A 1100 kg car rounds a curve of radius 68 m banked at an angle of 16 degrees. If the car is traveling at 95 km/h, will a frictio
1 answer:
Answer:
Yes. Towards the center. 8210 N.
Explanation:
Let's first investigate the free-body diagram of the car. The weight of the car has two components: x-direction: towards the center of the curve and y-direction: towards the ground. Note that the ground is not perpendicular to the surface of the Earth is inclined 16 degrees.
In order to find whether the car slides off the road, we should use Newton's Second Law in the direction of x: F = ma.
The net force is equal to
Note that 95 km/h is equal to 26.3 m/s.
This is the centripetal force and equal to the x-component of the applied force.
As can be seen from above, the two forces are not equal to each other. This means that a friction force is needed towards the center of the curve.
The amount of the friction force should be
Qualitatively, on a banked curve, a car is thrown off the road if it is moving fast. However, if the road has enough friction, then the car stays on the road and move safely. Since the car intends to slide off the road, then the static friction between the tires and the road must be towards the center in order to keep the car in the road.
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Answer:
a) The swimmer should travel perpendicular to the bank to minimize the spent in getting to the other side.
b) 133.33 m
c) 53.13°
d) 106.67 m
Explanation:
a) The swimmer should travel perpendicular to the bank to minimize the spent in getting to the other side.
b) velocity = distance * time
Let the velocity of the swimmer be = 1.5 m/s
The separation of the two sides of the river, d = 80 m
The time taken by the swimmer to get to the other end of the river bank,
t = 80/1.5
t = 53.33 s
The swimmer will be carried downstream by the river through a distance, s
Let the velocity of the river be = 2.5 m/s
S = 53.33 * 2.5
S = 133.33 m
c) To minimize the distance traveled by the swimmer, his resultant velocity must be perpendicular to the velocity of the swimmer relative to water
That is ,
d) Downstream velocity of the swimmer,
The vertical displacement is given by,
80 = 1.2 t
t = 80/1.2
t = 66.67 s
the horizontal speed,
The downstream horizontal distance of the swimmer,
x = 1.6 * 66.67
x = 106.67 m
Answer:
d = 3.5*10^4 m
Explanation:
In order to calculate the displacement of the airplane you need only the information about the initial position and final position of the airplane. THe initial position is at the origin (0,0,0) and the final position is given by the following vector:
The displacement of the airplane is obtained by using the general form of the Pythagoras theorem:
(1)
where x any are the coordinates of the final position of the airplane and xo and yo the coordinates of the initial position. You replace the values of all variables in the equation (1):
hence, the displacement of the airplane is 3.45*10^4 m