how do u find the horizontal force needed to push a wheel that weighs 300N and has a radius of 30m.it also lies on the stairs of
10m
To find the horizontal force needed to push the wheel, we need to consider several factors.
1. First, let's calculate the weight of the wheel using the equation: weight = mass × gravity.
Given that the weight of the wheel is 300N, we can use the approximate value of gravity, which is 9.8 m/s^2, to calculate the mass of the wheel.
So, mass = weight ÷ gravity = 300N ÷ 9.8 m/s^2 ≈ 30.61 kg.
2. Next, let's calculate the torque (rotational force) required to move the wheel on the stairs.
The torque can be calculated using the equation: torque = force × distance.
In this case, the distance is the radius of the wheel, which is 30m.
Since we need to move the wheel on the stairs, it will require a vertical force to overcome the gravitational force acting downward. The horizontal force will be the frictional force needed to move the wheel horizontally.
Considering the stairs have a height of 10m, we can calculate the distance using a right-angled triangle.
The horizontal distance can be calculated using the Pythagorean theorem: horizontal distance = sqrt(distance^2 - height^2) = sqrt((30m)^2 - (10m)^2) ≈ 28.28m.
3. Now, let's calculate the torque required by the wheel: torque = frictional force × horizontal distance.
Here, the torque should be equal to the torque caused by the weight of the wheel.
torque = (30.61 kg × 9.8 m/s^2) × 30m = 8,999.74 N·m.
4. Finally, let's calculate the frictional force needed to move the wheel horizontally.
frictional force = torque ÷ horizontal distance = 8,999.74 N·m ÷ 28.28m ≈ 317.62 N.
Therefore, the horizontal force needed to push the wheel on the stairs is approximately 317.62 Newtons.