Answer:
177.65
Explanation:
Work done by the force field,F along path C is given by:
Given that:
![F(r(t))=(t-sin \ t)i+(3-cos \ t)j\\\\\\W=\int\limits_C F.dr\\=\int\limits^{6\pi}_0(t-sin \ t)i+(3-cos \ t)j).((1-cos \ t)i+sin \ t \ j)dt\\\\=\int\limits^{6\pi}_0(t-sin \ t)(1-cos \ t)+(3-cos \ t)sin \ t \ dt\\\\=\int\limits^{6\pi}_0t-tcos \ t+2sin\ t\ dt\\\\=\int\limits^{6\pi}_0-tcos \ t\ dt+[\frac{t^2}{2}-2cos \ t]\limits^{6\pi}_0\\\\=-I+177.65](https://tex.z-dn.net/?f=F%28r%28t%29%29%3D%28t-sin%20%5C%20t%29i%2B%283-cos%20%5C%20t%29j%5C%5C%5C%5C%5C%5CW%3D%5Cint%5Climits_C%20F.dr%5C%5C%3D%5Cint%5Climits%5E%7B6%5Cpi%7D_0%28t-sin%20%5C%20t%29i%2B%283-cos%20%5C%20t%29j%29.%28%281-cos%20%5C%20t%29i%2Bsin%20%5C%20t%20%5C%20j%29dt%5C%5C%5C%5C%3D%5Cint%5Climits%5E%7B6%5Cpi%7D_0%28t-sin%20%5C%20t%29%281-cos%20%5C%20t%29%2B%283-cos%20%5C%20t%29sin%20%5C%20t%20%5C%20dt%5C%5C%5C%5C%3D%5Cint%5Climits%5E%7B6%5Cpi%7D_0t-tcos%20%5C%20t%2B2sin%5C%20t%5C%20dt%5C%5C%5C%5C%3D%5Cint%5Climits%5E%7B6%5Cpi%7D_0-tcos%20%5C%20t%5C%20dt%2B%5B%5Cfrac%7Bt%5E2%7D%7B2%7D-2cos%20%5C%20t%5D%5Climits%5E%7B6%5Cpi%7D_0%5C%5C%5C%5C%3D-I%2B177.65)
#Integrating I by parts:
![I=\int\limits^{6\pi}_0 tcos \ t \ dt\\\\=[\int \ tcos \ t \ dt]\limits^{6\pi}_0\\\\=[t\int cos \ t \ dt-\int (\frac{dt}{dt}\intcos \ t \ dt)dt]\limits^{6\pi}_0\\\\=[tsin\ t -\int sin\ t \ dt]\limits^{6\pi}_0\\\\=0](https://tex.z-dn.net/?f=I%3D%5Cint%5Climits%5E%7B6%5Cpi%7D_0%20tcos%20%5C%20t%20%5C%20dt%5C%5C%5C%5C%3D%5B%5Cint%20%5C%20tcos%20%5C%20t%20%5C%20dt%5D%5Climits%5E%7B6%5Cpi%7D_0%5C%5C%5C%5C%3D%5Bt%5Cint%20cos%20%5C%20t%20%5C%20dt-%5Cint%20%28%5Cfrac%7Bdt%7D%7Bdt%7D%5Cintcos%20%5C%20t%20%5C%20dt%29dt%5D%5Climits%5E%7B6%5Cpi%7D_0%5C%5C%5C%5C%3D%5Btsin%5C%20t%20-%5Cint%20sin%5C%20t%20%5C%20dt%5D%5Climits%5E%7B6%5Cpi%7D_0%5C%5C%5C%5C%3D0)
Hence, work done is 177.65
Answer:
926 N
Explanation:
Metric unit conversion:
R = 18 cm = 0.18 m
r = 5 cm = 0.05 m
The pressure exerted by the F = 12000N car on the wider arm would be ratio of the gravity over area
The pressure must be the same on the smaller pressure for it to be able to start lifting the car. We can calculate the force f acting on it:
Answer:
circular motion
Explanation:
Circular motion can be regarded as
movement of particular object along the circumference in a circle. It is
rotation of particular object along a circular path. Circular motion could be
uniform, along with constant angular rate of rotation as well as constant speed. It could also be non-uniform along with changing rate of rotation. The acceleration that is been experienced when one is in uniform circular motion is called"Centripetal acceleration"
Convection currents is type of current that takes place after a reservoir of fluid has been heated at the bottom, then cool at the top.the fluid expand as a result of Heat , then density decreases, the plates on top of them is been carried as a result of circular motion of the convection
By the work-energy theorem, the total work done on the car is equal to the change in its kinetic energy:
<em>W</em> = ∆<em>K</em>
<em>W</em> = 1/2 (0.34 kg) (22.9 m/s)² - 1/2 (0.34 kg) (6.5 m/s)²
<em>W</em> ≈ 82 J
You must know the masses of both objects and the gravitational constant used to calculate the gravitational force between the 2 objects.
