Recent content by asleight

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...

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.

How strict is your teacher? Do you think something cheap would work for him, elsewise, let's look at our other options.

Yes, that's exactly right.

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.

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...

BUMP. Can anyone help with this integration?

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...

x_f^2=x_i^2+2ad, W=Fd\rightarrow W=mg(x_f^2-x_i^2)/2a.

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.

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.

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...

Draw a free-body diagram around the car, itself. Only forces within the circle can be considered to analyze Newton's First Law.

Apply Newton's First Law to each of the objects and tell me what you decide.

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?