A load of 60kg is pushed up a 400m inclined plane of a platform 3m high, what is the velocity ratio of the plane
To calculate the velocity ratio of the inclined plane, we first need to understand the definitions of load, effort, and distance.
- Load: The load refers to the weight or mass being moved. In this case, the load is 60 kg.
- Effort: The effort is the force applied to move the load up the inclined plane. In this case, we assume a frictionless system, so the effort required would be equal to the weight of the load.
- Distance: The distance is the length of the inclined plane that the load is being moved along. In this case, the distance is 400 m.
Now, let's calculate the effort and distance.
Effort:
The effort required to move the load up the inclined plane is equal to the weight of the load. We can calculate it using the formula:
Effort = Load × Acceleration due to gravity
Acceleration due to gravity is approximately 9.8 m/s^2.
Effort = 60 kg × 9.8 m/s^2
Effort = 588 N
Distance:
The distance is given as 400 m.
Now, we can calculate the velocity ratio using the formula:
Velocity Ratio = Distance moved by the effort / Distance moved by the load
In this case, the distance moved by the effort is the same as the distance of the inclined plane, which is 400 m. The distance moved by the load can be calculated using trigonometry.
Distance moved by the load = Platform height / sin(angle of inclination)
The angle of inclination is given by the formula:
Angle of inclination = arctan(Platform height / Length of the inclined plane)
So, we can calculate the angle of inclination:
Angle of inclination = arctan(3 m / 400 m)
Angle of inclination ≈ 0.432 degrees
Next, we can calculate the distance moved by the load:
Distance moved by the load = 3 m / sin(0.432 degrees)
Distance moved by the load ≈ 414.06 m
Finally, we can calculate the velocity ratio:
Velocity Ratio = Distance moved by the effort / Distance moved by the load
Velocity Ratio = 400 m / 414.06 m
Velocity Ratio ≈ 0.966
Therefore, the velocity ratio of the plane is approximately 0.966.
To calculate the velocity ratio of an inclined plane, we need to understand the formula for velocity ratio, which is the ratio of the output distance to the input distance.
In this case, the load of 60kg is being pushed up a 400m inclined plane of a platform 3m high. Let's consider the input distance as the length of the inclined plane (400m) and the output distance as the vertical height of the platform (3m).
The velocity ratio can be calculated as follows:
Velocity Ratio = Output Distance / Input Distance
Velocity Ratio = 3m / 400m
Velocity Ratio = 0.0075
Therefore, the velocity ratio of the plane is 0.0075.
Please note that the velocity ratio only indicates the mechanical advantage of the inclined plane and does not take into account other factors like friction or the force required to push the load.
what do you mean by "velocity ratio"?
the ratio of vertical to horizontal speeds is
vy/vx = 3/√(400^2-3^2)