A laser pulse with wavelength 520 nm contains 4.40 mj of energy. how many photons are in the laser pulse?
1 answer:
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(a) 1.01 cm
First of all, we need to find the spring constant of the spring.
The force initially applied to the spring is equal to the weight of the block hanging on it:
where m = 4.32 kg is the mass of the block and g = 9.8 m/s^2 is the acceleration of gravity.
When this force is applied, the spring stretches by
We can find the spring constant by using Hooke's law:
where k is the spring constant. Solving for k,
Later, the first object is removed and another object of mass
m' = 1.50 kg
is hung on the spring. The weight of this object is
So, if we use Hooke's law again, we can find the new stretching of the spring:
(b) 1.16 J
The work that must be done on the spring is equal to the elastic potential energy that would be stored in the spring, therefore:
where we have
k = 1448.6 N/m is the spring constant
x = 4.00 cm = 0.04 m is the new stretching
Solving the equation, we find the work that must be done by the external force:
Answer:
a. The component of the net force which make up the apparent weight are added to each other at the bottom and subtracted (the centripetal force from the weight) at the top)
b. Apparent weight at the top is approximately 519.06 N
Apparent weight at the bottom is approximately 558.94 N
Explanation:
a. The apparent weight at the top is different from the apparent weight at the bottom of a moving Ferris wheel because of the opposite direction in which the centripetal force acts at the top and the bottom, which are upwards and downwards respectively, while the weight acts downwards constantly
b. The given parameters are
The radius of the Ferris wheel, r = 7.2 m
The period for one complete revolution, t = 28 seconds
The angle covered in one revolution, θ = 2·π radian
The mass of the person riding on the Ferris wheel, the passenger = 55 kg
Therefore, we have;
The angular speed, ω = Δθ/Δt = 2·π/(28)
From which we have;
Centripetal force, = m × ω² × r
Substituting the known values, we have = 55 kg × (2·π/(28 s))² × 7.2 m ≈ 19.94 N
The centripetal force, = 19.94 N always acting outward from the center
Weight = Mass × Acceleration due to gravity
The weight of the passenger = 55 kg × 9.8 m/s² = 539 N
The weight of the passenger = 539 N always acting downwards
At the top of the Ferris wheel the the centripetal force is acting upwards and the weight is acting downwards
Therefore;
The net force, which is the apparent weight of the passenger at the top = 539 N - 19.94 N ≈ 519.06 N
Apparent weight at the top ≈ 519.06 N
At the bottom of the Ferris wheel the weight is acting downwards and the centripetal force is also acting downwards
Therefore;
The net force at the bottom, which is the apparent weight of the passenger at the bottom = 539 N + 19.94 N ≈ 558.94 N
Apparent weight at the bottom ≈ 558.94 N.