A large spool in an electrician's workshop has 70 m of insulation-coated wire coiled around it. When the electrician connects a
1 answer:
Answer:
54.0m
Explanation:
#First we solve for
let's denote the initial and final length of the rope as respectively and given as:
is the initial resistance and Rf the final of the wire.
From the initial resistance
of the spooled wire are:
#Substituting eqtn 3 in 2, we get
#the length of wire remaining on the spool is 54.0m
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Answer:
126.99115 g
Explanation:
50 g at 90 cm
Stick balances at 61.3 cm
x = Distance of the third 0.6 kg mass
Meter stick hanging at 50 cm
Torque about the support point is given by (torque is conserved)
The mass of the meter stick is 126.99115 g
Taking into account the definition of kinetic, potencial and mechanical energy, when the brick hits the ground, it has a speed of 7,668 m/s.
<h3>Kinetic energy</h3>Kinetic energy is a form of energy. It is defined as the energy associated with bodies that are in motion and this energy depends on the mass and speed of the body.
Kinetic energy is defined as the amount of work necessary to accelerate a body of a given mass and at rest, until it reaches a given speed. Once this point is reached, the amount of accumulated kinetic energy will remain the same unless there is a change in speed or the body returns to its state of rest by applying a force.
The kinetic energy is represented by the following expression:
Ec= ½ mv²
Where:
- Ec is the kinetic energy, which is measured in Joules (J).
- m is the mass measured in kilograms (kg).
- v is the speed measured in meters over seconds (m/s).
On the other hand, potential energy is the energy that measures the ability of a system to perform work based on its position. In other words, this is the energy that a body has at a certain height above the ground.
Gravitational potential energy is the energy associated with the gravitational force. This will depend on the relative height of an object to some reference point, the mass, and the force of gravity.
So for an object with mass m, at height h, the expression applied to the gravitational energy of the object is:
Ep= m×g×h
Where:
- Ep is the potential energy in joules (J).
- m is the mass in kilograms (kg).
- h is the height in meters (m).
- g is the acceleration of fall in m/s².
Finally, mechanical energy is that which a body or a system obtains as a result of the speed of its movement or its specific position, and which is capable of producing mechanical work. Then:
Potential energy + kinetic energy = total mechanical energy
<h3>Principle of conservation of mechanical energy </h3>The principle of conservation of mechanical energy indicates that the mechanical energy of a body remains constant when all the forces acting on it are conservative (a force is conservative when the work it does on a body depends only on the initial and final points and not the path taken to get from one to the other.)
Therefore, if the potential energy decreases, the kinetic energy will increase. In the same way, if the kinetics decreases, the potential energy will increase.
<h3>This case</h3>A brick of mass 5 kg is released from rest at a height of 3 m. Then, at this height, the brick of mass has no speed, so the kinetic energy has a value of zero because it depends on the speed or moving bodies. But the potential energy is calculated as:
Ep= 5 kg× 9.8 × 3 m
Solving:
<u><em>Ep= 147 J</em></u>
So, the mechanical energy is calculated as:
Potential energy + kinetic energy = total mechanical energy
147 J + 0 J= total mechanical energy
147 J= total mechanical energy
The principle of conservation of mechanical energy can be applied in this case. Then, when the brick hits the ground, the mechanical energy is 147 J. In this case, considering that the height is 0 m, the potential energy is zero because this energy depends on the relative height of the object. But the object has speed, so it will have kinetic energy. Then:
Potential energy + kinetic energy = total mechanical energy
0 J + kinetic energy= 147 J
kinetic energy= 147 J
Considering the definition of kinetic energy:
½ 5 kg×v²= 147 J
v=7.668 m/s
Finally, when the brick hits the ground, it has a speed of 7,668 m/s.
Learn more about mechanical energy:
#SPJ1
Answer:
The magnitude of the resultant decreases from A+B to A-B
Explanation:
The magnitude of the resultant of two vectors is given by
where
A is the magnitude of the first vector
B is the magnitude of the second vector
is the angle between the directions of the two vectors
In the formula, A and B are constant, so the behaviour depends only on the function . The value of
are:
- 1 (maximum) when the angle is 0, so the magnitude of the resultant in this case is
- then it decreases, until it becomes 0 when the angle is 90 degrees, where the magnitude of the resultant is
- then it becomes negative, and continues to decrease, until it reaches a value of -1 when the angle is 180 degrees, and the magnitude of the resultant is