Answer:
Explanation:
The potential energy of the spring or the work done by the spring is given by :
............(1)
k is the spring constant
d is the compression
When the spring is compressed a distance d' = d/3, let W' is the work is required to load the second dart. Then the work done is given by :
.............(2)
Dividing equation (1) and (2) :
So, the work required to load the second dart compared to that required to load the first is one-Ninth as much. Therefore, the correct option is (E).
Answer:
(a). The angular speed of the rotating is 33.8 rad/s.
(b). The speed of its center is 2.7 m/s.
Explanation:
Given that,
Radius = 8.00 cm
Mass = 0.180 kg
Height = 75.0 m
We need to calculate the angular speed of the rotating
Using conservation of energy
Here, initial velocity and angular velocity are equal to zero.
Here, 
The angular speed of the rotating is 33.8 rad/s.
(b). We need to calculate the speed of its center
Using formula of speed
Put the value into the formula
Hence, (a). The angular speed of the rotating is 33.8 rad/s.
(b). The speed of its center is 2.7 m/s.
Amber is the answer to this question
Answer: 71.7 KJ
Explanation:
The rotational kinetic energy of a rotating body can be written as follows:
Krot = ½ I ω2
Now, any point on the rim of the flywheel, is acted by a centripetal force, according to Newton’s 2nd Law, as follows:
Fc = m. ac
It can be showed that the centripetal acceleration, is related with the angular velocity and the radius, as follows:
ac = ω2 r
We know that this acceleration has a limit value, so , we can take this limit to obtain a maximum value for the angular velocity also.
As the flywheel is a solid disk, the rotational inertia I is just ½ m r2.
Replacing in the expression for the Krot, we have:
Krot= ½ (1/2 mr2.ac/r) = ¼ mr ac = ¼ 67.0 Kg. 1.22 m . 3,510 m/s2 = 71. 7 KJ
