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1 answer:
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1) Gravitational potential energy: 73 500 J
2) Kinetic energy: 135 000 J
3) Mechanical energy: 208 500 J
Explanation:
1)
The gravitational potential energy of an object is the energy possessed by the object due to its position in the Earth's gravitational field, and it is given by
where
m is the mass of the object
is the acceleration of gravity
h is the height of the object relative to the ground
For the skydiver in this problem,
m = 75 kg is his mass
h = 100 m is his height above the Earth
Substituting, we find
2)
The kinetic energy of a body is the energy due to its motion, and it is given by
where
m is the mass of the body
v is its speed
For the skydiver in this problem,
m = 75 kg is his mass
v = 60 m/s is his speed
Substituting, we find the kinetic energy
3)
The mechanical energy of an object is the sum of the gravitational potential energy and the kinetic energy of the object:
where
U is the gravitational potential energy
K is the kinetic energy
For the skydiver in this problem,
U = 73,500 J is the gravitational potential energy
K = 135,000 J is the kinetic energy
Substituting, we find
Learn more about potential energy and kinetic energy:
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Answer:
2.22m/s to the left
Explanation:
Given parameters:
Initial position = +125m
Final position = -75m
Motion time = 90s
Unknown:
Velocity of the steel ball = ?
Solution:
The velocity of the steel ball is given as the displacement divided by the time;
Velocity =
The net displacement of the ball = 125- (-75) = 200m to the left
Input the parameters and solve for the velocity;
Velocity = = 2.22m/s to the left
1) 9.4 m/s
First of all, we can calculate the work done by the horizontal force, given by
W = Fd
where
F = 34.6 N is the magnitude of the force
d = 12.9 m is the displacement of the cart
Solving ,
W = (34.6 N)(12.9 m) = 446.3 J
According to the work-energy theorem, this is also equal to the kinetic energy gained by the cart:
Since the cart was initially at rest, , so
(1)
where
m is the of the cart
v is the final speed
The mass of the cart can be found starting from its weight, :
So solving eq.(1) for v, we find the final speed of the cart:
2)
The work done on the train is given by
W = Fd
where
F is the magnitude of the force
d is the displacement of the train
In this problem,
So the work done is
3)
According to the work-energy theorem, the change in kinetic energy of the train is equal to the work done on it:
where
W is the work done
is the change in kinetic energy
Therefore, the change in kinetic energy is
4) 37.2 m/s
According to the work-energy theorem,
where
is the final kinetic energy of the train
is the initial kinetic energy of the train, which is zero since the train started from rest
Re-writing the equation,
where
m = 36300 kg is the mass of the train
v is the final speed of the train
Solving for v, we find