Alexa is weighing a construction barrel up a ramp 4 feet long into the back of a truck. The barrel weighs 120 pounds and the ramp is 45 degrees from the horizontal. How much work is Alexa doing?
work done = PE gained = mgh
so, how high is the top of the ramp?
339 ft-lb
To calculate the work done by Alexa in this scenario, we need to use the formula:
Work = Force x Distance x cos(angle),
where:
Force is the force applied (in this case, the weight of the barrel),
Distance is the distance over which the force is applied (the length of the ramp), and
angle is the angle between the force and the direction of motion.
In this case, we have:
Force = 120 pounds (weight of the barrel)
Distance = 4 feet (length of the ramp)
Angle = 45 degrees (angle of the ramp)
Let's calculate the work:
Work = 120 pounds x 4 feet x cos(45 degrees).
To calculate the cosine of 45 degrees, we can use a calculator or refer to the trigonometric table:
cos(45 degrees) = 0.7071.
Now substituting the values into the equation:
Work = 120 pounds x 4 feet x 0.7071.
By performing the multiplication:
Work = 339.888 pounds-feet (rounded to three decimal places).
Therefore, Alexa is doing approximately 339.888 pounds-feet of work when weighing the construction barrel up the ramp into the back of the truck.