A force of F = 90 N is exerted on mass m₁ as shown. Both m₁ and m₂ accelerate to the right at 3 m/s along the frictionless surface. The force F makes an angle of 25 degrees to the horizontal. If m₂ = 10 kg, calculate the mass m₁. A) 2.7 kg B) 17 kg C) 27 kg D) 1.8 kg E) 24 kg

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Quizplus · Accepted Answer

The force F has two components: one horizontal (F_cosθ) and one vertical (F_sinθ). However, since the surface is frictionless and both masses accelerate to the right, only the horizontal component of the force is relevant. So, we can set up an equation for the horizontal force exerted on the system: F_cosθ = (m₁ + m₂) * a where a is the acceleration of both masses to the right. Substituting the given values, we get: 90 N * cos25° = (m₁ + 10 kg) * 3 m/s^2 Simplifying: m₁ = (90 N * cos25° - 30 kg) / 3 m/s^2 m₁ ≈ 17 kg Therefore, the answer is B (17 kg).

A Force of F = 90 N Is Exerted on Mass