The ram of a shaping machine has a mass of 200 kg. It moves in slides with a coefficient of friction of 0.07 between the ram and the slides. Calculate: 1.1 The horizontal force required to move the ram. 1.2 The coefficient of friction if the force to move the ram is increased by 30%.

The normal force is equal to the weight of the ram, as it's moving horizontally.

$$N = mg$$ $$N = (200 \text{ kg}) (9.81 \text{ m/s}^2)$$ $$N = 1962 \text{ N}$$

The horizontal force required to move the ram is equal to the force of friction ($F_f$).

$$F_h = F_f = \mu N$$ $$F_h = (0.07) (1962 \text{ N})$$ $$F_h = 137.34 \text{ N}$$

The horizontal force required to move the ram is:

$$\boxed{\text{137.34 N}}$$

The force is increased by 30% from the original force calculated in 1.1.

$$F_{h, \text{new}} = F_h + (0.30 \times F_h)$$ $$F_{h, \text{new}} = 137.34 \text{ N} + (0.30 \times 137.34 \text{ N})$$ $$F_{h, \text{new}} = 137.34 \text{ N} + 41.202 \text{ N}$$ $$F_{h, \text{new}} = 178.542 \text{ N}$$

The normal force ($N$) remains the same.

$$F_{h, \text{new}} = \mu_{\text{new}} N$$

Rearrange to solve for $\mu_{\text{new}}$:

$$\mu_{\text{new}} = \frac{F_{h, \text{new}}}{N}$$ $$\mu_{\text{new}} = \frac{178.542 \text{ N}}{1962 \text{ N}}$$ $$\mu_{\text{new}} \approx 0.0910$$

The new coefficient of friction is:

$$\boxed{\text{0.091}}$$