Given:
m = 0.32 kg
v = 11.5 m/s
To find:
1) Kinetic energy = ?
2) Work needed to stop the ball = ?
Formula used:
1) Kinetic energy = ![\frac{1}{2} m v^{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20m%20v%5E%7B2%7D%20%20%20)
2) Work = kinetic energy
Solution:
1)
Kinetic energy is given by,
Kinetic energy = ![\frac{1}{2} m v^{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20m%20v%5E%7B2%7D%20%20%20)
K.E. = ![\frac{1}{2} 0.32 \times 11.5 \times 11.5](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%200.32%20%5Ctimes%2011.5%20%5Ctimes%2011.5%20)
K.E. = 21.16 Joule
Thus, option (d) is the correct answer.
2)
Work needed to stop the ball is same as the kinetic energy because energy is the capacity to do work. Since, work is opposing the movement of the ball. Thus, Work = - Kinetic energy
Work = -21.16 Joule
Answer:
The value is ![w = 0.1167 \ rev/second](https://tex.z-dn.net/?f=w%20%3D%20%200.1167%20%5C%20rev%2Fsecond)
Explanation:
From the question we are told that
The rate at which the plate rotates is ![w =7.0 \ rev/min](https://tex.z-dn.net/?f=w%20%3D7.0%20%5C%20rev%2Fmin)
Generally the revolution per second is mathematically represented as
![w = \frac{7.0}{60}](https://tex.z-dn.net/?f=w%20%3D%20%20%5Cfrac%7B7.0%7D%7B60%7D)
=> ![w = 0.1167 \ rev/second](https://tex.z-dn.net/?f=w%20%3D%20%200.1167%20%5C%20rev%2Fsecond)
The ratio of the area of the plunger to the area of the piston will be 0.2323.
<h3>What is pressure?</h3>
The force applied perpendicular to the surface of an item per unit area across which that force is spread is known as pressure.
It is denoted by P. The pressure relative to the ambient pressure is known as gauge pressure.
The presure at the output remains the same
![\rm P_0=P_I \\\\\ \frac{F_0}{A_o} =\frac{F_I}{A_I} \\\\ \frac{A_0}{A_I} = \frac{F_0}{F_I} \\\\ \frac{A_0}{A_I} =\frac{39}{1675} \\\\ \frac{A_0}{A_I} =0.2323](https://tex.z-dn.net/?f=%5Crm%20P_0%3DP_I%20%5C%5C%5C%5C%5C%20%5Cfrac%7BF_0%7D%7BA_o%7D%20%3D%5Cfrac%7BF_I%7D%7BA_I%7D%20%5C%5C%5C%5C%20%5Cfrac%7BA_0%7D%7BA_I%7D%20%3D%20%5Cfrac%7BF_0%7D%7BF_I%7D%20%5C%5C%5C%5C%20%5Cfrac%7BA_0%7D%7BA_I%7D%20%3D%5Cfrac%7B39%7D%7B1675%7D%20%5C%5C%5C%5C%20%5Cfrac%7BA_0%7D%7BA_I%7D%20%3D0.2323)
Hence, the ratio of the area of the plunger to the area of the piston will be 0.2323.
To learn more about the pressure refer to the link;
brainly.com/question/356585
#SPJ1
True. For example the Big Bang theory; no one knows what really happened, but based on evidences that were found, it was found as a good way to explain the world's origin.