A 59-kg housepainter stands on a 16-kg aluminum platform. The platform is attached to a rope that passes through an overhead pulley, which allows the painter to raise herself and the platform. (Ignore the mass of the pulley and any friction in the pulley.)

(a) With what force F must she pull down on the rope to accelerate herself and the platform upward at a rate of 0.74 m/s2?

b) When her speed reaches 1.1 m/s, she pulls in such a way that she and the platform go up at a constant speed. What force is she exerting on the rope now? (Ignore the mass of the rope.)

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To solve these problems, we can use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.

(a) First, let's determine the total mass of the system. The system consists of the housepainter and the platform, so we add their masses together:

Total mass = mass of housepainter + mass of platform
Total mass = 59 kg + 16 kg
Total mass = 75 kg

The force required to accelerate the system can be calculated using Newton's second law:

Force (F) = Total mass x Acceleration
F = 75 kg x 0.74 m/s^2
F = 55.5 N

Therefore, she must pull down on the rope with a force of 55.5 Newtons to accelerate herself and the platform upward at a rate of 0.74 m/s^2.

(b) When the speed reaches 1.1 m/s, it means that the acceleration is zero because the velocity is constant. This implies that the net force is also zero. Since there is no friction or other forces acting on the system in the vertical direction, the force she exerts on the rope must cancel out the force due to the weight of the system.

The weight of the system can be calculated using the equation:

Weight = mass x gravitational acceleration
Weight = Total mass x 9.8 m/s^2
Weight = 75 kg x 9.8 m/s^2
Weight = 735 N

Therefore, to keep the system moving at a constant speed, she exerts a force of 735 Newtons on the rope.