A concrete highway curve of radius is banked at a angle. What is the maximum speed with which a rubber tired car can take this curve without sliding?
The maximum sped the car can move without sliding is .
A concrete highway curve of radius is banked at a angle.
We need to draw a graph for analyze the situation.
From the graph we can obtain the expression for the horizontal direction;
: The maximum force required
: Normal force
: Radius of the curve
: mass of the car
: Banking angle
Expression for vertical force:
Dividing expression (a) by expression (b), we get
Therefore, the maximum speed the care can move without sliding is .
The father of Example 8.2 stands at the summit of a conical hill as he spins his 20 kg child around on a 5.0 kg cart with a 2.0-m-long rope. The sides of the hill are inclined at 20o. He again keeps the rope parallel to the ground, and friction is negligible. What rope tension will allow the cart to spin with the same 14 rpm it had in the example?
A 60 g ball is tied to the end of a 50-cm-long string and swung in a vertical circle. The center of the circle, as shown in FIGURE P8.57, is 150 cm above the floor. The ball is swung at the
minimum speed necessary to make it over the top without the string going slack. If the string is released at the instant the ball is at the top of the loop, how far to the right does the ball hit the ground?
In an amusement park ride called The Roundup, passengers stand inside a 16-m-diameter rotating ring. After the ring has acquired sufficient speed, it tilts into a vertical plane, as shown in FIGURE P8.51.
a. Suppose the ring rotates once every 4.5 s. If a rider’s mass is 55 kg, with how much force does the ring push on her at the top of the ride? At the bottom? b. What is the longest rotation period of the wheel that will prevent the riders from falling off at the top?
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