a crane does 62,500. J of work lifting a 120.-N backpack?
a. How high did you lift the backpack?
b. How much did the backpack weigh in pounds? (Hint: There are 4.448 N in one pound.)
a. 62,500 J = M g H
M g = 120 N.
Solve for H
b. 120 N/4.448 N/lb = ____lb
whaaattt
To find the answers to these questions, we can use the formula for work:
Work = Force × Distance × cos(θ)
Where:
- Work is measured in joules (J)
- Force is measured in newtons (N)
- Distance is measured in meters (m)
- θ is the angle between the force and the direction of displacement (in this case, it is assumed to be 0 degrees, so cos(θ) = 1)
a. How high did you lift the backpack?
To solve for the distance, we need to rearrange the formula:
Distance = Work / (Force × cos(θ))
Given:
Work = 62,500 J
Force = 120 N
cos(θ) = 1 (since the angle is assumed to be 0 degrees)
Substituting the values:
Distance = 62,500 J / (120 N × 1) = 520.83 meters (rounded to two decimal places)
Therefore, the backpack was lifted to a height of approximately 520.83 meters.
b. How much did the backpack weigh in pounds? (Hint: There are 4.448 N in one pound.)
To find the weight of the backpack in pounds, we can convert the weight from newtons to pounds using the conversion factor provided.
Given:
Force = 120 N
Conversion: 1 pound = 4.448 N
To convert from newtons to pounds:
Weight (in pounds) = Force (in N) / Conversion Factor
Substituting the values:
Weight (in pounds) = 120 N / 4.448 N = 26.98 pounds (rounded to two decimal places)
Therefore, the backpack weighed approximately 26.98 pounds.