Answer :
Final answer:
The magnitude of force F required to hold the 20.0 kg mass at rest on a frictionless incline is 49.1 N. (b)
Explanation:
To determine the force required to hold the mass at rest on the incline, we need to consider the forces acting on the mass. Since the incline is frictionless, the only forces acting on the mass are its weight (mg) and the force (F) holding it in place. The weight of the mass can be calculated using the equation w = mg, where m is the mass (20.0 kg) and g is the acceleration due to gravity (9.81 m/s²). Therefore, w = 20.0 kg × 9.81 m/s² = 196.2 N.
Since the mass is held at rest, the force holding it in place (F) must be equal in magnitude and opposite in direction to its weight (mg). Therefore, F = 196.2 N. However, in the provided options, force F is given in Newtons, so we need to convert the weight from Newtons to the correct unit. Since 1 Newton (N) is equal to 1 kg⋅m/s², the weight of the mass is already in Newtons. Hence, the magnitude of force F is equal to the weight of the mass, which is 196.2 N.
In conclusion, option b, 49.1 N, represents the magnitude of force F required to hold the 20.0 kg mass at rest on the frictionless incline. (b)
