A "swing" ride at a carnival consists of chairs that are swung in a circle by L = 15.8 m cables attached at an angle of θ = 57.4° to a vertical rotating pole, as the drawing below shows. Suppose the total mass of a chair and its occupant is 161 kg. Calculate the tension in the cable attached to the chair.

A block with some mass m is connected to a string that is attached to the ceiling. The block on the end of the string is going around a circular path with a constant radius r and constant speed.  Applying Newton's second law to the x and y components of forces seperately in order to find the expressions for the tension of the string in terms of mass m, angle θ, and constant g.

Timmy and Billy are using a ramp to load furniture into a truck. While rolling a 220-pound piano up the ramp, they discover that the truck is too full with other furniture for the piano to fit. Billy holds the piano in place on the ramp while Timmy repositions other items to make room for it in the truck. If the angle of inclination of the ramp is 25°, how many pounds of force must Billy exert to hold the piano in position? Billy must exert pounds of force. (Type an integer or decimal rounded to one decimal place as needed.) 25° 220 lb

In the figure, a rectangular slab of slate rests on a bedrock surface inclined at angle = 25.6°. The slab has length L = 43.4 m, thickness T = 6.23 m, and width W = 13.6 m, and 1.0 cm³ of it has a mass of 3.2 g. The coefficient of static friction between slab and bedrock is 0.351. (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 6.42 cm² and will snap under a shearing stress of 3.57 × 108 N/m², what is the minimum number of bolts needed? Assume that the bolts do not affect the normal force.

Two blocks of mass m, = 10 kg and mg =5 kg are connected by a massless string that passes over a pulley as MA shown in the figure. The system is in static equilibrium. There is friction between m, and the inclined surface (30.4). Neglect the friction between the string and the pulley. Determine the static friction force in the system. 10 kg 5.0 kg 37 49.0 N 29.3 N 39.2 N 33.9 N O 9.98 N

Two blocks of mass m1 = 3.0kg and m2 = 2.5kg are attached with a rope. The rope goes around several ideal pulleys.  Two of the pulleys are attached directly to the ceiling (grey shaded region at the top) and will not move up or down. The lower pulley will move with block 1.  Block 1 is free hanging and will move vertically.  Block 2 rests on an inclined ramp at angle θ = 30°. The ramp is frictionless.  Block 1 is observed to accelerate upwards.  The experiment is done on earth, g = 9.8 m/s2  What is the tension in the long rope?  by using variables only

In the figure, a 499 kg construction bucket is suspended by a cable A that is attached at O to two other cables B and C, making angles 0₁ = 51.0° and 9₂ = 54.0° with the horizontal. Find the tensions in (a) cable A, (b) cable B, and (c) cable C. (Hint: To avoid solving two equations in two unknowns, position the axes as shown in the figure.) B C 0₂

A girl swings a 0.190 kg rock attached to a taut string in a circle around her head; her hand holds the end of the string above her head, and the string angles down slightly. The string is massless and 0.680 m long. A coordinate system lies with its origin at the location where the string comes out of the girl's hand. The positive z-axis points vertically upwards, the positive y- axis points horizontally towards the right, and the positive x-axis points out of the screen. At a certain instant, the rock makes 3.25 revolutions per second (rev/s) in a counterclockwise direction, as seen from above. The string is inclined at an angle of 0 = 12.4° below the xy-plane, and the projection of the string onto the xy- plane makes an angle o = 36.8° with the positive x-axis. What is the tangential velocity vector v in meters per second (m/s) at this instant? Report your answer using ijk unit vector notation. i = v, i + vyj+ vz k m/s

a 1.34 kg ball is connected by means of two massless strings, each of length L = 1.70 m, to a vertical, rotating rod. The strings are tied to the rod with separation d = 1.70 m and are taut. The tension in the upper string is 35 N. What are the (a) tension in the lower string, (b) magnitude of the net force  on the ball, and (c) speed of the ball? (d) What is the direction of the net force?

In the figure, a rectangular slab of slate rests on a bedrock surface inclined at angle 8 = 22.8°. The slab has length L = 48.9 m, thickness T = 6.61 m, and width W = 12.7 m, and 1.0 cm³ of it has a mass of 3.2 g. The coefficient of static friction between slab and bedrock is 0.312. (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 6.47 cm² and will snap under a shearing stress of 3.59 x 108 N/m², what is the minimum number of bolts needed? Assume that the bolts do not affect the normal force.