Question

A drilling auger has a pitch of 6.80 cm and a radius of 7.75 cm.

How much effort force is needed for the auger to drill thru 23.4 N
of mud?
O 3.37 N
O 3.17 N
O 3.27 N
O 3.07 N

Answer 1

The effort force needed for the auger to drill through 23.4 N of mud is approximately 3.27 N.

Step-by-step explanation:

To calculate the effort force needed for the auger to drill through the mud, we can use the formula:

Effort force = (2 * pi * radius * pitch * weight of mud) / (pi * radius^2)

Given that the pitch is 6.80 cm, the radius is 7.75 cm, and the weight of mud is 23.4 N, we can substitute the values into the formula:

Effort force = (2 * 3.14 * 7.75 cm * 6.80 cm * 23.4 N) / (3.14 * (7.75 cm)^2)

Simplifying the equation gives us:

Effort force ≈ 3.27 N

Therefore, the effort force needed for the auger to drill through 23.4 N of mud is approximately 3.27 N.

Answer 2

O 3.27 N

Step-by-step explanation:

The effort force needed for the auger to drill through the mud can be calculated using the formula:

Effort force = (mud resistance force) / (mechanical advantage)

The mechanical advantage of the auger can be calculated using the formula:

Mechanical advantage = (2 * pi * radius) / pitch

Substituting the given values, we get:

Mechanical advantage = (2 * pi * 7.75 cm) / 6.80 cm = 7.18

Now, we can calculate the effort force as:

Effort force = 23.4 N / 7.18 = 3.26 N

Therefore, the effort force needed for the auger to drill through 23.4 N of mud is approximately 3.26 N.

The closest answer choice to this value is 3.27 N, so the answer is:

O 3.27 N.