1. A vertical seawater lock is 4m wide and 2m high. The water level is 2 m above the base of the lock on one side, there being no water on the other side. The mass of the lock is 2.5 t and the coefficient of friction between the lock and the slides is 0.25. Determine the force necessary to raise the lock. (Density of seawater = 1025 kg/m3)

To determine the force necessary to raise the lock, we need to consider two factors: the weight of the lock and the friction between the lock and the slides.

Step 1: Calculate the weight of the lock.
The weight of an object can be calculated using the formula:
Weight = mass * acceleration due to gravity (g)
Given that the mass of the lock is 2.5 t, we need to convert it to kilograms:
1 t = 1000 kg
So, the mass of the lock in kilograms is:
2.5 t * 1000 kg/t = 2500 kg

Using the acceleration due to gravity (g) as 9.8 m/s^2, we can calculate the weight of the lock:
Weight = 2500 kg * 9.8 m/s^2
Weight = 24,500 N

Step 2: Calculate the frictional force.
The frictional force can be calculated using the formula:
Frictional Force = coefficient of friction * Normal force
The normal force is the force exerted by the lock on the slides perpendicular to them.

The normal force can be determined by considering the water pressure at the base of the lock. The pressure at a certain depth in a fluid can be calculated as:
Pressure = density of fluid * gravity * height

The density of seawater is given as 1025 kg/m^3, so the pressure at the base of the lock can be calculated as:
Pressure = 1025 kg/m^3 * 9.8 m/s^2 * 2 m
Pressure = 20,090 N/m^2

The normal force is equal to the pressure at the base of the lock multiplied by the area of the lock:
Normal force = pressure * area
Area = width * height
Area = 4 m * 2 m = 8 m^2

Normal force = 20,090 N/m^2 * 8 m^2
Normal force = 160,720 N

Then, we can calculate the frictional force:
Frictional force = 0.25 * 160,720 N
Frictional force = 40,180 N

Step 3: Calculate the force necessary to raise the lock.
The force necessary to raise the lock is equal to the weight of the lock plus the frictional force:
Force necessary to raise the lock = weight + frictional force
Force necessary to raise the lock = 24,500 N + 40,180 N
Force necessary to raise the lock = 64,680 N

Therefore, the force necessary to raise the lock is 64,680 N.

To determine the force necessary to raise the lock, we need to consider the buoyant force and the force due to friction.

1. Buoyant force:
The buoyant force is the upward force exerted on an object submerged in a fluid. It can be calculated using the formula:

F_buoyant = density * volume * g

In this case, the density of seawater is 1025 kg/m^3. The volume of the lock can be calculated by multiplying the width, height, and depth (which is the water level):

Volume = width * height * depth = 4m * 2m * 2m = 16 m^3

Now we can calculate the buoyant force:

F_buoyant = 1025 kg/m^3 * 16 m^3 * 9.81 m/s^2 = 159,360 N

2. Force due to friction:
The force due to friction is calculated using the equation:

F_friction = coefficient_of_friction * normal_force

The normal force is the force perpendicular to the surface, which in this case is the weight of the lock:

Normal_force = mass * g = 2.5 t * 1000 kg/t * 9.81 m/s^2 = 24,525 N

Now we can calculate the force due to friction:

F_friction = 0.25 * 24,525 N = 6131.25 N

3. Total force:
The force necessary to raise the lock is the sum of the buoyant force and the force due to friction:

Total_force = F_buoyant + F_friction = 159,360 N + 6131.25 N = 165,491.25 N

Therefore, the force necessary to raise the lock is approximately 165,491.25 Newtons.