# Racing Racing Cars A and B are traveling on circular portions of a racetrack.

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Racing Racing Cars A and B are traveling on circular portions of a racetrack. In the instant shown, the speed of A is decreasing auto rate of $$\displaystyle{8}\frac{{m}}{{s}^{{2}}}$$, and the speed of B is increasing at the rate of $$\displaystyle{3}\frac{{m}}{{s}^{{2}}}$$. For the positions shown, determine (a) the velocity of B relative to A, (b) the acceleration of B relative to A.

2020-10-19

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### Relevant Questions

A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure below. The length of the arc ABC is 235 m, and the car completes the turn in 33.0 s. (Enter only the answers in the input boxes separately given.)
(a) What is the acceleration when the car is at B located at an angle of 35.0°? Express your answer in terms of the unit vectors $$\displaystyle\hat{{{i}}}$$ and $$\displaystyle\hat{{{j}}}$$.
1. (Enter in box 1) $$\displaystyle\frac{{m}}{{s}^{{2}}}\hat{{{i}}}+{\left({E}{n}{t}{e}{r}\in{b}\otimes{2}\right)}{P}{S}{K}\frac{{m}}{{s}^{{2}}}\hat{{{j}}}$$
(b) Determine the car's average speed.
3. ( Enter in box 3) m/s
(c) Determine its average acceleration during the 33.0-s interval.
4. ( Enter in box 4) $$\displaystyle\frac{{m}}{{s}^{{2}}}\hat{{{i}}}+$$
5. ( Enter in box 5) $$\displaystyle\frac{{m}}{{s}^{{2}}}\hat{{{j}}}$$
An alpha particle (a He nucleus, containing two protons and two neutrons and having a mass of $$\displaystyle{6.64}\cdot{10}^{{-{27}}}$$ kg) traveling horizontally at 35.6 km/s enters a uniform, vertical, 1.10 T magnetic field.
A) What is the diameter of the path followed by this alpha particle?
B) What effect does the magnetic field have on the speed of the particle?
C) What are the magnitude of the acceleration of the alpha particle while it is in the magnetic field?
D) What are the direction of the acceleration of the alpha particle while it is in the magnetic field?
The dominant form of drag experienced by vehicles (bikes, cars,planes, etc.) at operating speeds is called form drag. Itincreases quadratically with velocity (essentially because theamount of air you run into increase with v and so does the amount of force you must exert on each small volume of air). Thus
$$\displaystyle{F}_{{{d}{r}{u}{g}}}={C}_{{d}}{A}{v}^{{2}}$$
where A is the cross-sectional area of the vehicle and $$\displaystyle{C}_{{d}}$$ is called the coefficient of drag.
Part A:
Consider a vehicle moving with constant velocity $$\displaystyle\vec{{{v}}}$$. Find the power dissipated by form drag.
Express your answer in terms of $$\displaystyle{C}_{{d}},{A},$$ and speed v.
Part B:
A certain car has an engine that provides a maximum power $$\displaystyle{P}_{{0}}$$. Suppose that the maximum speed of thee car, $$\displaystyle{v}_{{0}}$$, is limited by a drag force proportional to the square of the speed (as in the previous part). The car engine is now modified, so that the new power $$\displaystyle{P}_{{1}}$$ is 10 percent greater than the original power ($$\displaystyle{P}_{{1}}={110}\%{P}_{{0}}$$).
Assume the following:
The top speed is limited by air drag.
The magnitude of the force of air drag at these speeds is proportional to the square of the speed.
By what percentage, $$\displaystyle{\frac{{{v}_{{1}}-{v}_{{0}}}}{{{v}_{{0}}}}}$$, is the top speed of the car increased?
Express the percent increase in top speed numerically to two significant figures.
A racetrack has the shape of an inverted cone. On the surface the cars race in circles that are parallel to the ground. For a speed of 34 m/, at what value of the distance should a driver locate his car if he wishes to stay on a circular path without depending on friction?
A truck engine transmits 28 kW (27.5 hp) to the driving wheels when the truck is traveling at a constant velocity of magnitude 60 km/h (37.3 m/h) on a level road. (a) What is the resisting force acting on the truck? (b) Assume that 65% of the resisting force is due to rolling friction and that the remainder is due to air resistance. If the force of rolling friction is independent of speed and the force of air resistance is proportional to the square of speed, what power will drive the truck at 30 km/h? at 120 km/h? give your answers in kilowatts and in horsepower.
A stunt man whose mass is 70 kg swings from the end ofa 4.0 m long rope along thearc of a vertical circle. Assuming that he starts from rest whenthe rope is horizontal, find the tensions in the rope that are required to make him follow his circular path at each of the following points.
(a) at the beginning of his motion N
(b) at a height of 1.5 m above the bottom of the circular arc N
(c) at the bottom of the arc N
Car 1 has a mass of m1 = 65 ❝ 103 kg and moves at a velocity of v01 = +0.81 m/s. Car 2, with a mass of m2 = 92 ❝ 103 kg and a velocity of v02 = +1.2 m/s, overtakes car 1 and couples to it. Neglect the effects of friction in your answer.
(a) Determine the velocity of their center of mass before the collision m/s
(b) Determine the velocity of their center of mass after the collision m/s
(c) Should your answer in part (b) be less than, greater than, or equal to the common velocity vf of the two coupled cars after the collision? less than greater than equal to
A 10 kg objectexperiences a horizontal force which causes it to accelerate at 5 $$\displaystyle\frac{{m}}{{s}^{{2}}}$$, moving it a distance of 20 m, horizontally.How much work is done by the force?