the gravitational force between two objects is 1600 and what will be the gravitational force between the objects if the distance
1 answer:
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a)
b) See plot attached
c) 10.0 m
d) 0.500 cm
Explanation:
a)
The position of the tip of the lever at time t is described by the equation:
(1)
The generic equation that describes a wave is
(2)
where
A is the amplitude of the wave
T is the period of the wave
t is the time
By comparing (1) and (2), we see that for the wave in this problem we have
Therefore, the period is
b)
The sketch of the profile of the wave until t = 4T is shown in attachment.
A wave is described by a sinusoidal function: in this problem, the wave is described by a sine, therefore at t = 0 the displacement is zero, y = 0.
The wave than periodically repeats itself every period. In this sketch, we draw the wave over 4 periods, so until t = 4T.
The maximum displacement of the wave is given by the value of y when , and from eq(1), we see that this is equal to
y = 0.500 cm
So, this is the maximum displacement represented in the sketch.
c)
When standing waves are produced in a string, the ends of the string act as they are nodes (points with zero displacement): therefore, the wavelength of a wave in a string is equal to twice the length of the string itself:
where
is the wavelength of the wave
L is the length of the string
In this problem,
L = 5.00 m is the length of the string
Therefore, the wavelength is
d)
The amplitude of a wave is the magnitude of the maximum displacement of the wave, measured relative to the equilibrium position.
In this problem, we can easily infer the amplitude of this wave by looking at eq.(1).
And by comparing it with the general equation of a wave:
In fact, the maximum displacement occurs when the sine part is equal to 1, so when
which means that
And therefore in this case,
So, this is the displacement.
Horizontal velocity: 81.9 km/h
Vertical velocity: 57.4 km/h
Explanation:
We can solve this problem by resolving the velocity vector into its component along the horizontal and vertical direction.
The horizontal velocity of the stunt bike is given by:
where
v = 100 km/h is the magnitude of the velocity
is the angle of projection
Substituting, we find
The vertical velocity instead is given by
where
Substituting,
Learn more about vector components:
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