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Q. 74

Expert-verified
Found in: Page 260

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

A sled starts from rest at the top of the frictionless, hemispherical, snow-covered hill shown in FIGURE CP10.74. a. Find an expression for the sled’s speed when it is at angle . b. Use Newton’s laws to find the maximum speed the sled can have at angle without leaving the surface. c. At what angle does the sled “fly off” the hill?

(a) Expression for the sled's speed is found to be .

(b) The maximum speed the sled can have at an angle

(c) The angle at which the sled flies off the hill .

See the step by step solution

Step 1: Given information (part a)

The following figure is given.

Step 2: Explanation (part a)

Apply the conservation energy equation at the initial position of the sled and when the sled is at an angle . Consider the velocity of the sled when it is at an angle is . The initial velocity

Step 3: Given information (part b)

The following figure is given.

Step 4: Explanation (part b)

According to Newton's law, the net force on the sled is

The acceleration of the sled while moving on the hill

The force acting on the sled is normal force (n) and force due to gravity along the axis. Therefore the net force,

The normal force (n) decreases as v increases. If the sled leaves the hill. But n can't be negative, so the fastest speed at which the sled stays on the hill is the speed The maximum speed of the sled at which it stays on the hill is when .

Therefore the maximum speed of the sled is

Step 5: Given information (part c)

The following figure is given.

Step 6: Explanation (part c)

The speed of the sled at

The maximum speed of the sled at

Equate the equation and