A 50-N crate is pulled up a 5-m inclined plane by a worker at constant velocity. If the plane is inclined at an angle of 37° to
the horizontal and there exists a constant frictional force of 10 N between the crate and the surface, what is the force applied by the worker?
1 answer:
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The two light bulbs are connected in series, this means that their equivalent resistance is just the sum of the two resistances:
And so, the current through the circuit is (using Ohm's law):
And since the two bulbs are connected in series, the current through each bulb is the same.
2) 4 W and 8 W
The power dissipated by each bulb is given by the formula:
where I is the current and R is the resistance.
For the first bulb:
For the second bulb:
3) 12 W
The total power dissipated in both bulbs is simply the sum of the power dissipated by each bulb, so:
At the point of maximum displacement (a), the elastic potential energy of the spring is maximum:
while the kinetic energy is zero, because at the maximum displacement the mass is stationary, so its velocity is zero:
And the total energy of the system is
Viceversa, when the mass reaches the equilibrium position, the elastic potential energy is zero because the displacement x is zero:
while the mass is moving at speed v, and therefore the kinetic energy is
And the total energy is
For the law of conservation of energy, the total energy must be conserved, therefore
. So we can write
that we can solve to find an expression for v:
while the kinetic energy is zero, because at the maximum displacement the mass is stationary, so its velocity is zero:
And the total energy of the system is
Viceversa, when the mass reaches the equilibrium position, the elastic potential energy is zero because the displacement x is zero:
while the mass is moving at speed v, and therefore the kinetic energy is
And the total energy is
For the law of conservation of energy, the total energy must be conserved, therefore
that we can solve to find an expression for v: