The figure shows a gymnast preparing to hold a handstand on a balance beam. The beam is 10 cm wide. The gymnast's coach asks the gymnast to make small movem...
Question 1 Report
The figure shows a gymnast preparing to hold a handstand on a balance beam. The beam is 10 cm wide. The gymnast's coach asks the gymnast to make small movements at the hips and shoulders so that the vertical line from the centre of mass stays above the beam. If the line reaches an edge, that edge acts as a pivot. The gymnast's weight acts towards the centre of Earth, regardless of the position of the arms.
(a) Name the force acting through the gymnast's centre of mass. [1]
(b) Describe where the vertical line through the centre of mass must fall for the handstand to be stable. [1]
(c) Explain why raising one leg sideways may cause the gymnast to lose balance. [2]
(d) Give one movement that could restore balance if the centre of mass has moved to the left. [1]
Fig. 1 shows a stage technician lifting one end of a long uniform lighting bar before fixing it to the ceiling. The bar has two lamps of equal mass fitted at equal distances from its middle. The technician supports the bar at point S. It remains horizontal without needing an upward force at either end. The lights convert electrical energy into light, but their cables are flexible and their weight is ignored in this model.
(a) What can be concluded about the centre of mass of the loaded bar? [1]
(b) Give the position of S relative to the middle of the bar. [1]
(c) Explain why the bar does not rotate when held at S. [2]
(d) Describe what happens to the centre of mass if one lamp is replaced by a heavier lamp. [1]
Answer Details
Gymnast on the beam
(a) The force is weight, or gravitational force. [1]
(b) The vertical line through the centre of mass must fall within the width of the beam, between its edges. [1]
(c) Raising a leg sideways shifts the combined centre of mass sideways. If its weight line passes beyond the beam edge, that edge becomes a pivot and the weight creates a turning moment, causing loss of balance. [2]
(d) Move another body part, such as the hips or arms, to the right. [1]
Loaded lighting bar
(a) The centre of mass of the loaded bar is at the middle of the bar. [1]
(b) S is at the middle, directly below the centre of mass. [1]
(c) The weight acts through S. Therefore clockwise and anticlockwise moments are balanced, so the resultant moment is zero and the bar does not rotate. [2]
(d) The centre of mass moves towards the heavier lamp. [1]
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