00:01
In this problem on the topic of force and motion, we have a car that weighs 10 .7 kilo -neutons traveling at a speed of 13 .4 meters per second around an unbanked curve, which has a radius of 61 meters.
00:14
We want to find the magnitude of the friction of force in the tires that is keeping the car on its circular path, and the coefficient of static friction is given to be 0 .35 between the tires and the road, and we want to know if the attempt at taking the curve will be successful.
00:33
Now, the free body diagram is shown as follows, and the mass of the car m is equal to its weight 10 ,700 newtons over g, which is 9 .8 meters per square second.
00:48
This gives us the mass of the car to be 1 .09 times 10 to the 3kg.
00:57
We'll choose inward, which is horizontally toward the center of the circular path as positive, and the normal force fn is equal to the weight of the car mg.
01:12
And the required frictional force fs is responsible for subtropital motion, so this is equal to mv squared over r.
01:23
Now with a speed of v is equal to 13 .4 meters per second and a radius of 61 meters, newton's second law tells us that this frictional force is the only force providing this interpinal motion, and so that's equal to mv squared over r...