a block of mass 20 K/g is pulled up with a constant velocity over an inclined plane surface 20m long that make angle of 530 with a horizontal surface. calculate A, the effort needed if the inclined plane is smooth B, the input and output C,AMA and VR if coefficient of kinetic is 0.2.
Let's first break down the given information:
- mass of block (m) = 20 kg
- inclined plane's length (L) = 20 m
- angle of inclination (theta) = 53 degrees
- coefficient of kinetic friction (mu) = 0.2
A) To find the effort needed to pull the block up the inclined plane with constant velocity, we need to find the force required to overcome the gravitational force acting on the block parallel to the inclined plane (effective gravitational force) and the frictional force (if not smooth).
Effective gravitational force (Fg_parallel) = m * g * sin(theta)
where g is the acceleration due to gravity (approximately 9.81 m/s^2).
Fg_parallel = 20 kg * 9.81 m/s^2 * sin(53 degrees) = 20 * 9.81 * 0.8 (rounded value) = 156.96 N (rounded value)
Now, if the inclined plane is smooth, there is no frictional force, and the effort needed is equal to the effective gravitational force:
Effort (smooth plane) = Fg_parallel = 156.96 N
B) The input work is the work done by the applied force (effort) in pulling the block up the inclined plane. The output work is the work done against gravity in lifting the block to its final height.
Work (input) = Effort (smooth plane) * length of inclined plane = 156.96 N * 20 m = 3139.2 J (rounded value)
Output height (h) = L * sin(theta) = 20 m * sin(53 degrees) = 20 m * 0.8 (rounded value) = 16 m
Work (output) = m * g * h = 20 kg * 9.81 m/s^2 * 16 m = 3139.2 J
Since the plane is smooth, the input work is equal to the output work, indicating that all the effort done is used to lift the block.
C) The actual mechanical advantage (AMA) is the ratio of the output force (in this case, effective gravitational force) to the input force (effort).
AMA = Output force / Input force = Fg_parallel / Effort = 156.96 N / 156.96 N = 1
The velocity ratio (VR) is the ratio of the distance traveled by the input force (length of inclined plane) to the distance traveled by the output force (height of block).
VR = Length of inclined plane / height of block = 20 m / 16 m = 1.25
Note: The above calculations assumes the inclined plane to be smooth. If there is a frictional force, then the effort needed will be greater and will affect the input work, AMA, and VR. The frictional force can be calculated using:
Frictional force = mu * Normal force = mu * (m * g * cos(theta))
In this case, Normal force = 20 * 9.81 * cos(53 degrees) = 20 * 9.81 * 0.6 = 117.72 (rounded value)
Frictional force = 0.2 * 117.72 N = 23.54 N
In this case, the effort required would be:
Effort (with friction) = Fg_parallel + Frictional force = 156.96 N + 23.54 N = 180.5 N (rounded value)