Practice 15B Answers are available in the classroom and on the website. Scan this QR code for a direct link.

Equilibrium: Forces and Torques

16. Lynn walks across a 9.0 m long plank bridge. The mass of the bridge is 20 kg and Lynn’s mass is 52 kg. What are the forces on the supports due to the plank bridge when she stops 2.0 m from the right side to answer her phone?

17. One end of a 1.2-meter-long uniform beam of mass 16 kg is attached to a wall with a hinge. A wire supports the other end.

a. Find the tension in the wire. b. What is the horizontal component of the force of the hinge on the beam? c. What is the vertical component of the force of the hinge on the beam?

18. Determine the following forces acting on the boom in the system (heavy line). The weight of the uniform boom is 130 N.

a. Tension in the cable. b. Find the magnitude and direction of the force from the ground at the base of the boom.

           20°  

     30°  

HINGE

250  N  

20°   35°  

30°  40°  

19. A scaffold of mass 60 kg and length 5.0 m is supported in a horizontal position by a vertical cable at each end. A window washer of mass 80 kg stands at a point 1.5 m from one end. What is the tension in each cable?

20. The system in the figure is in equilibrium. A concrete block of mass 225 kg hangs from the end of the uniform strut of mass 45.0 kg. For the angles shown, find (a) the tension T in the cable, (b) the horizontal component of the force on the strut from the hinge (c) the vertical component of the force on the strut from the hinge (d) the magnitude and direction of the force on the strut from the hinge.

21. The bar shown here is positioned horizontally and has a mass of 1.6 kg. A 500-gram object has been hung 10 cm from the end. (a) Find the tension in the diagonal wire that supports the bar. (b) Find the magnitude and direction of the force exerted by the hinge on the bar.

50  cm  

30  cm

 

10  cm  

hinge  

22. The figure shows a diver of weight 580 N standing at the end of a diving board with a length of L = 4.5 m and negligible mass. The board is fixed to two pedestals (supports) that are separated by distance d = 1.5 m. For each force state the magnitude and direction (up or down). (a) The force from the left pedestal on the board. (b) The force from the right pedestal on the board. 23. In the figure, one end of a uniform beam of weight 221 N is hinged to a wall; the other end is supported by a wire that makes angle θ = 25.0° with both wall and beam. (a) Find the tension in the wire, (b) the horizontal component of the force of the hinge on the beam (c) the vertical component of the force of the hinge on the beam. COLLABORATION QUESTION: To be whiteboarded in class. 24. A 100-N monkey climbs a uniform ladder with weight 120 N and length L as shown in the figure. The ladder rests against the wall at an angle of θ = 53°. The upper and lower ends of the ladder rest on frictionless surfaces, with the lower end fastened to the wall by a horizontal rope that is frayed and that can support a maximum tension of only 110 N.

(a) Draw a free-body diagram for the ladder. (b) Find the normal force exerted by the bottom of the ladder. (c) Find the tension in the rope when the monkey is one-third of the way up the ladder. (d) Find the maximum distance d that the monkey can climb up the ladder before the rope breaks. Express your answer as a fraction of L. (e) If the horizontal surface were rough and the rope were removed, how would the questions be changed? How would your analysis of the problem be changed? What other information would you need to answer parts (c) and (d)?

25. In the figure, a climber with a weight of 533.8 N is held by a belay rope connected to her climbing harness and belay device; the force of the rope on her has a line of action through her center of mass. The indicated angles are φ = 30.0° and θ = 40.0°. If her feet are on the verge of sliding on the vertical wall, what is the coefficient of static friction between her climbing shoes and the wall? 26. In the figure, what magnitude of (constant) force 𝐹 applied horizontally at the axle of the wheel is necessary to raise the wheel over an obstacle of height h = 3.00 m? The wheel’s radius is r = 6.00 cm, and its mass is m = 0.800 kg. Blast from the Past:

27. An 18-cm-diameter solid ball of mass 1.4 kg rolls without slipping at 8.4 m/s. What is its kinetic energy?

28. A 0.600-kg hollow ball is released from rest at the top of a 1.2-m-tall ramp. Assuming that the ball rolls without slipping, find the linear velocity of the ball at the bottom of the ramp.

Practice 15C

Rolling Motion

29. A hollow spherical shell is rolling without slipping down a board that is tilted at an angle of 35.0° with respect to the horizontal. What is the linear acceleration of the sphere? 30. A solid disk rolls without slipping down a board that is tilted at an angle of 25.0° with respect to the horizontal. Determine the minimum value of the coefficient of static friction. 31. A constant horizontal force of magnitude 10 N is applied to a wheel of mass 10 kg and radius 0.30 m. The wheel rolls smoothly on the horizontal surface, and the acceleration of its center of mass has magnitude 0.60 m/s2. (a) What is the direction of the frictional force, left or right? (b) What is the magnitude of the frictional force on the wheel? (c) What is the rotational inertia of the wheel about the axis through its center of mass?

32. In the figure, a constant horizontal force Fapp of magnitude 30 N is applied to a uniform solid cylinder by fishing line wrapped around the cylinder. The mass of the cylinder is 24 kg, its radius is 0.32 m, and the cylinder rolls smoothly on the horizontal surface.

(a) What is the direction of the frictional force, left or right?

(b) What is the magnitude of the acceleration of the center of mass of the cylinder?

(c) What is the magnitude of the angular acceleration of the cylinder about the center of mass? (d) What is the magnitude of the frictional force acting on the cylinder?

33. A uniform sphere rolls without slipping down an incline. (a) What must be the incline angle if the linear acceleration of the center of the sphere is to be 0.10g? (b) For this angle, what would be the acceleration of the sphere if the contact point was frictionless?