The truck drives on a horizontal road with a constant velocity: It eventually halted by a set of crash barrels. The number of barrels and sand within the barrels ar...

Runaway Truck In Fig. $10-33$, a runaway truck with failed brakes is moving downgrade at $130 \mathrm{~km} / \mathrm{h}$ just before the driver steers the truck up a frictionless emergency escape ramp with an in- clination of $15^{\circ} .$ The truck's mass is $5000 \mathrm{~kg} .$ (a) What minimum length $L$ must the ramp have if the truck is to stop (momentarily) along it? (Assume the truck is a particle, and justify that assumption.) Does the minimum length $L$ increase, decrease, or remain the same if (b) the truck's mass is decreased and (c) its speed is decreased?

Let's do party, eh? Kinetic energy. Our initial Connecticut Or she is equal to have em. We I square. Let's ah, substitute values one divided by two multiplied by m We have m witches 2268 2268 And we have initial velocity, which is 20 and solving this initial Connecticut Receiving a quote Thio 453 point six Qilong Jules All right and further using work energy principle you know, I bless work done is equal to you f u i is the initial potential energy in the u F is the final potential energy where w is the work done? Well, this can't be returnees initial Connecticut or seat less, uh, work done w is equal to ah final kinetic energy pless a change in but internal energy. All right, now let's like in values Ah, any show of kinetic energy uh, bliss? Oh, work done well worked on his hero. It's equal to, uh, finally kinetic energy is also Zito and we have internal energy and, uh, internal energy is equal to initially Connecticut machine and we know they, uh initial kinetic energy is equal to 453.6 Kinlaw and chilled. All right. No, um, calculating the stopping distance delta you internal can be written these f k which is the kinetic friction times distance. Well, uh, internal energy is internal energy is a four or five for 53 six double zero. It's equal to 800 times D and D is equal to 567 meters, so e equals 567 meters. Now, uh, let's to part B well behaviour vehicle traveling at the same speed we traveled further. So have you, uh, heavier vehicle vehicle will travel further credible. Further if the friction force remand the same. Since the system is more energy to convert into internal energy and the pickup truck wheels are seemed not to be skidding on and rolling resistance would be higher for behavior car. So answer would depend on the assumptions about the total resisted for for so answer would depend. Answer would depend, um, on the assumptions on the assumptions about the total resisting force about the talkto resisting force, resisting force

We need to determine the magnitude of the net force between the tires of the van and the barge during the maneuver, so we have The relative is equal to 15 mph. The not relative is equal to zero miles per hour. S nine is equal to zero As is equal to 80 ft. And we have the relative squared equals B, not Relative Squared -2 A. That's minus that's not So solving for a. And we get 3.03 feet per second and the force is equal to the mass times acceleration. So this is the weight over G. TMC acceleration, which gives us £376..

Mhm. The explanation of the solution is that that first we find the acceleration off the truck using the following reaction that this square minus you square equal toe s hair. The final velocity off the track is we The initial velocity of the truck is you on their distance? Moved by the truck is as now we substitute 45 AM I par are for V zero for you and 2 to 5 f t four s. So here, putting the values in the equation. Yeah, and calculating this we get the value off A is 9.68 FT per s square. Yeah. Now draw the free body diagram off the gate. This is a free body diagram. Now, from this we considered movements. About all this is all here that they questioned it too. And name Multiply by 10 minus w multiply by 48 by eight. Sign trade. Agree Max Emma, Multiply by 48 by two, cause third degree physical to zero. Now here the sharing force at each page that there are two pages is any The weight off the gate is W and the mass of the gate is m. So now we substitute the values that substitute 60 B for W that it's 60 divided by 32.2 stuck far. Okay, square for em on 9.68 f t police car for a. So by substituting the values in the equation and solving, we get an equal to 25.4 be. Therefore, the maximum sharing force developed in each off the two pages during the exploration is 25 point for be. This is the final answer, So this is a complete explanation of the solution. When you tell a step by step, let's go to

So here in this problem, we are given this truck and the weight of the truck is £12,000. And this truck is used at Buffalo demonstration And on this truck, gravel leaves the hopper at the raid off 10 ft/s. So the velocity is 10 ft per second and the mask for it for the gravel is to 20 pound per second. Now the attractive force between the wheel driving wheels is £380 that you can see here and the frictional erode origins is £200 that I've shown her. Now, this one is working as a positive success and we have to calculate the acceleration of the truck After four seconds. So time is four seconds and at this time the velocity for the truck is 1.5 mile per hour. This is what we are given the question. Now, to solve this problem will be using variable mass approach and by this approach we can write data, sigma ethics, as he calls to M V dot plus I am not to you where U. Is the letter velocity of the truck and the gravels now will be first converting the units. So we are given that the velocity of the truck r equals to four second is 1.5 MPH and the rest data is given and feed L. B. F and so on. So I'll be converting the unit and two ft per second. So if we convert this thing into feet per second We will get to be 2.2 free person. So did have lost to the truck. Now you is the little velocity of the truck and this gravels so you would be equal to This would be 2.2 at his the velocity of the truck minus the velocity of this gravel. And we'll take the x component. So it would be 10 co sign 60 degree. So this would be called to -2.803/s. Now, next this is a mass of the truck but we consider the mass of the truck at equals to four seconds. Now at equals to force again, the mass of the truck would be equal to this £12,000 is the weight of the empty truck. So the mask would be 12,000 divided by 22.2. Now we have to also add the weight of the gravel that is added on the truck at equals to four seconds in four seconds. The mass added would be Mask for it. This is we have to £20 per second. So let's convert the unit divided with 22.2 multiplied with four. So this is the total mass of the truck at equals to four seconds. So this would be called to nearly 400 pound second square over feet. Now we have calculated m video, what we have to calculate m dot we know it is this much. You also we have calculated how can but the values The Sigma is the net force in the exploration. So this would be 380 minus 200 and it would be called to mv have this much 400 V. is the execution. Were basically means that solution that we have to calculate Plus I am not I? M not we have to £20 per second but would convert the units. So to 20 divided by 22.2 times you And you we have negative 2.80. Now you can sell it for every dot and from here Video it comes out to be as nearly 0.498 three per second square. So this is basically the acceleration of the truck art equals to four seconds. So there's a final answer for the given problem. I hope you have understood the problem. Thank you.