) = mass × acceleration due to gravity
Force = 9.8 * 10 = 98N
W done by bucket = 98×11 = 1078 Joules
Work done to lift the rope:
At Height of x meters (0≤x≤11)
Mass of rope = weight of rope × change in distance
= 0.8kg/m × (11-x)m
W done = integral of (mass×g ×distance) with upper 11 and lower limit 0
W done =
Note : upper limit is 11 not 1, problem with math editor
W done = 7.84 (11x-x²/2)upper limit 11 to lower limit 0
W done = 7.84 [(11×11-(11²/2)) - (11×0-(0²/2))]
=7.84(60.5 -0) = 474.32 Joules
Work done in lifting the water
At Height of x meters (0≤x≤11)
Rate of water leakage = 36kg ÷ 11m = kg/m
Mass of rope = weight of rope × change in distance
= kg/m × (11-x)m = 3.27kg/m × (11-x)m
W done = integral of (mass×g ×distance) with upper 11 and lower limit 0
W done =
Note : upper limit is 11 not 1, problem with math editor
W done = 32.046 (11x-x²/2)upper limit 11 to lower limit 0
W done = 32.046 [(11×11-(11²/2)) - (11×0-(0²/2))]
= 32.046(60.5 -0) = 1938.783 Joules
the work done to lift the bucket =W done by bucket+ W done by rope +W done by water)
the work done to lift the bucket = 1078 +474.32+1938.783 = 3491.103
the work done to lift the bucket = 3491 Joules
A) Acceleration in part A:
B) Acceleration in part B:
C) Acceleration in part C:
Explanation:
A)
The picture of the problem is missing: find it in attachment.
The acceleration of a body is equal to the rate of change of its velocity:
where
v is the final velocity
u is the initial velocity
is the time it takes for the velocity to change from u to v
In part A of the race, we have:
u = 0
v = 5.5 m/s (estimate)
So the acceleration is
B)
In part B of the race, we have:
u = 5.5 m/s is the initial velocity (estimate)
v = 9.5 m/s is the final velocity (estimate)
is the time interval between the two points considered
Therefore, using the equation for the acceleration, we can find the acceleration in part B:
C)
In part C of the race, we have:
u = 9.5 m/s is the initial velocity (estimate)
v = 11 m/s is the final velocity (estimate)
is the time interval between the two points considered
And therefore, the acceleration in part C of the race is:
Learn more about acceleration:
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