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Protium_H1
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Homework Statement
A car is lifted vertically by a jack placed at the car's rear end 40cm off the central axis, so that the weight of the car is supported by the jack and the two front wheels. The distance between the front wheels is 1.60m, the distance from the axis connecting the two wheels to the center of mass of the car is 80cm, and the distance from the rear of the car to the center of mass is 2.10m. What fraction of the car's weight is carried by each of the wheels, and what fraction is carried by the jack? (Note: the weight on the wheels will not be symmetrically distributed).
Homework Equations
[/B]
Net Torque: [itex] \Sigma \vec{\tau} = I \alpha = \tau_{1} + \tau_{2} + ... [/itex]
Net Force: [itex] \Sigma \vec{F} = ma = F_{1} + F_{2} + ... [/itex]
3. The Attempt at a Solution
- Made my coordinates like so, plus I made clockwise rotation be positive.
- Wrote the restriction [itex] \vec{F}_{NL} \neq \vec{F}_{NR} [/itex] and that [itex] \vec{F}_{NL} > \vec{F}_{NR} [/itex]
- Wrote the net force formula in vector form.
- [tex] \Sigma \vec{F}=\hat{j}Ma=\hat{j}(F_{NL}+F_{NR}+F_{NJ} - Mg) [/tex]
- Wrote the net torque formula in vector form,
- [tex] \Sigma \vec{\tau}_{about CM} = I_{car} \alpha = [\hat{j}F_{NJ} \times (\hat{k}2.10 + \hat{i}0.40)] - [\hat{j}F_{NL} \times (\hat{-k}0.80 + \hat{-i}0.80)] - [\hat{j}F_{NR} \times (\hat{-k}0.80 + \hat{i}0.80)] [/tex]
- Simplified torque to,
- [tex] \Sigma \vec{\tau}_{about CM} = \hat{-i}(2.10F_{NJ}+0.80F_{NL}+0.80F_{NB}) + \hat{k}(0.40F_{NJ}+0.80F_{NL}-0.80F_{NR}) [/tex]
- Note: So far this makes sense since [itex] \vec{\tau} [/itex] can't be parallel to the [itex] \vec{F}_{applied} [/itex] (i.e.: [itex] \Sigma \vec{\tau} [/itex] has not [itex] \hat{j} [/itex] component.)
- After this, I'm totally stuck since I have 3unknownss and only 2 equation (net force and net torque). I don't even know if my choice of using the center of mass (CM) of the car to find torque was a good idea, since the car is pivotted in the position of the two wheels. I don't even know if this system is [itex] \Sigma \vec{F} = 0 [/itex] and [itex] \Sigma \vec{\tau} = 0 [/itex]
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