Answer:Rolling friction is friction that acts on objects when they are rolling over a surface. Rolling friction is much weaker than sliding friction or static friction. This explains why most forms of ground transportation use wheels, including bicycles, cars, 4-wheelers, roller skates, scooters, and skateboards.
Explanation:
Answer:
a)
, b)
, c)
, d)
, e)
, f) ![v\approx 3.422\,\frac{m}{s}](https://tex.z-dn.net/?f=v%5Capprox%203.422%5C%2C%5Cfrac%7Bm%7D%7Bs%7D)
Explanation:
a) The frequency of oscillation is:
![f = \frac{76}{127\,hz}](https://tex.z-dn.net/?f=f%20%3D%20%5Cfrac%7B76%7D%7B127%5C%2Chz%7D)
![f = 0.598\,hz](https://tex.z-dn.net/?f=f%20%3D%200.598%5C%2Chz)
b) The angular frequency is:
![\omega = 2\pi \cdot f](https://tex.z-dn.net/?f=%5Comega%20%3D%202%5Cpi%20%5Ccdot%20f)
![\omega = 2\pi \cdot (0.598\,hz)](https://tex.z-dn.net/?f=%5Comega%20%3D%202%5Cpi%20%5Ccdot%20%280.598%5C%2Chz%29)
![\omega = 3.757\,\frac{rad}{s}](https://tex.z-dn.net/?f=%5Comega%20%3D%203.757%5C%2C%5Cfrac%7Brad%7D%7Bs%7D)
Lastly, the speed at the equilibrium position is:
![v_{max} = \omega \cdot A](https://tex.z-dn.net/?f=v_%7Bmax%7D%20%3D%20%5Comega%20%5Ccdot%20A)
![v_{max} = (3.757\,\frac{rad}{s} )\cdot (0.985\,m)](https://tex.z-dn.net/?f=v_%7Bmax%7D%20%3D%20%283.757%5C%2C%5Cfrac%7Brad%7D%7Bs%7D%20%29%5Ccdot%20%280.985%5C%2Cm%29)
![v_{max} = 3.701\,\frac{m}{s}](https://tex.z-dn.net/?f=v_%7Bmax%7D%20%3D%203.701%5C%2C%5Cfrac%7Bm%7D%7Bs%7D)
c) The spring constant is:
![\omega = \sqrt{\frac{k}{m}}](https://tex.z-dn.net/?f=%5Comega%20%3D%20%5Csqrt%7B%5Cfrac%7Bk%7D%7Bm%7D%7D)
![k = \omega^{2}\cdot m](https://tex.z-dn.net/?f=k%20%3D%20%5Comega%5E%7B2%7D%5Ccdot%20m)
![k = (3.757\,\frac{rad}{s} )^{2}\cdot (1.09\,kg)](https://tex.z-dn.net/?f=k%20%3D%20%283.757%5C%2C%5Cfrac%7Brad%7D%7Bs%7D%20%29%5E%7B2%7D%5Ccdot%20%281.09%5C%2Ckg%29)
![k = 15.385\,\frac{N}{m}](https://tex.z-dn.net/?f=k%20%3D%2015.385%5C%2C%5Cfrac%7BN%7D%7Bm%7D)
d) The potential energy when the particle is located 38.1 % of the amplitude away from the equilibrium position is:
![U = \frac{1}{2}\cdot (15.385\,\frac{N}{m} )\cdot (0.375\,m)^{2}](https://tex.z-dn.net/?f=U%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20%2815.385%5C%2C%5Cfrac%7BN%7D%7Bm%7D%20%29%5Ccdot%20%280.375%5C%2Cm%29%5E%7B2%7D)
![U = 1.081\,J](https://tex.z-dn.net/?f=U%20%3D%201.081%5C%2CJ)
e) The maximum potential energy is:
![U_{max} = \frac{1}{2}\cdot (15.385\,\frac{N}{m} )\cdot (0.985\,m)^{2}](https://tex.z-dn.net/?f=U_%7Bmax%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20%2815.385%5C%2C%5Cfrac%7BN%7D%7Bm%7D%20%29%5Ccdot%20%280.985%5C%2Cm%29%5E%7B2%7D)
![U_{max} = 7.463\,J](https://tex.z-dn.net/?f=U_%7Bmax%7D%20%3D%207.463%5C%2CJ)
The kinetic energy when the particle is located 38.1 % of the amplitude away from the equilibrium position is:
![K = U_{max} - U](https://tex.z-dn.net/?f=K%20%3D%20U_%7Bmax%7D%20-%20U)
![K = 7.463\,J - 1.081\,J](https://tex.z-dn.net/?f=K%20%3D%207.463%5C%2CJ%20-%201.081%5C%2CJ)
![K = 6.382\,J](https://tex.z-dn.net/?f=K%20%3D%206.382%5C%2CJ)
f) The speed when the particle is located 38.1 % of the amplitude away from the equilibrium position is:
![K = \frac{1}{2}\cdot m \cdot v^{2}](https://tex.z-dn.net/?f=K%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20m%20%5Ccdot%20v%5E%7B2%7D)
![v = \sqrt{\frac{2\cdot K}{m} }](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7B%5Cfrac%7B2%5Ccdot%20K%7D%7Bm%7D%20%7D)
![v = \sqrt{\frac{2\cdot (6.382\,J)}{1.09\,kg} }](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7B%5Cfrac%7B2%5Ccdot%20%286.382%5C%2CJ%29%7D%7B1.09%5C%2Ckg%7D%20%7D)
![v\approx 3.422\,\frac{m}{s}](https://tex.z-dn.net/?f=v%5Capprox%203.422%5C%2C%5Cfrac%7Bm%7D%7Bs%7D)
Complete Question
A student bikes to school by traveling first dN = 0.900 miles north, then dW = 0.300 miles west, and finally dS = 0.100 miles south.
Similarly, let d⃗ W be the displacement vector corresponding to the second leg of the student's trip. Express d⃗ W in component form.
Express your answer as two numbers separated by a comma. Be careful with your signs.
Answer:
The value is ![dT = ( -0.3, 0.8)](https://tex.z-dn.net/?f=dT%20%20%3D%20%20%28%20-0.3%2C%20%200.8%29)
Explanation:
From the question we are told that
The first displacement is
i.e positive y-axis
The second displacement is
i.e negative x-axis
The final displacement is
i.e negative y-axis
Generally dW in component for is
Generally the total displacement of the student is mathematically represented as
![dT = ( -0.3, (0.90 - 0.10))](https://tex.z-dn.net/?f=dT%20%20%3D%20%20%28%20-0.3%2C%20%20%280.90%20-%200.10%29%29)
![dT = ( -0.3, 0.8)](https://tex.z-dn.net/?f=dT%20%20%3D%20%20%28%20-0.3%2C%20%200.8%29)
It would be A since the axe head acts as a wedge and the handle is a basic lever