A scraper is drawn over a tooth 22 times, each time moving a distance of 0.75 cm. The scraper is held against the tooth with a normal force of 5.4 N. Assuming a coefficient of kinetic friction of 0.90 between the scraper and the tooth, determine the work done to clean the tooth.

67.5

To determine the work done to clean the tooth, we need to calculate the total work done by the applied force (normal force) in moving the scraper over the tooth.

Work done (W) = Force applied (F) x Distance moved (d) x cosine(theta)

The force applied here is the normal force (N) and the distance moved is the total distance moved by the scraper over the tooth (d_total).

Given:
Normal force (N) = 5.4 N
Distance moved (d) = 0.75 cm
Number of times scraped (n) = 22

First, let's calculate the total distance moved by the scraper over the tooth:

Total distance moved (d_total) = Distance moved (d) x Number of times scraped (n)
= 0.75 cm x 22
= 16.5 cm

Now, let's convert the total distance moved to meters:

Total distance moved (d_total) = 16.5 cm = 0.165 meters

Next, let's calculate the angle (theta) between the applied force and the direction of motion. Since the scraper is drawn over the tooth, the angle between the normal force and the direction of motion is 0 degrees (cosine(0) = 1).

Now, we can calculate the work done:

Work done (W) = Force applied (N) x Distance moved (d_total) x cosine(theta)
= 5.4 N x 0.165 m x 1
= 0.891 J

Therefore, the work done to clean the tooth is 0.891 Joules.

To determine the work done to clean the tooth, we need to calculate the total work done by the friction force as the scraper moves over the tooth.

First, let's break the problem down into steps:

1. Calculate the force of friction acting on the scraper.
2. Calculate the distance moved by the scraper.
3. Calculate the work done by the friction force.

Step 1: Calculate the force of friction.
The force of friction, F_friction, can be calculated using the formula:

F_friction = coefficient of kinetic friction * normal force

Given:
Coefficient of kinetic friction, μ = 0.90
Normal force, N = 5.4 N

Substituting the values into the formula:

F_friction = 0.90 * 5.4

Step 2: Calculate the distance moved by the scraper.
The distance moved by the scraper, d, can be calculated by multiplying the number of times the scraper is drawn over the tooth by the distance moved in each stroke.

Given:
Number of strokes, n = 22
Distance moved in each stroke, s = 0.75 cm = 0.75/100 m

Substituting the values into the formula:

d = n * s
d = 22 * 0.75/100

Step 3: Calculate the work done by the friction force.
The work done by the friction force, W_friction, can be calculated using the formula:

W_friction = F_friction * d

Substituting the values into the formula:

W_friction = (0.90 * 5.4) * (22 * 0.75/100)

Now, let's calculate the work done to clean the tooth:

W_friction = (0.90 * 5.4) * (22 * 0.75/100) = 0.8754 Joules

Therefore, the work done to clean the tooth is approximately 0.8754 Joules.

5.4 * 0.90 * 0.75 * 22 = ____ Joules