Final answer:
The force exerted by the man on the piano can be calculated using the component of gravitational force along the ramp considering the piano's mass, acceleration due to gravity, and angle of the incline. The calculated force is approximately 636.36 N. However, this value is not among the given options, suggesting a potential discrepancy in the options provided.
Step-by-step explanation:
To find the force exerted by the man on the piano, we need to consider the components of gravitational force along the ramp, since the piano is sliding down at a constant velocity and we are neglecting friction. The component of gravitational force along the ramp is equal to the force the man needs to apply to keep the piano moving at constant velocity. This component can be calculated using the equation F = mg × sin(θ), where m is the mass of the piano, g is the acceleration due to gravity, and θ is the angle of the incline.
Given that the mass m is 190 kg, acceleration due to gravity g is 9.8 m/s², and the angle θ is 20°, we can use the following steps to find the force:
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Carrying out the calculation:
F = 190 × 9.8 × sin(20°) ≈ 190 × 9.8 × 0.342 ≈ 636.36 N
Since the available options do not include this value, we need to recheck the provided options for a potential error or choose the closest value if rounding is considered.