A 20 kg dog stands on a 40 kg platform that is supported by two ropes. One rope is attached to the right edge of the platform and the other is attached 50 cm from the left edge of the platform. The dog sits 50 cm from the right edge of the platform. A 5.0 kg cat jumps up, but is wary of the dog abs stays all the way on the left edge. The platform is 2.0 m long. What is the tension in each rope?

alfa ll a 0: 44 I 12:49 MENG250 - Assig... 4/10 •2–33. If F, = 600 N and $ = 30°, determine the magnitude of the resultant force acting on the eyebolt and its direction measured clockwise from the positive x axis. 60° F = 500 N F = 450 N

2. Consider the curve ø(t) = (t² – 4t + 2, cos(t²), ' sin(t²)) for t E (0, 1). (a) Find the work required to bend a straight rod into ø, assuming a stiff- ness of M 2. (b) Find the work required to bend a straight rod into ø, assuming a stiff- ness of M(x, y, z) = /1+ x² + y² + 2².

What is the x-component y X 40° of this force? 10 N A. 10 sin 40° B. 10 cos 40° C. -10 cos 40° D. 10/sin 40°

A Frisbee flies across a field. Determine if the system has translational kinetic energy, rotational kinetic energy, neither, or both as determined by the observer in each of the following cases. a. The observer watches the flight of the Frisbee across the field from a park bench. b. The observer is a dog that runs directly beneath the Frisbee. c. The observer is an ant at rest on the Frisbee.

A bicycle is turned upside down while its owner repairs a flat tire on the rear wheel. A friend spins the front wheel, of radius 0.381 m, and observes that drops of water fly off tangentially in an upward direction when the drops are at the same level as the center of the wheel. She measures the height reached by drops moving vertically (Fig. P10.74 on page 332). A drop that breaks loose from the tire on one turn rises h = 54.0 cm above the tangent point. A drop that breaks loose on the next turn rises 51.0 cm above the tangent point. The height to which the drops rise decreases because the angular speed of the wheel decreases. From this information, determine the magnitude of the average angular acceleration of the wheel.

Review. Consider the system shown in Figure P10.36 with m1 = 20.0 kg, m2 = 12.5 kg, R = 0.200 m, and the mass of the pulley M = 5.00 kg. Object m2 is resting on the floor, and object m1 is 4.00 m above the floor when it is released from rest. The pulley axis is frictionless. The cord is light, does not stretch, and does not slip on the pulley. (a) Calculate the time interval required for m1 to hit the floor. (b) How would your answer change if the pulley were massless?

A light rod of length 2L is free to rotate in a vertical plane about a frictionless pivot through its center. A particle of mass m1 is attached at one end of the rod, and a mass m2 is at the opposite end, where m1 m2. The system is released from rest in the vertical position shown in Figure P8.84a, and at some later time, the system is rotating in the Position shown in Figure P8.84b. Take the reference point of the gravitational potential energy to be at the pivot, (a) Find an expression for the system's total mechanical energy in the vertical position. (b) Find an expression for the total mechanical energy in the rotated position shown in Figure P8.84b. (c) Using the fact that the mechanical energy of the system is conserved, how would you determine the angular speed co of the system in the rotated position? (d) Find the magnitude of the torque on the system in the vertical position and in the routed position. Is the torque constant? Explain what these results imply regarding the angular momentum of the system, (c) Find an expression for the magnitude of the angular acceleration of the system in the rotated position. Does your result make sense when the rod is horizontal? When it is vertical? Explain. Figure P8.84

Children playing pirates have suspended a uniform wooden plank with mass 15.0 kg and length 2.50 m as shown in Figure P14.27. What is the tension in each of the three ropes when Sophia, with a mass of 23.0 kg, is made to walk the plank and is 1.50 m from reaching the end of the plank? FIGURE P14.27