A model airplane of mass 0.820 kg flies with a speed of 35.0 m/s in a horizontal circle at the end of a 54.0-m control wire as shown in Figure (a). The forces exerted on the airplane are shown in Figure (b): the tension in the control wire, the gravitational force, and aerodynamic lift that acts at θ = 20.0° inward from the vertical. Compute the tension in the wire, assuming it makes a constant angle of θ = 20.0° with the horizontal.  N

A speedboat with a mass of 505 kg (including the driver) is tethered to a fixed buoy by a strong 29.7 m cable. The boat's owner loves high speed, but does not really want to go anywhere. So the owner revs up the boat's engine, makes a lot of noise, and runs the boat in circles around the buoy with the cable supplying all the necessary centripetal force. When the tension of the cable is steady at 12300 N, with what force is the boat's engine pushing the boat? Different physics textbooks treat drag force somewhat differently and use different formulas. For the present purpose, take the water's drag force on the boat to be (450 kg/m) × v², where v denotes the boat's speed. Ignore any drag force on the cable. force: N & TOOLS x10

Deduce an expression for a rotation operation along z-axis R₂(a)= exp. La ħ

An air puck of mass 0.30 kg is tied to a string and allowed to revolve in a circle of radius 1.3 m on a frictionless horizontal table. The other end of the string passes through a hole in the center of the table, and a mass of 1.5 kg is tied to it. The suspended mass remains in equilibrium while the puck on the tabletop revolves. (a) What is the tension in the string? N (b) What is the force causing the centripetal acceleration on the puck? (c) What is the speed of the puck? m/s Need Help? Read It

A 1.5-lb slider is propelled upward at A along the fixed curved bar which lies in a vertical plane. If the slider is observed to have a speed of 10.6 ft/sec as it passes position B, determine (a) the magnitude N of the force exerted by the fixed rod on the slider and (b) the rate v at which the speed of the slider is changing (positive if speeding up, negative if slowing down). Assume that friction is negligible. 29 2.8' Answers: N = Ib i ft/sec?

A small block of mass 1.26 kg slides without friction on a horizontal table. Initially it moves in a circle of radius Ro = 0.6 m with a speed 1.5 m/s. It is held in its path by a string that passes through a small hole at the center of the circle. The string is then pulled down a distance of 0.12 m.( Ro - R = 0.12 m.) It is pulled so slowly that the object continues to move in a circle of continually decreasing radius. 1) While the string in pulling in the block, which of the following qualities of the block is conserved (circle all that are correct): a) Rotational kinetic energy (b) Angular momentum c) Linear momentum d) Mechanical energy e) None of the above √/2) What is the final linear speed of the block (in m/sec)? 1.5 m/sec (3) How much work was done by the force that pulled on the string?0.915

One end of a cord is fixed and a small 0.550-kg object is attached to the other end, where it swings in a section of a vertical circle of radius 1.50 m, as shown in the figure below. When ? = 17.0°, the speed of the object is 6.00 m/s. At this instant, find the total acceleration and degree below the cord.

You are swinging a 0.45 kg water balloon vertically. The distance from your shoulder (acting as the center of rotation) and the water balloon is about 0.70 m. You estimate the water balloon is traveling at 6.0 m/s. At the very bottom of the circular path, how much force is your hand holding the water balloon?

A small object of mass 0.500 kg is attached by a 0.840 m-long cord to a pin set into the surface of a frictionless table top. The object moves in a circle on the horizontal surface with a speed of 8.80 m/s. What is the magnitude of the radial acceleration of the object?