Question

A load of 400 N Was moved up a plane inclined at an angle of 30° to the horizontal if the vertical through which the load was raised was 2 m. Calculate the mechanical advantage ?

A) 1.5
B) 2
C) 2.5
D) 3

Answer 1

The mechanical advantage of an inclined plane with a load of 400 N lifted through a vertical height of 2 m at an angle of 30° is 2, calculated using trigonometry and the formula MA = Load/Effort.

Step-by-step explanation:

The student is asking about the mechanical advantage (MA) of an inclined plane. Mechanical advantage is a measure of how much a machine multiplies the input force. In the context of an inclined plane, the mechanical advantage can be calculated using the formula MA = Load/Effort.

In this case, we are given that the load (L) is 400 N, and the vertical height (h) is 2 m. To find the length of the plane (d), we can use trigonometry, knowing that the sine of the angle θ (30°) is equal to the opposite side (h) over the hypotenuse (d): sin 30° = h/d. Solving for d, we get d = h/sin 30° = 2 m / 0.5 = 4 m.

Now, the effort (E) required to move the load up the plane is the force exerted along the length of the plane, which is the weight of the load distributed over the distance d. Therefore, E = L x sin 30° = 400 N x 0.5 = 200 N.

The mechanical advantage can now be calculated: MA = L/E = 400 N / 200 N = 2.

Thus, the correct answer is B) 2.