1. Crane with a weight on the hook of it. Find the upward force of the rear wheels given the centre of gravity
a. Length of arm of crane (30m), weight of object on hook (in N), height (3.5m), length of crane (10m) 2 the centre of gravity which was 7m from the front wheel and 1m above the axels. Angle of the arm is 35.4
To find the upward force of the rear wheels of the crane, we need to understand the concept of moments and equilibrium. The crane is in equilibrium when the sum of all the clockwise moments is equal to the sum of all the anticlockwise moments.
First, let's calculate the force exerted by the weight on the hook. The weight is given in Newtons (N), and we can calculate the force using the formula:
Force = Mass × Gravity
The mass is given in kilograms (kg), and we can calculate it by dividing the weight by the acceleration due to gravity:
Mass = Weight / Gravity
Once we have the mass, we can calculate the force:
Force = Mass × Gravity
Since the weight is given in Newtons, we can simply use this value for the force.
Next, let's calculate the clockwise and anticlockwise moments acting on the crane.
The clockwise moments are generated by the weight on the hook and can be calculated using the formula:
Clockwise Moment = Force × Perpendicular Distance
The perpendicular distance is the horizontal distance from the rear wheels to the line of action of the force. In this case, the line of action of the force is the length of the arm of the crane.
Now, let's calculate the anticlockwise moments. The only anticlockwise moment in this scenario comes from the weight of the crane itself acting at its center of gravity.
Anticlockwise Moment = Weight of Crane × Perpendicular Distance
Again, the perpendicular distance is the horizontal distance from the rear wheels to the center of gravity of the crane.
Finally, to find the upward force of the rear wheels, we need to equate the sum of all the clockwise moments to the sum of all the anticlockwise moments:
Sum of Clockwise Moments = Sum of Anticlockwise Moments
Rear Wheel Upward Force × Perpendicular Distance = (Force × Arm Length) + (Weight of Crane × Perpendicular Distance)
Rear Wheel Upward Force = [(Force × Arm Length) + (Weight of Crane × Perpendicular Distance)] / Perpendicular Distance
Now substitute the given values into the formula and calculate:
Arm Length = 30 m
Force = Weight of Object on Hook
Weight of Object on Hook = given
Weight of Crane = Weight of Crane per meter × Length of Crane
Weight of Crane per meter = Weight of Crane / Length of Crane
Angle of the Arm = 35.4 degrees
Perpendicular Distance = Height of Crane - (Height of Crane × sin(Angle of the Arm))
Height of Crane = given
Length of Crane = 10 m
Gravity = 9.8 m/s^2
By substituting the given values into the formula, you can calculate the upward force of the rear wheels of the crane.