1) The final velocity of the device is 14.7 m/s
2) The momentum of the device is 14.7 kg m/s
3) The potential energy of the device before it is dropped is 108 J
4) The final kinetic energy is 108 J
Explanation:
1)
The motion of the device is a free fall motion, which is a uniformly accelerated motion (=constant acceleration of [tex]g=9.8 m/s^2[/tex] downward), therefore it can be studied by using the following suvat equation:
[tex]v=u+at[/tex]
where
v is the final velocity
u is the initial velocity
a is the acceleration
t is the time
For the device in this problem, we have:
u = 0 (it is dropped from rest)
[tex]a=g=9.8 m/s^2[/tex] is the acceleration (we have taken downward as positive direction)
Substituting t = 1.5 s, we find the final velocity of the device:
[tex]v=0+(9.8)(1.5)=14.7 m/s[/tex]
2)
The momentum of an object is given by
[tex]p=mv[/tex]
where
m is the mass of the object
v is its velocity
Here, the mass of the device is not given. I assume it is
m = 1 kg
Its velocity just before hitting the ground is (part 1)
v = 14.7 m/s
Substituting into the equation, we find the final momentum of the device:
[tex]p=(1)(14.7)=14.7 kg m/s[/tex]
3)
First of all, we need to find the height from which the device was dropped. This can be done by using the suvat equation:
[tex]h=ut+\frac{1}{2}at^2[/tex]
where
h is the vertical displacement (which is equal to the initial height of the device)
u = 0 is the initial velocity
[tex]a=9.8 m/s^2[/tex] is the acceleration
t = 1.5 s is the time of flight
Substituting,
[tex]h=0+\frac{1}{2}(9.8)(1.5)^2=11.0 m[/tex]
Now we can find the potential energy of the device before it is dropped by using the equation
[tex]PE=mgh[/tex]
where
m = 1 kg is the mass
[tex]g=9.8 m/s^2[/tex]
h = 11.0 m
Substituting,
[tex]PE=(1)(9.8)(11.0)=108 J[/tex]
4)
The kinetic energy of the device just before hitting the ground is given by
[tex]K=\frac{1}{2}mv^2[/tex]
where
m is the mass of the device
v is the final velocity of the device
In this problem, we have:
m = 1 kg is the mass
v = 14.7 m/s is the final velocity
Substituting,
[tex]KE=\frac{1}{2}(1)(14.7)^2=108 J[/tex]
We observe that this energy is equal to the initial potential energy of the device before being dropped: this is a consequence of the law of conservation of energy, which states that the total mechanical energy (potential+kinetic) of the device remains conserved during the fall. Therefore, the initial potential energy has simply converted into kinetic energy during the fall.
Learn more about free fall:
brainly.com/question/1748290
brainly.com/question/11042118
brainly.com/question/2455974
brainly.com/question/2607086
About kinetic energy and potential energy:
brainly.com/question/6536722
brainly.com/question/1198647
brainly.com/question/10770261
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