Recent content by SheldonG

Stringy - thank you *so* much. That is a tremendous help. Much appreciated! Shelly

Homework Statement This is from Spivak, Vol. 4 Page 102-103 Given |x-x_0| < 1, |x-x0| < Epsilon/(2(|y_0|+1)) Also given |y-y_0| < Epsilon/(2(|x_0| + 1)) Prove |xy-x_0y_0| < Epsilon Homework Equations See above The Attempt at a Solution The proof proceeds clearly enough...

Try considering it from the frame of the water. i.e., the water is motionless, and the bank is moving at 1 m/s. Sheldon

I think you can assume the engine is running constantly, providing a force to push the train. But the train is not accelerating, it is traveling at 10 m/s. When the engine fails, the resistive force that keeps the train traveling at 10 m/s is the only force remaining, since the brakes also fail...

I understand now, thank you so much. I see my mistake now. I was thinking of the situation where the incline was increased to overcome the static friction and cause the block to slide at constant velocity. But after further calculation, I see that this is an impossibility, such an angle does...

Why assume this? The problem doesn't say what happened prior to the constant velocity of the block down the incline. Perhaps the block was placed on the incline, wouldn't move, and then someone gave it a push. On the other hand, perhaps the block was placed on the incline, wouldn't move, and...

I'm still a bit confused, unless we are both saying the same thing in a different way. Since the block travels at constant velocity down the incline, we have m(0) = mg\sin\theta - \mu_k mg\cos\theta which leads to \mu_k = \tan\theta If the block stops and does not slide back down...

Homework Statement A block slides with constant velocity down an inclined plane with slope angle \theta . The block is then projected up the same plane with an initial speed v_o . How far up the plane will it move before coming to rest, and after coming to rest, will it slide down the plane...

Thank you, Astronuc. I am in your debt. What a stupid error :-) Sheldon

Homework Statement If a car goes around a banked curve too fast, the car will slide out of the curve. Find an expression for the car speed v_{max} that puts the car on the verge of sliding out. What is the value for R=200, \theta = 10 , \mu_s = 0.60 ? Homework Equations a = v^2/r...

Won't v point in the same direction as the skis? As I read the problem, the angle of the slope is three degrees less than this.

You want to eliminate t. v_{avg} = D/(t_1 + t_2) And for each half: D/2 = v_1t_1\quad D/2 = v_2t_2 Solve these last equations for time, and then substitute them in the first equation.

Yes, you're right. Thanks.

Sorry, forgot to answer this bit. There is a period where the car is traveling at 60 and a period where it is traveling at 90. But since the change is not instantaneous, there will be a 3rd period where the car is traveling between 60 and 90. So the average of the end points will be too high in...

Average velocity is the displacement divided by the time it takes to travel that displacement. Your problem doesn't give the distance or the time, but it does say that 1/2 of the displacement is traveled at each velocity. Since velocity is constant, D/2 = v1*t1 and D/2 = v2*t2. You want the...