The coefficient of rolling friction between the floor and the hardened steel balls of an anesthesia trolley (anesthesia machine with ventilator and monitor) is 0.0015. If a hospital crew needs 77 N to push the trolley at an angle of 30 degrees below the horizontal with constant speed, whay is the weight of anesthesia trolley?
To determine the weight of the anesthesia trolley, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration (F = ma). In this case, since the trolley is moving at a constant speed, its acceleration is zero. Therefore, the net force acting on the trolley is also zero.
We can break down the forces acting on the trolley into two components: the force of gravity (its weight) and the force of rolling friction. The force of rolling friction can be calculated by multiplying the coefficient of rolling friction (μ) by the normal force (N) exerted on the trolley.
Given that the crew needs 77 N of force to push the trolley at an angle of 30 degrees below the horizontal, we can resolve this force into its components. The force pulling the trolley downwards parallel to the floor can be calculated as F_parallel = F * sin(theta), where theta is the angle of 30 degrees.
F_parallel = 77 N * sin(30 degrees)
F_parallel ≈ 38.5 N
Since there is no vertical component to the force required to push the trolley (as it is being supported by the floor), the normal force equals the force pulling the trolley downwards parallel to the floor.
N = 38.5 N
Now, we can calculate the force of rolling friction (F_friction) using the formula:
F_friction = μ * N
Given that the coefficient of rolling friction (μ) is 0.0015 and the normal force (N) is 38.5 N, we can calculate the force of rolling friction:
F_friction = 0.0015 * 38.5 N
F_friction ≈ 0.0578 N
Since the net force acting on the trolley is zero, the force of rolling friction must be equal to the force applied by the crew:
F_friction = 0.0578 N = 77 N
Now, we can find the weight of the anesthesia trolley by setting up an equation:
Weight of trolley - Force of rolling friction = 0
Weight of trolley = Force of rolling friction
Therefore, the weight of the anesthesia trolley is approximately 0.0578 N.