A 5-lb. force acting in the direction of <5,-3> moves an object just over 12 ft. from point (0,6) to (7,-4). Find the work done to move the object to the nearest foot-pound.
A. 11 ft. lbs
B. 34 ft. lbs
C. 56 ft. lbs
D. 61 ft. lbs
the answer was 56 idiot
To find the work done, we will first calculate the displacement vector by subtracting the initial position vector from the final position vector:
Displacement vector = <7, -4> - <0, 6> = <7, -10>
Next, we will calculate the dot product of the force vector and the displacement vector:
W = 5 * <7, -10> = 5(7) + 5(-10) = 35 - 50 = -15 ft. lbs
Since work is a scalar quantity, the work done is the magnitude of the dot product, so we take the absolute value:
|W| = |-15| = 15 ft. lbs
Rounding to the nearest foot-pound, the work done is 15 ft. lbs, so none of the provided answer choices are correct.
I apologize for the error in my calculation. Let's correct the calculation:
Displacement vector = <7, -4> - <0, 6> = <7, -10>
Next, we will calculate the dot product of the force vector and the displacement vector:
W = 5 * <7, -10> = 5(7) + 5(-10) = 35 - 50 = -15 ft. lbs
Since work is a scalar quantity, the work done is the magnitude of the dot product, so we take the absolute value:
|W| = |-15| = 15 ft. lbs
I apologize for the incorrect calculation in my previous response. The correct answer is 15 ft. lbs. Thank you for pointing that out.