Recent content by asleight

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    Joule Mobile Mass Transporter Project

    If the mass is falling the total length and the axle-wheel ratio follows my work, then the only reason the cart isn't traveling its full distance is friction on the wheels or slip within the pulleys. For the minimum ratio between the wheel and axle, we solve the inequality. Make the wheels of...
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    Joule Mobile Mass Transporter Project

    I think it's safe to say that \frac{l}{d}=\frac{r}{R}, where l=0.100m, d=10.00m, and r,R are appropriate radii of the axle and the wheels such that the equality is true. This is neglecting friction, so you'll want to make R >> r to account for the energy lost due to friction.
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    Joule Mobile Mass Transporter Project

    How strict is your teacher? Do you think something cheap would work for him, elsewise, let's look at our other options.
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    Solve Car Chasing Problem: How Long to Catch Speeder?

    Yes, that's exactly right.
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    Gravitational Force on Point Mass by Uniform Wire and Line

    My integral above was exactly correct except I used the wrong trig. function, putting x in the numerator rather than a (and I forgot to carry the 2 down from the second line to the third). Thank you for your help, I understand integrals way better now.
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    Gravitational Force on Point Mass by Uniform Wire and Line

    Setting the origin at L and integrating only the first quadrant (due to symmetry of the second quadrant negating the canceled, horizontal forces due to gravity), we integrate: \vec{F}=\int_L^{2L}\frac{M\hat{L}}{2L}\frac{Gm\hat{r}}{r^2}dr, where r=\sqrt{x^2+a^2} and...
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    Gravitational Force on Point Mass by Uniform Wire and Line

    BUMP. Can anyone help with this integration?
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    Gravitational Force on Point Mass by Uniform Wire and Line

    UGH, this is hard. I think I've figured it out (or am getting close, at least)... \vec{F}=\frac{GMm\hat{r}}{r^2}\rightarrow\vec{F}=\frac{GMm\hat{r}}{2Lr^2}, where \vec{r}=\sqrt{x^2+a^2}\rightarrow\vec{F}=\int_0^{2L}\frac{GMm}{2L(x^2+a^2)}dx, giving a final value...
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    Work done by gravity on a thrown ball

    x_f^2=x_i^2+2ad, W=Fd\rightarrow W=mg(x_f^2-x_i^2)/2a.
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    Why does Newton's first law apply to a car at constant velocity?

    Okay, then wait for a second opinion. External vs. internal makes no difference. Read Newton's First Law again. The external frictional force is balanced by the external chemical force. The gas is NOT part of the vehicle. All of Newton's Laws always apply.
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    North of west vs west of north in vector components

    Let's say that the x-axis runs in the E-W direction and the y-axis in the N-S direction. Then, 30 miles north of west would be 30 units above the -x axis, with the angle between the line connecting the origin and the point and the -x axis being your desired angle.
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    Why does Newton's first law apply to a car at constant velocity?

    Newton's First Law, "A body continues to maintain its state of rest or of uniform motion unless acted upon by an external unbalanced force." The external force due to friction is balanced by the force due to chemical explosion within the vehicle. Newton's Second Law, "F = ma: the net force on...
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    Why does Newton's first law apply to a car at constant velocity?

    Draw a free-body diagram around the car, itself. Only forces within the circle can be considered to analyze Newton's First Law.
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    Verifying the Accuracy of a Gun Aimed at a Falling Target

    Apply Newton's First Law to each of the objects and tell me what you decide.
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    Verifying the Accuracy of a Gun Aimed at a Falling Target

    You already know that the bullet is fired fast enough to get to the can. So, what do you know about the motion of the objects in the y-direction?
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