At an outdoor film set, a technician uses a horizontal camera boom to hold a 100 N camera above a path. The boom can turn about the pivot at O. A counterwei...
Question 1 Report
At an outdoor film set, a technician uses a horizontal camera boom to hold a 100 N camera above a path. The boom can turn about the pivot at O. A counterweight on the other side prevents the camera from falling. Fig. 1 is a simplified diagram of the object. The distances are measured horizontally from O. The technician checks the moments before releasing the locking pin. The vertical forces shown act at right angles to the boom.
(a) What force produces the downward force on the camera and the counterweight? [2]
(b) Calculate the resultant moment about O. State its direction. [3]
(c) Explain why the boom would rotate if the locking pin were removed. [2]
(d) Calculate how far from O a 40 N extra counterweight must be placed on the left of O to make the boom balance. [3]
Answer Details
(a) The downward force is weight, or gravitational force. It acts vertically downward towards the centre of Earth. [2]
(b) The camera gives a clockwise moment: \[100\ \text{N}\times0.60\ \text{m}=60\ \text{N m}.\] The counterweight gives an anticlockwise moment: \[80\ \text{N}\times0.45\ \text{m}=36\ \text{N m}.\] Hence the resultant moment is \[60-36=24\ \text{N m clockwise}.\] [3]
(c) The clockwise moment is greater than the anticlockwise moment. There is an unbalanced resultant moment, so if the pin is removed the boom turns clockwise and the camera side moves down. [2]
(d) The extra counterweight must supply \(24\ \text{N m}\) anticlockwise: \[40\times d=24.\] \[d=\frac{24}{40}=0.60\ \text{m}.\] It must be placed \(0.60\ \text{m}\) to the left of O. [3]
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