A small mass m is tied to a string of length L and is whirled in vertical circular motion. The speed of the mass v is such that
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Answer:
The object measures 6 m in distance and 2 m in height.
It creates a virtual image that is upright.
Explanation:
Provided data includes:
Focal length = 0.25 m
Image height = 0.080 m
Image distance = 0.24 m
We are to determine the object's distance.
Using the lens formula:
Substituting values into the formula:
We also need to calculate magnification:
Applying the magnification formula:
Substituting values into this formula:
Next, we need to find the height of the object:
Using the magnification formula once more:
A convex mirror generates a virtual and upright image on its backside.
Consequently, the object is at a distance of 6 m and has a height of 2 m.
The image formed is virtual and upright.
1) The work performed on the spores is
2) The spores land 0.32 m away
Explanation:
1)
According to the work-energy principle, the work done on the spores equals their change in kinetic energy:
where
W is work done
m represents the spore's mass
v is the final velocity
u is the initial velocity
Given:
spore mass =
initial velocity u = 0 (starting from rest)
final velocity v = 7.0 m/s
Calculating the work:
2)
The spores follow projectile motion, moving along a parabolic trajectory made of two motions:
- Constant speed horizontally
- Vertically accelerated due to gravity
Considering vertical motion first, using kinematics:
where
s = 0.01 m (shooting height)
u = 0 (no initial vertical velocity, horizontal ejection)
t = time of flight
g = acceleration due to gravity
Solving for t:
Now for horizontal displacement, when velocity is constant:
where
horizontal velocity =
time t = 0.045 s
Calculating distance d:
Thus, the spores land 0.32 meters away.
Learn more about work:
Learn more about projectile motion:
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