Answer:
(a) work required to lift the object is 1029 J
(b) the gravitational potential energy gained by this object is 1029 J
Explanation:
Given;
mass of the object, m = 35 kg
height through which the object was lifted, h = 3 m
(a) work required to lift the object
W = F x d
W = (mg) x h
W = 35 x 9.8 x 3
W = 1029 J
(b) the gravitational potential energy gained by this object is calculated as;
ΔP.E = Pf - Pi
where;
Pi is the initial gravitational potential energy, at initial height (hi = 0)
ΔP.E = (35 x 9.8 x 3) - (35 x 9.8 x 0)
ΔP.E = 1029 J
Some devices are used while moving around from place to place ... like in the car, on a bicycle, running, or walking the dog. If not for batteries, those devices would need very long extension cords.
Answer:
The velocity at the top of its path will be zero (0)
Explanation:
We can solve this problem or particular situation using the principle of energy conservation.
Which tells us that energy is transformed from kinetic energy to potential energy and vice versa. A reference point should be considered at which the potential energy is zero, and at this point the initial velocity of 40 [m/s] is printed to the ball.
![Ek=Ep\\where:\\Ek=kinetic energy [J]\\Ep=potencial energy [J]](https://tex.z-dn.net/?f=Ek%3DEp%5C%5Cwhere%3A%5C%5CEk%3Dkinetic%20energy%20%5BJ%5D%5C%5CEp%3Dpotencial%20energy%20%5BJ%5D)
The potential energy is determined by:
![Ep=m*g*h\\where:\\m=mass of the ball[kg}\\g=gravity[m/s^2]\\h=heigth [m]\\](https://tex.z-dn.net/?f=Ep%3Dm%2Ag%2Ah%5C%5Cwhere%3A%5C%5Cm%3Dmass%20of%20the%20ball%5Bkg%7D%5C%5Cg%3Dgravity%5Bm%2Fs%5E2%5D%5C%5Ch%3Dheigth%20%5Bm%5D%5C%5C)
The kinetic energy is determined by:
![Ek=\frac{1}{2}*m*v_{0} ^{2} \\where\\v_{0} = initial velocity[m/s]](https://tex.z-dn.net/?f=Ek%3D%5Cfrac%7B1%7D%7B2%7D%2Am%2Av_%7B0%7D%20%5E%7B2%7D%20%20%5C%5Cwhere%5C%5Cv_%7B0%7D%20%3D%20initial%20velocity%5Bm%2Fs%5D)
![Ek=Ep\\\frac{1}{2} *m*v_{0} ^{2} =m*9.81*h\\h=\frac{40^{2}}{2*9.81} \\h=81.5[m]](https://tex.z-dn.net/?f=Ek%3DEp%5C%5C%5Cfrac%7B1%7D%7B2%7D%20%2Am%2Av_%7B0%7D%20%5E%7B2%7D%20%3Dm%2A9.81%2Ah%5C%5Ch%3D%5Cfrac%7B40%5E%7B2%7D%7D%7B2%2A9.81%7D%20%5C%5Ch%3D81.5%5Bm%5D)
This will be the maximum path but, its velocity at this point will be zero. Because now all the kinetic energy has been transformed in potential energy.
Answer:
your friend did a work of 1717.34 J
Explanation:
The sum of the work made by your friend and you is equal the change in the kinetic energy, so:

Where
is the work that you did,
is the work that your friend did, m is the mass of the satellite and
and
are the final and initial speeds
Additionally the work that you did is equal to:

Where F and s are vectors. So, the vector s that said the displacement is calculated as:
s = <2.3, 2.6, -11.8> - <3.3, -1.6, 2.0>
s = <-1 , 4.2 , -13.8>
Therefore,
is:


Then, replacing the values on initial equation and solving for
, we get:

Finally, your friend did a work of 1717.34 J