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A block of mass 5 kg starting from rest pulled up on a smooth incline plane making an angle of 30$$^\circ$$ with horizontal with an effective acceleration of 1 m s$$^{-2}$$. The power delivered by the pulling force at $$t = 10$$ s from the start is _______ W.
[Use $$g = 10$$ m s$$^{-2}$$]
Correct Answer: 300
Given: Mass = 5 kg, angle = 30°, acceleration = 1 m/s², starts from rest, g = 10 m/s².
First, we find the net pulling force.
Along the incline, the pulling force must overcome gravity and provide acceleration:
$$F = m(a + g\sin\theta) = 5(1 + 10 \times \sin 30°) = 5(1 + 5) = 30 \text{ N}$$
Next, we find velocity at t = 10 s.
$$v = u + at = 0 + 1 \times 10 = 10 \text{ m/s}$$
From this, we power delivered.
$$P = Fv = 30 \times 10 = 300 \text{ W}$$
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