Calculate Work Done and Screw Jack IMA

1. How much work is done in raising 120 pounds to a height of 15.0 feet?

Find the work done in raising 250 grams a distance of 215 centimeters.

Answer:

1. 1800 lb ft

2. 5.27 J

1. Work is the change in energy. The work done in raising an object is given by the formula W = mgh, where W is the work done, m is the mass of the object, g is the acceleration due to gravity, and h is the height the object is raised to. Calculating the work done for raising 120 pounds to a height of 15.0 feet:

W = mgh

W = 120 lb * 15.0 ft

W = 1800 lb ft

For raising 250 grams a distance of 215 centimeters, the work done can be calculated by the same formula using the metric system:

W = mgh

W = 0.250 kg * 9.8 m/s² * 2.15 m

W = 5.27 J

2. What is the Ideal Mechanical Advantage (IMA) of a screw jack with a handle radius of 36 inches and thread pitch of 0.25 inches?

Calculate the IMA of the jack.

The IMA of a screw jack is determined by the formula IMA = circumference of the screw / pitch. For the handle (lever) IMA, it is IMA = 2πR / 2πr. To find the total IMA, we multiply the two:

IMA = (2πR / 2πr) * (2πr / p)

Substitute the given values:

IMA = (2π * 36) / 0.25

IMA = 905