B12. A Production Engineer student man wishes to load a refrigerator onto a truck using a ramp at angle @ as shown in Figure 4. This will help in the design of a conveyer belt to lift goods from the ground to a height h above the ground. He claims that less work would be required to load the truck if the length L of the ramp were increased. Discuss whether his claim is valid or not.
In order to determine whether the student's claim is valid or not, we need to analyze the concepts of work and mechanical advantage.
Work is defined as the amount of force applied over a distance. Mathematically, work is calculated as the product of force and displacement along the direction of the force. So, in this case, less work would mean less force or less displacement.
The mechanical advantage of a ramp is determined by the ratio of the length of the ramp (L) to the height it lifts an object (h). Mechanical advantage is a measure of how much the ramp reduces the force needed to move an object vertically.
If the length of the ramp (L) is increased, the mechanical advantage of the ramp also increases. This means that the ramp would reduce the force required to lift the refrigerator onto the truck. Therefore, in terms of force, the student's claim appears to be valid. With a longer ramp, less force would be required to do the same amount of work.
However, it is important to note that although less force may be required with a longer ramp, the distance over which the force is applied (displacement) would also increase. Therefore, while the force required may be reduced, the work done (force multiplied by displacement) would remain the same.
In summary, the student's claim is valid in terms of reducing the force required to load the truck when using a longer ramp. However, the total work done would remain the same regardless of the ramp length.
To determine whether the claim is valid or not, we need to consider the concept of work in physics.
Work is defined as the product of the force applied on an object and the displacement of the object in the direction of the force. Mathematically, work (W) can be represented as:
W = F * d * cos(theta)
where F is the force applied, d is the displacement in the direction of the force, and theta is the angle between the force and the displacement vector.
In the case of loading a refrigerator onto a truck using a ramp, the force applied is the weight of the refrigerator (mg), where m is the mass of the refrigerator and g is the acceleration due to gravity. The displacement is the distance covered along the ramp (L) and the angle between the force and displacement vectors is the angle of the ramp (@).
By analyzing the formula for work, we can see that the work required would depend on the horizontal displacement (L * cos(@)) along the ramp and not on the length of the ramp itself. Increasing the length of the ramp does not change the horizontal displacement required to load the fridge onto the truck.
Therefore, the claim that less work would be required with an increased length of the ramp is not valid. The work required to load the truck remains the same regardless of the length of the ramp.