Answer:
I think it is pulling the sled off the ice covered back yard.
Answer:
The force is ![F = 1041.7N](https://tex.z-dn.net/?f=F%20%3D%201041.7N)
Explanation:
The moment of Inertia I is mathematically evaluated as
![I = MR_A^2](https://tex.z-dn.net/?f=I%20%3D%20MR_A%5E2)
Substituting
for M(Mass of the wheel) and
for
(Radius of wheel)
![I = 1.9 * 0.33^2](https://tex.z-dn.net/?f=I%20%3D%201.9%20%2A%200.33%5E2)
![= 0.207kgm^2](https://tex.z-dn.net/?f=%3D%200.207kgm%5E2)
The torque on the wheel due to net force is mathematically represented as
![\tau = FR_B - F_rR_A](https://tex.z-dn.net/?f=%5Ctau%20%3D%20FR_B%20%20-%20F_rR_A)
Substituting 135 N for
(Force acting on sprocket),
for
(radius of the chain) and F is the force acting on the sprocket due to the chain which is unknown for now
![\tau = F (0.0435) - 135 (0.33)](https://tex.z-dn.net/?f=%5Ctau%20%3D%20F%20%280.0435%29%20-%20135%20%280.33%29)
This same torque due to the net force is the also the torque that is required to rotate the wheel to have an angular acceleration of
and this torque can also be represented mathematically as
![\tau = \alpha I](https://tex.z-dn.net/?f=%5Ctau%20%3D%20%5Calpha%20I)
Now equating the two equation for torque
Making F the subject
![F = \frac{\alpha I + (135*0.33) }{0.0435}](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7B%5Calpha%20I%20%2B%20%28135%2A0.33%29%20%7D%7B0.0435%7D)
Substituting values
![F = \frac{(3.70 * 0.207) + (135*0.33)}{0.0435}](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7B%283.70%20%2A%200.207%29%20%20%2B%20%28135%2A0.33%29%7D%7B0.0435%7D)
![= 1041.7N](https://tex.z-dn.net/?f=%3D%201041.7N)
Suvat
we have s, u, v and we want a
the suvat equation with these values in is: v^2 = u^2 - 2as
so a = (-v^2 + u^2)/-2s
plug numbers in
a = (-85^2 + 0^2)/-2*36 = 7225/72 = 100.3... ms^-2
Common symbol of the volume (L)
Answer:
![\theta=53.13^o](https://tex.z-dn.net/?f=%5Ctheta%3D53.13%5Eo)
Explanation:
<u>2-D Projectile Motion</u>
In 2-D motion, there are two separate components of the acceleration, velocity and displacement. The horizontal component has zero acceleration, while the acceleration in the vertical direction is always the acceleration due to gravity. The basic formulas for this type of movement are
![V_x=V_{ox}=V_ocos\theta](https://tex.z-dn.net/?f=V_x%3DV_%7Box%7D%3DV_ocos%5Ctheta)
![V_y=V_{oy}-gt=V_osin\theta-gt](https://tex.z-dn.net/?f=V_y%3DV_%7Boy%7D-gt%3DV_osin%5Ctheta-gt)
![x=V_{ox}t](https://tex.z-dn.net/?f=x%3DV_%7Box%7Dt)
![\displaystyle y=y_o+V_{oy}t-\frac{gt^2}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3Dy_o%2BV_%7Boy%7Dt-%5Cfrac%7Bgt%5E2%7D%7B2%7D)
![\displaystyle x_{max}=\frac{2V_{ox}V_{oy}}{g}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x_%7Bmax%7D%3D%5Cfrac%7B2V_%7Box%7DV_%7Boy%7D%7D%7Bg%7D)
![\displaystyle y_{max}=\frac{V_{oy}^2}{2g}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y_%7Bmax%7D%3D%5Cfrac%7BV_%7Boy%7D%5E2%7D%7B2g%7D)
The projectile is fired in such a way that its horizontal range is equal to three times its maximum height. We need to find the angle \theta at which the object should be launched. The range is the maximum horizontal distance reached by the projectile, so we establish the base condition:
![x_{max}=3y_{max}](https://tex.z-dn.net/?f=x_%7Bmax%7D%3D3y_%7Bmax%7D)
![\displaystyle \frac{2V_{ox}V_{oy}}{g}=3\frac{V_{oy}^2}{2g}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B2V_%7Box%7DV_%7Boy%7D%7D%7Bg%7D%3D3%5Cfrac%7BV_%7Boy%7D%5E2%7D%7B2g%7D)
Using the formulas for ![V_{ox}, V_{oy}:](https://tex.z-dn.net/?f=V_%7Box%7D%2C%20V_%7Boy%7D%3A)
![\displaystyle \frac{2V_{o}cos\theta V_{o}sin\theta}{g}=3\frac{V_{o}^2sin^2\theta}{2g}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B2V_%7Bo%7Dcos%5Ctheta%20V_%7Bo%7Dsin%5Ctheta%7D%7Bg%7D%3D3%5Cfrac%7BV_%7Bo%7D%5E2sin%5E2%5Ctheta%7D%7B2g%7D)
Simplifying
![4cos\theta sin\theta=3sin^2\theta](https://tex.z-dn.net/?f=4cos%5Ctheta%20sin%5Ctheta%3D3sin%5E2%5Ctheta)
Dividing by ![sin\theta](https://tex.z-dn.net/?f=sin%5Ctheta)
![4cos\theta=3sin\theta](https://tex.z-dn.net/?f=4cos%5Ctheta%3D3sin%5Ctheta)
Rearranging
![tan\theta=\frac{4}{3}](https://tex.z-dn.net/?f=tan%5Ctheta%3D%5Cfrac%7B4%7D%7B3%7D)
![\theta=arctan\frac{4}{3}](https://tex.z-dn.net/?f=%5Ctheta%3Darctan%5Cfrac%7B4%7D%7B3%7D)
![\theta=53.13^o](https://tex.z-dn.net/?f=%5Ctheta%3D53.13%5Eo)