HW8 solutions

# HW8 solutions - HomeWork 8 solutions 1 Chapter 6 problem 26...

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HomeWork 8 solutions Physics 203 1. Chapter 6 problem 26 REASONING a. The magnitude s of the displacement that occurs while the snowmobile coasts to a halt is the distance that we seek. The work W done by the net external force F acting on the snowmobile during the coasting phase is given by W = ( F cos θ ) s (Equation 6.1), and we can use this expression to obtain s . To do so, we will need to evaluate W . This we will do with the aid of the work-energy theorem as given by 22 11 f0 W mv mv = (Equation 6.3), since we know the mass m and the final and initial velocities v f and v 0 , respectively. The net external force F during the coasting phase is just the horizontal force of kinetic friction (magnitude = f k ), since the drive force is shut off and the vertical forces balance (there is no vertical acceleration). This frictional force has a magnitude of 205 N. This follows because, while the snowmobile is moving at a constant 5.50 m/s, it is not accelerating, and the drive force must be balancing the frictional force, which exists both before and after the drive force is shut off. Finally, to use W = ( F cos θ ) s (Equation 6.1) to determine s , we will need a value for the angle θ between the frictional force and the displacement. The frictional force points opposite to the displacement, so θ = 180°. b. By using only the work-energy theorem it is not possible to determine the time t during which the snowmobile coasts to a halt. To determine t it is necessary to use the equations of kinematics. We can use these equations, if we assume that the acceleration during the coasting phase is constant. The acceleration is determined by the force of friction (assumed constant) and the mass of the snowmobile, according to Newton’s second law. For example, we can use ( ) 1 2 0f s v vt = + (Equation 2.7) to determine t once we know the magnitude of the displacement s , which is the distance in which the snowmobile coasts to a halt.

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HW8 solutions - HomeWork 8 solutions 1 Chapter 6 problem 26...

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