A simple pendulum consists of a 4.9 kg point mass hanging at the end of a 3.1 m long light string that is connected to a pivot point. Calculate the magnitude of the torque (due to the force of gravity) around this pivot point when the string makes a 3.1 ◦ angle with the vertical. The acceleration of gravity is 9.81 m/s 2 . Answer in units of N · m.

Next a skier is pulled by a tow rope up a frictionless ski slope that makes an angle of 15 with the horizontal. the rope moves parallel to the slope with a constant speed of 0.69 m/s. the force of the rope does 800 3 of work on the skier as the skier moves a distance of 8.4 m up the incline. (a) if the rope moved with a constant speed of 2.2 m/s how much work would the force of the rope do on the skier as the skler moved a distance of 8.4 m up the incline? at what rate is the force of the rope doing work on the skier when the rope moves with a speed of (b) 0.69 m/s and (c) 2.2 m/s?

An object weighs 40n in air, weighs 20n when submerged in water and 30n when submerged in a liquid of unknown density. what is the density of the liquid?

Automobile fuel efficiency is often measured in miles that the car can be driven per gallon of fuel (mpg). heavier cars tend to have lower fuel efficiencies (lower mpg ratings). which variable (weight or fuel efficiency) is most naturally considered the explanatory (predictor) variable in this context?