Question

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

Answer 1

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.

Answer 2

the answer was 56 idiot

Answer 3

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.