Struggling with Torque Problems?

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SUMMARY

This discussion addresses torque calculations in various mechanical scenarios. The first problem involves calculating the maximum torque for a crane with a 20.0 m arm and a maximum load of 445 N at a 25.0° angle, using the formula torque = force × distance × sin(theta). The second problem focuses on a car's torque around its back wheels when raised at an 8.0° angle, requiring the calculation of the lever arm and the force due to gravity. The third scenario examines the forces exerted by ropes supporting a scaffold with a weight of 208 N and a worker weighing 675 N, emphasizing the importance of static equilibrium in torque calculations.

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  • Understanding of torque calculations and the formula torque = force × distance × sin(theta)
  • Knowledge of static equilibrium principles in mechanics
  • Familiarity with basic physics concepts such as weight (W = mg) and center of mass
  • Ability to perform trigonometric calculations, particularly with angles in degrees
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  • Study advanced torque calculations in mechanical systems
  • Learn about static equilibrium and its applications in engineering
  • Explore the effects of angle on torque in various mechanical setups
  • Investigate the role of center of mass in determining forces in static structures
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Students and professionals in mechanical engineering, physics educators, and anyone involved in practical applications of torque and static equilibrium in mechanical systems.

hshphyss
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Can anyone help me with these problems? they are really stressing me out, thanx

1) The arm of a crane is 20.0 m long and makes an angle of 25.0° with the horizontal. Assume that the maximum load for the crane is limited by the amount of torque the load produces around the base of the arm.
What is the maximum torque the crane can withstand if the maximum load is 445 N?

I know that torque=fr sintheta, but this isn't as straight forward as it looks.

2.) A mechanic jacks up a car to an angle of 8.0° to change the front tires. The car is 3.20 m long and has a mass of 1160 kg. Its center of mass is located 1.12 m from the front end. The rear wheels are 0.40 m from the back end. Calculate the torque exerted by the car around the back wheels.

I know that to find the lever arm it's going to be cos8 2.4=-0.349. So then to find the torque it would be (870 kg)(9.8)(-0.349)=T The force would be the mass times 9.8 correct?


3.)A window washer is standing on a scaffold supported by a vertical rope at each end. The scaffold weighs 208 N and is 2.80 m long. What is the force each rope exerts on the scaffold when the 675 N worker stands 1.00 m from one end of the scaffold? (smaller force and larger force)
 
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1) One is given the maximum load, from which one calculates the maximum torque. Using the load, which acts in the vertical, calculate the component of the load which is normal (perpendicular) to the boom.

2) Weight (force) of the car, W = mg, acts at the center of mass about the pivot point.

3) The force (or tension) on each rope can be determined by picking one end and calculating the sum of the moments about that end, which should add to zero, since the system is static. Also, the sum of the tensions must equal the suspended weight. Assume the weight of the scaffold acts at its center of mass.
 
the angle that you take the sine of sweeps from the r_vector to the F_vector.
In prob#1, this is MORE than 25 degrees.

your calculator seems to be in radian mode in prob.#2,
and the center-of-mass is NOT 2.4m in front of the rear axle.
 

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