A small insect viewed through a convex lens is 1.5 cmcm from the lens and appears 2.5 times larger than its actual size. Part A
1 answer:
Answer:
The focal length of the lens is 2.5 cm
Explanation:
Use the two equations for thin lenses combined: the one for magnification (m), and the one that relates distances of object , of image
, and focal length;
Since we know the value of the magnification (m), we can write the image distance in terms of the object distance, and then use it to replace the image distance in the second equation:
then, solving for the focal distance knowing that the object distance is 1.5 cm:
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The total mechanical energy of the system at any time t is the sum of the kinetic energy of motion of the ball and the elastic potential energy stored in the spring:
where m is the mass of the ball, v its speed, k the spring constant and x the displacement of the spring with respect its rest position.
Since it is a harmonic motion, kinetic energy is continuously converted into elastic potential energy and vice-versa.
When the spring is at its maximum displacement, the elastic potential energy is maximum (because the displacement x is maximum) while the kinetic energy is zero (because the velocity of the ball is zero), so in this situation we have:
Instead, when the spring crosses its rest position, the elastic potential energy is zero (because x=0) and therefore the kinetic energy is at maximum (and so, the ball is at its maximum speed):
Since the total energy E is always conserved, the maximum elastic potential energy should be equal to the maximum kinetic energy, and so we can find the value of the maximum speed of the ball:
where m is the mass of the ball, v its speed, k the spring constant and x the displacement of the spring with respect its rest position.
Since it is a harmonic motion, kinetic energy is continuously converted into elastic potential energy and vice-versa.
When the spring is at its maximum displacement, the elastic potential energy is maximum (because the displacement x is maximum) while the kinetic energy is zero (because the velocity of the ball is zero), so in this situation we have:
Instead, when the spring crosses its rest position, the elastic potential energy is zero (because x=0) and therefore the kinetic energy is at maximum (and so, the ball is at its maximum speed):
Since the total energy E is always conserved, the maximum elastic potential energy should be equal to the maximum kinetic energy, and so we can find the value of the maximum speed of the ball:
The work done is B.
Explanation:
The work done by a force on an object is given by
where
F is the magnitude of the force
d is the displacement of the object
is the angle between the direction of the force and of the displacement
For the boat in this problem, we have:
F = 250 N (force applied)
d = 50 m (displacement)
Substituting, we find the work done:
Learn more about work:
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Answer:
c. nine times as low.
Explanation:
Sound intensity is defined as the acoustic power transferred by a sound wave per unit of normal area to the direction of propagation:
Since the sound wave has a spherical wavefront of radius r, then the area is given by:
Here r is the distance from the source of the sound. Thus sound intensity decreases as: