12. The total torque supplied to the pulley attached to the spindle of a drilling machine is 45 N m . Calculate the force exerted at each of the 15 mm diameter drill's cutting edges which are fitted to the spindle. The torque needed to overcome friction in the spindle bearings is equal to $$ 45 \% $$ of the total torque driving the drill.

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To solve this problem, we need to follow these steps:

1. **Extract known conditions:**
   - Total torque ($$ T $$) supplied to the pulley: $$ 45 \, \text{N m} $$
   - Diameter of the drill ($$ d $$): $$ 15 \, \text{mm} = 0.015 \, \text{m} $$
   - Torque needed to overcome friction is $$ 45\% $$ of the total torque.

2. **Calculate the torque used to overcome friction:**
   $$
   T_f = 0.45 \times T
   $$

3. **Calculate the effective torque available for cutting:**
   $$
   T_c = T - T_f
   $$

4. **Calculate the radius of the drill:**
   $$
   r = \frac{d}{2}
   $$

5. **Use the relationship between torque, force, and radius:**
   $$
   T_c = F \times r
   $$
   where $$ F $$ is the force exerted at the cutting edges.

6. **Rearrange to find the force:**
   $$
   F = \frac{T_c}{r}
   $$

Now, let's perform the calculations step by step.

### Step 1: Calculate the torque needed to overcome friction
$$
T_f = 0.45 \times 45
$$

### Step 2: Calculate the effective torque available for cutting
$$
T_c = 45 - T_f
$$

### Step 3: Calculate the radius of the drill
$$
r = \frac{0.015}{2}
$$

### Step 4: Calculate the force exerted at the cutting edges
$$
F = \frac{T_c}{r}
$$

Now, let's perform these calculations.
Calculate the value by following steps:
- step0: Calculate:
  $$0.45\times 45$$
- step1: Multiply the numbers:
  $$20.25$$
Calculate or simplify the expression $$ 0.015 / 2 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{0.015}{2}$$
- step1: Convert the expressions:
  $$\frac{\frac{3}{200}}{2}$$
- step2: Multiply by the reciprocal:
  $$\frac{3}{200}\times \frac{1}{2}$$
- step3: Multiply the fractions:
  $$\frac{3}{200\times 2}$$
- step4: Multiply:
  $$\frac{3}{400}$$
Calculate or simplify the expression $$ 45 - 20.25 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$45-20.25$$
- step1: Subtract the numbers:
  $$24.75$$
Calculate or simplify the expression $$ 24.75 / 0.0075 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{24.75}{0.0075}$$
- step1: Convert the expressions:
  $$\frac{\frac{99}{4}}{\frac{3}{400}}$$
- step2: Multiply by the reciprocal:
  $$\frac{99}{4}\times \frac{400}{3}$$
- step3: Reduce the numbers:
  $$33\times 100$$
- step4: Multiply the numbers:
  $$3300$$
Now, let's summarize the calculations step by step:

1. **Torque needed to overcome friction:**
   $$
   T_f = 0.45 \times 45 = 20.25 \, \text{N m}
   $$

2. **Effective torque available for cutting:**
   $$
   T_c = 45 - 20.25 = 24.75 \, \text{N m}
   $$

3. **Radius of the drill:**
   $$
   r = \frac{0.015}{2} = 0.0075 \, \text{m}
   $$

4. **Force exerted at the cutting edges:**
   $$
   F = \frac{T_c}{r} = \frac{24.75}{0.0075} = 3300 \, \text{N}
   $$

### Final Answer:
The force exerted at each of the drill's cutting edges is $$ 3300 \, \text{N} $$.
The force exerted at each drill's cutting edge is 3300 N.

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