a block of weight 10kg, and 10cm in each edge is pulled up a plane, inclined to the horizontal at 15degree Celcius cover a film of viscosity=. special of the block is constant 3m/s and oil film thickness d= 0.03mm. The velocity profile of the film is linear. Find the force required.
To find the force required to pull the block up the inclined plane, we need to consider the forces acting on the block.
1. Weight (W): The weight of the block acts vertically downward. Given that the weight is 10 kg, we can calculate the weight using the formula W = m * g, where m is the mass of the block and g is the acceleration due to gravity (approximately 9.8 m/s^2). So, W = 10 kg * 9.8 m/s^2 = 98 N.
2. Normal Force (N): The normal force acts perpendicular to the inclined plane and opposes the weight of the block. In this case, the normal force is equal in magnitude to the component of the weight that acts perpendicular to the inclined plane. Since the inclined plane is inclined at 15 degrees to the horizontal, the angle between the inclined plane and the vertical direction is 90 degrees - 15 degrees = 75 degrees. Therefore, the normal force (N) can be calculated using the formula N = W * cos(θ), where θ is the angle of inclination. So, N = 98 N * cos(75 degrees) = 98 N * 0.2588 = 25.40 N.
3. Frictional Force (f): The frictional force opposes the motion of the block up the inclined plane. In this case, the frictional force is due to the viscosity of the oil film between the block and the inclined plane. Since the velocity profile of the film is linear, the viscosity-related frictional force can be calculated using the formula f = η * A * (dv/dy), where η is the viscosity of the oil film, A is the contact area between the block and the inclined plane, dv/dy is the velocity gradient (change in velocity with respect to the distance). Given that the viscosity is 0 (since no value is provided), the frictional force due to viscosity is zero.
4. Force Required (F): The force required to pull the block up the inclined plane is the sum of the forces acting on the block. So, F = W * sin(θ) + f, where W is the weight, θ is the angle of inclination, and f is the frictional force. Since the frictional force is zero, the force required is simply F = W * sin(θ). Therefore, F = 98 N * sin(15 degrees) = 25.35 N.
Hence, the force required to pull the block up the inclined plane is approximately 25.35 Newtons.