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Mechanical Advantage = Force by Hammer / Force by Nail = 160/40 = 4
Answer:
The angular velocity is 
Explanation:
From the question we are told that
The mass of each astronauts is 
The initial distance between the two astronauts 
Generally the radius is mathematically represented as 
The initial angular velocity is 
The distance between the two astronauts after the rope is pulled is 
Generally the radius is mathematically represented as 
Generally from the law of angular momentum conservation we have that

Here
is the initial moment of inertia of the first astronauts which is equal to
the initial moment of inertia of the second astronauts So

Also
is the initial angular velocity of the first astronauts which is equal to
the initial angular velocity of the second astronauts So

Here
is the final moment of inertia of the first astronauts which is equal to
the final moment of inertia of the second astronauts So

Also
is the final angular velocity of the first astronauts which is equal to
the final angular velocity of the second astronauts So

So

=> 
=> 
=> 
=> 
Answer:
a) frequency = 0.1724 Hz
b) Period = 5.8 sec
c) speed = 7.04 m/s
d) acceleration = 7.62 m/s²
Explanation:
Given that;
radius = 6.5m
time period = 5.8 sec every circle
a) the frequency
frequency is the number of rotation in unit time
frequency = 1 / time period = 1/5.8
frequency = 0.1724 Hz
b) the period
period is time taken in one rotation
period = total time / rotation = 5.8 / 1
Period = 5.8 sec
c) the speed
speed = distance/time = circumference/time period = 2πr / t = (2π×6.5) / 5.8
speed = 7.04 m/s
d) acceleration
To find the acceleration we take the linear velocity squared divided by the radius of the circle.
so
acceleration = v² / r = (7.04)² / 6.5 = 49.5616 / 6.5
acceleration = 7.62 m/s²
Answer:
W = 30 J
Explanation:
given,
Work done = 10 J
Stretch of spring, x = 0.1 m
We know,
dW = F .dx
we know, F = k x


![W = k[\dfrac{x^2}{2}]_0^{0.1}](https://tex.z-dn.net/?f=W%20%3D%20k%5B%5Cdfrac%7Bx%5E2%7D%7B2%7D%5D_0%5E%7B0.1%7D)

k = 2000
now, calculating Work done by the spring when it stretched to 0.2 m from 0.1 m.

![W = 2000 [\dfrac{x^2}{2}]_{0.1}^{0.2} dx](https://tex.z-dn.net/?f=W%20%3D%202000%20%5B%5Cdfrac%7Bx%5E2%7D%7B2%7D%5D_%7B0.1%7D%5E%7B0.2%7D%20dx)
W = 1000 x 0.03
W = 30 J
Hence, work done is equal to 30 J.