91Ó°ÊÓ

A 0.150-kg toy is undergoing SHM on the end of a horizontal spring with force constant k = 300 N/m. When the toy is 0.0120 m from its equilibrium position, it is observed to have a speed of 0.400 m/s. What are the toy’s (a) total energy at any point of its motion; (b) amplitude of motion; (c) maximum speed during its motion?

29) According to the shop manual, when drilling should have a 12.7-mm-diameter in wood, plastic, or aluminum a drill should have a speed of 1250 rev/min. For a 12.7-mm-diameter drill bit turning at a constant 1250 rev/min .find

a) the maximum linear speed of any part of the bit and

b) the maximum radical acceleration of any part of the bit.

A 0.60-kg book slides on a horizontal table. The kinetic friction force on the book has magnitude 1.8 N. (a) How much work is done on the book by friction during a displacement of 3.0 m to the left? (b) The book now slides 3.0 m to the right, returning to its starting point. During this second 3.0-m displacement, how much work is done on the book by friction? (c) What is the total work done on the book by friction during the complete round trip? (d) On the basis of your answer to part (c), would you say that the friction force is conservative or non-conservative? Explain.

A Ferris wheel with radius 14.0 m is turning about a horizontal axis through its center (Fig. E3.27). The linear speed of a passenger on the rim is constant and equal to 6.0 m/s. What are the magnitude and direction of the passenger’s acceleration as she lowest passes through (a) the point in her circular motion and (b) the highest point in her circular motion? (c) How much time does it take the Ferris wheel to make one revolution?

Compute the x- and y-components of the vectors$\stackrel{→}{A},\stackrel{→}{B},\stackrel{→}{C}\mathbf{and}\stackrel{→}{D}$in Fig. E1.24.

A 12-pack of Omni-Cola (mass 4.30 kg) is initially at rest on a horizontal floor. It is then pushed in a straight line for by a trained dog that exerts a horizontal force with magnitude 36.0 N. Use the work–energy theorem to find the final speed of the 12-pack if

(a) there is no friction between the 12-pack and the floor, and

(b) the coefficient of kinetic friction between the 12-pack and the floor is 0.30.

Two ice skaters, Daniel (mass 65.0 kg) and Rebecca (mass 45.0 kg), are practicing. Daniel stops to tie his shoelace and while at rest, is struck by Rebecca, who is moving at 13.0 m/s before she collides with him. After the collision, Rebecca has a velocity of magnitude 8.00 m/s at an angle of 53.1 degrees from her initial direction. Both skaters move on the frictionless, horizontal surface of the rink. (a) What are the magnitude and direction of Daniel’s velocity after the collision? (b) What is the change in total kinetic energy of the two skaters as a result of the collision?

The star ${\mathbf{Rho}}^{\mathbf{1}}$Cancri is 57 light-years from the earth and has a mass 0.85 times that of our sun. A planet has been detected in a circular orbit around ${\mathbf{Rho}}^{\mathbf{1}}$Cancri with an orbital radius equal to 0.11 times the radius of the earth’s orbit around the sun. What are (a) the orbital speed and (b) the orbital period of the planet of ${\mathbf{Rho}}^{\mathbf{1}}$Cancri?

Compute the x- and y-components of the vectors $\stackrel{â‡\P Ä}{A}$,$\stackrel{â‡\P Ä}{B}$, $\stackrel{â‡\P Ä}{C}$and $\stackrel{â‡\P Ä}{D}$in Fig. E1.24.

A stockroom worker pushes a box with mass 16.8 kg on a horizontal surface with a constant speed of 3.50 m/s. The coefficient of kinetic friction between the box and the surface is 0.20. (a) What horizontal force must the worker apply to maintain the motion? (b) If the force calculated in part (a) is removed, how far does the box slide before coming to rest?