Final answer:
The pressure in the press is approximately 127.39 Pa. The thrust exerted by the ram is approximately 40,000 N. The displacement of the ram, if the plunger has moved 10 m, is approximately 0.0797 cm.
Step-by-step explanation:
a) To find the pressure in the hydraulic press, we can use the equation:
pressure = force / area
Given that the force applied to the plunger is 100 N and the plunger has a diameter of 1 cm (radius = 0.5 cm), the area of the plunger can be calculated using the formula:
area = π * radius^2
Substituting the values, we get:
area = π * (0.5 cm)^2 = π * 0.25 cm^2 = 0.785 cm^2
Now we can calculate the pressure:
pressure = 100 N / 0.785 cm^2 ≈ 127.39 Pa
b) To find the thrust exerted by the ram, we can use the equation:
thrust = pressure * area
Given that the ram has a diameter of 20 cm (radius = 10 cm), the area of the ram can be calculated using the formula:
area = π * radius^2
Substituting the values, we get:
area = π * (10 cm)^2 = π * 100 cm^2 = 314.16 cm^2
Now we can calculate the thrust:
thrust = 127.39 Pa * 314.16 cm^2 ≈ 40,000 N
c) To find the displacement of the ram, we can use the equation:
displacement = force * distance / (pressure * area)
Given that the plunger has moved 10 m, we can substitute the values into the formula:
displacement = 100 N * 10 m / (127.39 Pa * 314.16 cm^2) ≈ 0.0797 cm