Solution:
f ( t )= 20 S ( t ) + 55/30 tS ( t )− 55/30 ( t − 30 ) S ( t − 30 )
• Taking the Laplace Transform:
F ( s ) = 20/s + 55/30 ( 1/s^2 ) – 55/30 ( 1/s^2) e^-30s = 20/s + 55/30 ( 1/s^2 ) ( 1 – e^-30s)
Answer:
51.2 J, 86.2 J, 137.4 J
Explanation:
The kinetic energy of the ball is given by:
where
m = 0.40 kg is its mass
v = 16 m/s is its speed
Substituting,
The potential energy of the ball is given by
where
m = 0.40 kg
is the acceleration of gravity
h = 22 m is the heigth of the cliff
Substituting,
Finally, the total mechanical energy is the sum of the kinetic energy and the potential energy:
Work = force * distance.
We must produce twice as much energy as we are lifting the weight twice as high.
But we are not increasing the force so we must increase the length of the ramp ( distance ) instead.
The new length will be twice as great as the previous length.
So 8 metres is required.
25 kg * 8 m = work = 100 kg * 2 m
