Amazing video! I have one question, why is friction acting that way and not the opposite? I would intuitively think friction is the only force counter-acting the x-component of the Normal reaction, therefore acting with an angle of 30deg with the x-axis and to the right.
In this case, the key word is 'maximum'. I'll try to explain by imagining the case where the car goes too slow, then then when the car goes too fast. One way to think of this is to have the angle theta equal to 80 degrees (or even 90 degrees) and to imagine what would happen to the car if it was going too slow. Check out 'wall of death' (th-cam.com/video/HWrWo7_w4Ag/w-d-xo.html). When the car goes too slow, the car will slide down the incline. The car is about to slide down the incline, so we would see friction acting up the incline. There will be some speed where its just right, and there will be no need for friction to provide support forces. At some point, the car will go too fast. The tendency will be for the car to slide outwards because the speed is so fast that it begins to slide outwards. The example I have done is for this case where the car is at the limit of going too fast. (unfortunately/fortunately for the drivers) I haven't been able to find any videos for the case of going too fast. Maybe a NASCAR driving fan that come by this post can help me out here.
In this question, the car is travelling at a constant speed. As a result, the forces in the tangential direction are balanced. There will be some frictional force on the tyres (in the tangential direction) which will need to be sufficient to overcome drag forces due to air. In this set of working, I have assumed the drag force due to air to be negligible.
why do we assume there will be no tangential acceleration? I thought we could only use a constant velocity when it was given, which wasnt the case here. I dont know, Im probably just overthinking it but if someone could please explain it to me😭
In this case the tangential acceleration is equal to zero. If it was non-zero then it would mean there would be a component of the friction force in the tangential direction. I've made the assumption that tangential acceleration is zero to make the question a bit easier.
what would be the answer if the question ask you to find the minimum safe speed instead of the maximum?
Amazing video! I have one question, why is friction acting that way and not the opposite? I would intuitively think friction is the only force counter-acting the x-component of the Normal reaction, therefore acting with an angle of 30deg with the x-axis and to the right.
In this case, the key word is 'maximum'. I'll try to explain by imagining the case where the car goes too slow, then then when the car goes too fast.
One way to think of this is to have the angle theta equal to 80 degrees (or even 90 degrees) and to imagine what would happen to the car if it was going too slow. Check out 'wall of death' (th-cam.com/video/HWrWo7_w4Ag/w-d-xo.html). When the car goes too slow, the car will slide down the incline. The car is about to slide down the incline, so we would see friction acting up the incline.
There will be some speed where its just right, and there will be no need for friction to provide support forces.
At some point, the car will go too fast. The tendency will be for the car to slide outwards because the speed is so fast that it begins to slide outwards. The example I have done is for this case where the car is at the limit of going too fast. (unfortunately/fortunately for the drivers) I haven't been able to find any videos for the case of going too fast. Maybe a NASCAR driving fan that come by this post can help me out here.
Why don't we consider equations of motion and kinematics in the tangential direction?
In this question, the car is travelling at a constant speed. As a result, the forces in the tangential direction are balanced. There will be some frictional force on the tyres (in the tangential direction) which will need to be sufficient to overcome drag forces due to air.
In this set of working, I have assumed the drag force due to air to be negligible.
thanks cornelis!
You are welcome :-)
why do we assume there will be no tangential acceleration? I thought we could only use a constant velocity when it was given, which wasnt the case here. I dont know, Im probably just overthinking it but if someone could please explain it to me😭
In this case the tangential acceleration is equal to zero. If it was non-zero then it would mean there would be a component of the friction force in the tangential direction. I've made the assumption that tangential acceleration is zero to make the question a bit easier.