the inclined plane is 30* from the ground
a) What is the mechanical advantage of the inclined plane?
b) A weight of 100N is to be lifted using the inclined plane. What is the minimum applied force for this job?
c) Suppose that an applied force of 200N is needed to move a block of unknown mass along the inclined plane. What is the weight and mass of the block? Assume that the incline is frictionless.
The MA is horizontal distance/height gained, or MA= cotangent 30 deg
To solve these questions related to the inclined plane, we need to understand the concept of mechanical advantage and the trigonometry involved.
a) Mechanical Advantage (MA) of an inclined plane is calculated by dividing the length of the inclined plane (L) by the height (H) of the inclined plane. In this case, the angle of the inclined plane is given as 30 degrees.
To find the length of the inclined plane (L), we can use the trigonometric function cosine (cos). The formula for finding the length of the inclined plane is L = H / cos(angle).
Substituting the values, L = H / cos(30) = H / (√3/2) = 2H / √3.
Therefore, the mechanical advantage (MA) of the inclined plane is given by MA = L / H = (2H / √3) / H = 2 / √3 ≈ 1.15 (approximate to two decimal places).
b) To find the minimum applied force required to lift a weight using the inclined plane, we can use the formula:
Minimum Applied Force = Weight / MA.
Given that the weight is 100N and the mechanical advantage is approximately 1.15, substituting these values into the formula, we get:
Minimum Applied Force = 100 / 1.15 ≈ 87N (approximate to two decimal places).
Therefore, the minimum applied force required to lift a weight of 100N using the inclined plane is approximately 87N.
c) To determine the weight and mass of the block when an applied force of 200N is needed to move it along the inclined plane, we need to consider the mechanical advantage of the inclined plane.
The weight is given by the formula:
Weight = Force Applied / MA.
Given that the force applied is 200N and the mechanical advantage is approximately 1.15, substituting these values into the formula, we get:
Weight = 200 / 1.15 ≈ 173.91N (approximate to two decimal places).
Therefore, the weight of the block is approximately 173.91N.
To determine the mass of the block, we can use the formula:
Weight = Mass × Gravity.
Rearranging the formula to solve for mass, we get:
Mass = Weight / Gravity.
Given that the weight is approximately 173.91N and the acceleration due to gravity is approximately 9.8 m/s^2, substituting these values into the formula, we get:
Mass = 173.91 / 9.8 ≈ 17.74 kg (approximate to two decimal places).
Therefore, the mass of the block is approximately 17.74 kg.