(a) Explanation Newton’s second law. F → net = m a → Given information : The mass of the skier is 65 kg. The angle of the slope is 32 ° Calculation: Show the free body diagram of forces as shown in Figure 1. Here, n → is normal force exerted by the slope and w → is weight. Determine the net force using the formula. F → net = m a → (1) Determine the net force by applying equation of equilibrium in horizontal and vertical direction. m a → = n sin θ i ^ + [ n cos ( θ ) − w ] j ^ (2) The skier does not accelerate in the normal force direction, therefore the forces in the direction should cancel. Express the normal force as follows: n = w cos θ Express the weight ( w ) as follows: w = m g Substitute w cos θ for n and mg for w in Equation (2). a → = ( w cos θ ) sin θ i ^ + [ ( w cos θ ) cos ( θ ) − m g ] j ^ = [ w cos θ sin θ ] i ^ + [ w cos θ cos θ − m g ] j = [ m g cos θ sin θ ] i ^ + [ m g cos 2 θ − m g ] j = [ g cos θ sin θ ] i ^ + [ g cos 2 θ − g ] j (3) Find the acceleration of a skier. Substitute 9.8 m / s 2 for g , and 32 ° for θ in Equation (3). a → = [ 9 (b) To determine To find : The force exerted by snow on the skier.

4th Edition

ISBN: 9780134988559

Author: Wolfson, Richard

Publisher: Pearson Education,

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Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force betwe…

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Chapter 5, Problem 38P

(a)

To determine

To find: The acceleration of a skier.

(b)

To determine

To find: The force exerted by snow on the skier.

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Chapter 5, Problem 37E

Chapter 5, Problem 39P

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The acceleration of a skier.

Solution Summary: The author explains the acceleration of a skier using Newton's second law.

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To find: The acceleration of a skier.

To find: The force exerted by snow on the skier.

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Chapter 5 Solutions