A heavy ball hangs from the ceiling of a motor car by a light string. When the car is stationary, a transverse pulse travels on the string at a speed of 60 cm s ⁻¹ . When the car accelerates along a horizontal road, the pulse travels at 62 cm s ⁻¹ . Determine the acceleration of the car. Take g = 10 m s ⁻² .

Step-by-step solution

Let m be the mass of the heavy ball and be the mass per unit length of the string. When the car is stationary, the tension in the string is T₁ = mg . The speed of the transverse pulse is given by v₁ = T₁ = mg = 60 cm s ⁻¹ . When the car accelerates horizontally with acceleration a , the effective acceleration due to gravity becomes g_ eff = g^2 + a^2 . The new tension in the string is T₂ = m g^2 + a^2 . The new speed of the transverse pulse is v₂ = T₂ = m g^2 + a^2 = 62 cm s ⁻¹ . Taking the ratio of the speeds: v₂