PROBLEM SET 5: Forces II 1. Components Two ropes are connected to a steel cable that supports a hanging weight as shown. (a) Draw a free-body diagram showing all of the forces acting at the knot that connects the two ropes to the steel cable. Based on your force diagram, which of the two ropes will have the greater tension? (b) If the maximum tension either rope can sustain without breaking is 5000 N, determine the maximum value of the hanging weight that these ropes can safely support. You can ignore the weight of the ropes and the steel cable. 2. Ramp A block slides down a frictionless plane having an inclination of 15.0°. The block starts from rest at the top, and the length of the incline is 2.00 m. (a) Draw a free-body diagram of the block. Find (b) the acceleration of the block and (c) its speed when it reaches the bottom of the incline. 3. Ramp A block is given an initial velocity of 5.00 m/s up a frictionless incline with an angle of 20.0° from horizontal. How far up the incline does the block slide before turning around? 4. Acceleration Constraints Assume the three blocks portrayed move on a frictionless surface and a 42-N force acts as shown on the 3.0-kg block. Determine (a) the acceleration given this system, (b) the tension in the cord connecting the 3.0-kg and the 1.0-kg blocks, and (c) the force exerted by the 1.0-kg block on the 2.0-kg block. 5. Pulley Block A in the figure weighs 1.90 N, and block B weighs 4.20 N. The coefficient of kinetic friction between all surfaces is 0.30. Find the magnitude of the horizontal force necessary to drag block B to the left at constant speed if A and B are connected by a light, flexible cord passing around a fixed, frictionless pulley 6. Pulley Two blocks of mass 3.50 kg and 8.00 kg are connected by a massless string that passes over a frictionless pulley. The inclines are frictionless. Find (a) the magnitude of the acceleration of each block and (b) the tension in the string. 7. Friction A 25.0-kg block is initially at rest on a horizontal surface. A horizontal force of 75.0 N is required to set the block in motion, after which a horizontal force of 60.0 N is required to keep the block moving with constant speed. Find (a) the coefficient of static friction and (b) the coefficient of kinetic friction between the block and the surface. 8. Friction A 12.0-kg box rests on the flat floor of a truck. The coefficients of friction between the box and floor are μs = 0.19 and μk = 0.15. The truck stops at a stop sign and then starts to move with an acceleration of 2.20 m/s2. If the box is 1.80 m from the rear of the truck when the truck starts, how much time elapses before the box falls off the truck? How far does the truck travel in this time? 9. Consider the following system of blocks and ropes. All the ropes and pulleys are massless and frictionless, and the surfaces are frictionless. The ramp angle is 𝜃 = 30°. (a) Suppose blocks 1 and 2 have mass 𝑚1 = 2.0 kg and 𝑚2 = 1.0 kg, respectively. What must be the mass of block 3 to ensure that none of the blocks move? (b) Suppose block 3 has the mass you calculated in part a. Suddenly rope 2 breaks at time t = 0. How far across the plateau does block 2 slide between 𝑡 = 0 and 𝑡 = 1.0 s, assuming that it does not crash into the pulley during that time interval? 10. Three objects are connected on a table as shown. The coefficient of kinetic friction between the block of mass m2 and the table is 0.350. The objects have masses of m1 = 4.00kg, m2 = 1.00kg, and m3 = 2.00 kg, and the pulleys are frictionless. (a) Draw a free- body diagram of each object. (b) Determine the acceleration of each object, including its direction. (c) Determine the tensions in the two cords. What If? (d) If the tabletop were smooth, would the tensions increase, decrease, or remain the same? Explain.