A small round ball of mass 3 kg hangs by a thin rope from the roof of a train carriage like a pendulum. The train moves off from the platform with a constant acceleration of ‘a’ m/s2 This causes the round ball to effectively swing backwards and adopt a position with the rope at angle theta ( θ = 250 ) to the vertical. It stays in this position due to constant acceleration. By applying Newton’s second law: a) Derive an expression for the acceleration of the train Consider the horizontal and vertical components of the tension force in the rope, your expression will be in terms of the acceleration ‘a’ and the gravitational acceleration g (9.81 m/s2 ), and the angle ( θ ). b) Calculate the acceleration of the train, m/s2 ? c) Calculate the tension, N in the rope.
A small round ball of mass 3 kg hangs by a thin rope from the roof of a train carriage like a
pendulum. The train moves off from the platform with a constant acceleration of ‘a’ m/s2 This
causes the round ball to effectively swing backwards and adopt a position with the rope at angle
theta ( θ = 250
) to the vertical. It stays in this position due to constant acceleration. By applying
Newton’s second law:
a) Derive an expression for the acceleration of the train Consider the horizontal and
vertical components of the tension force in the rope, your expression will be in terms
of the acceleration ‘a’ and the gravitational acceleration g (9.81 m/s2
), and the angle
( θ ).
b) Calculate the acceleration of the train, m/s2
?
c) Calculate the tension, N in the rope.
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