You are in a helicopter towing a 129-kg laser detector that is mapping out the thickness of the Brunt Ice Shelf along the coast of Antarctica. The original cable used to suspend the detector was damaged and replaced by a lighter one with a maximum tension rating of 309 pounds, not much more than the weight of the detector. The replacement cable would work without question in the case that the detector and helicopter were not accelerating. However, some acceleration of the helicopter is inevitable. In order to monitor the tension force on the cable to make sure the maximum is not exceeded (and therefore to not lose the very expensive detector) you calculate the maximum angle the cable can make with the vertical without the cable exceeding the tension limit. (a) Assuming straight and level flight of the helicopter, what is that maximum angle? (b) What is the corresponding acceleration? (c) Your colleague wants to add a 8.00-kg infrared camera to the detector. What is the maximum allowable angle now? (a) Number i (b) Number i (c) Number i Units Units Units +

Two packing crates of masses m₁ = 10.0 kg and m₂ = 7.10 kg are connected by a light string that passes over a frictionless pulley as in the figure below. The 7.10-kg crate lies on a smooth incline of angle 41.0°. Find the following. m₁ m₂ 8 (a) the acceleration of the 7.10-kg crate 4.123 X m/s² (up the incline) (b) the tension in the string N

Consider two blocks connected . Block A has mass 2.00 kg, and block B has mass 5.00 kg. The table on which B sits is frictionless, the cord connecting the blocks is light and flexible, and the pulley is light and frictionless. The horizontal force F S has magnitude F = 20.0 N, and block B moves to the left with an acceleration of 1.50 m/s2. What is the tension in the cord that connects the two blocks?

In the figure, a rectangular slab of slate rests on a bedrock surface inclined at angle θ = 28.4°. The slab has length L = 32.4 m, thickness T = 5.92 m, and width W = 14.3 m, and 1.0 cm3 of it has a mass of 3.2 g. The coefficient of static friction between slab and bedrock is 0.385. (a) Calculate the component of the gravitational force on the slab parallel to the bedrock surface. (b) Calculate the magnitude of the static frictional force on the slab. By comparing (a) and (b), you can see that the slab is in danger of sliding. This is prevented only by chance protrusions of bedrock. (c) To stabilize the slab, bolts are to be driven perpendicular to the bedrock surface (two bolts are shown). If each bolt has a cross-sectional area of 6.05 cm2 and will snap under a shearing stress of 3.34 × 108 N/m2, what is the minimum number of bolts needed? Assume that the bolts do not affect the normal force.

A chandelier with mass m is attached to the ceiling of a large concert hall by two cables. Because the ceiling is covered with intricate architectural decorations (not indicated in the figure, which uses a humbler depiction), the workers who hung the chandelier couldn't attach the cables to the ceiling directly above the chandelier. Instead, they attached the cables to the ceiling near the walls. Cable 1 has tension T1 and makes an angle of θ1 with the ceiling. Cable 2 has tension T2 and makes an angle of θ2 with the ceiling. Find an expression for T1, the tension in cable 1, that does not depend on T2.

A package of weather instruments is attached to a weather balloon. The package has a mass of 12.4 kg. The system is released vertically from rust. The weather balloon provides a constant lift force of 122.5 N for 6 minutes. calculate the magnitude and direction of the instruments acceleration during the first six minutes of flight ignore air resistance.

A 83.2 kg person is standing inside an elevator. The elevator is moving upward at 2.54 m/s and is decreasing speed at a rate of 1.82 m/s^2. What is the normal force that is acting on the person?

A chandelier with mass m is attached to the ceiling of a large concert hall by two cables. Because the ceiling is covered with intricate architectural decorations (not indicated in the figure, which uses a humbler depiction), the workers who hung the chandelier couldn't attach the cables to the ceiling directly above the chandelier. Instead, they attached the cables to the ceiling near the walls. Cable 1 has tension T1 and makes an angle of θ1 with the ceiling. Cable 2 has tension T2 and makes an angle of θ2 with the ceiling. Find an expression for  T1, the tension in cable 1, that does not depend on  T2. Express your answer in terms of some or all of the variables m,  θ1, and  θ2, as well as the magnitude of the acceleration due to gravity g. You must use parentheses around θ1 and  θ2, when they are used as arguments to any trigonometric functions in your answer.