Some trainyards have very large horizontal disks that engines can drive onto, which then rotate to turn the engine around to face the opposite direction. Suppose the train engine is 12 m long and centered at the disk's axis. A 500 N force is applied 5.0 m from the center of the engine, with a rope that makes a $35°$ angle with the side of the engine. What magnitude torque is being applied to the train engine?

(II) The bolts on the cylinder head of an engine require tightening to a torque of 95 m • N.

(b) If the six-sided bolt head is 15 mm across (Fig. 10–55), estimate the force applied near each of the six points by a wrench.

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(II) An engineer estimates that under the most adverse expected weather conditions, the total force on the highway sign in Fig. 11–33 will be F→ = (± 2.4 î - 4.1 ĵ) kN, acting at the cm. What torque does this force exert about the base O?

A particle of mass m uniformly accelerates as it moves counterclockwise along the circumference of a circle of radius R:

r→ = î R cos θ + ĵ R sin θ

with θ = ω₀t + (1/2)αt² , where the constants ω₀ and α are the initial angular velocity and angular acceleration, respectively. Determine the object’s tangential acceleration a→_tan and determine the torque acting on the object using

(a) τ→=r→×F

(II) The origin of a coordinate system is at the center of a wheel which rotates in the xy plane about its axle which is the z axis. A force F = 215 N acts in the xy plane, at a 28.0° angle to the x axis, at the point x = 28.0 cm, y = 33.5 cm. Determine the magnitude and direction of the torque produced by this force about the axis.

You pull with a 100 N at the edge of a 25 cm long wrench, to tighten a bolt (gold), as shown. The angle shown is 53° . Calculate the torque your force produces on the wrench, about an axis perpendicular to it and through the bolt.