A window washer pulls herself upward using the bucket-pulley apparatus shown in the figure . The mass of the person plus the bucket is 63 kg. How hard must she pull downward to raise herself slowly at constant speed?
To determine the force the window washer must exert, we need to consider the forces acting on her.
1. Weight (W): The weight of the person plus the bucket can be calculated using the formula: W = m * g, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s^2). Therefore, W = 63 kg * 9.8 m/s^2 = 617.4 N.
2. Tension in the rope (T): The tension in the rope is the force that the window washer must exert downward. Since the washer is moving at constant speed, the tension in the rope is equal to the weight. Therefore, T = W = 617.4 N.
Thus, the window washer must pull downward with a force of 617.4 N to raise herself slowly at a constant speed.
To find out how hard the window washer must pull downward to raise herself at a constant speed, we can use Newton's second law of motion. This law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
In this case, we know that the window washer wants to move at a constant speed, which means her acceleration is zero. Therefore, the net force acting on her must also be zero.
Let's break down the forces acting on the system:
1. The weight of the person and the bucket, which can be calculated using the formula: weight = mass * gravitational acceleration (g).
Given that the mass of the person plus the bucket is 63 kg, and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the weight:
weight = 63 kg * 9.8 m/s² = 617.4 N
2. The tension in the rope, which is the force the person exerts downward to counterbalance her weight.
To keep the system in equilibrium (zero net force), the tension in the rope must be equal in magnitude to the weight of the person and the bucket. Therefore, she must pull downward with a force of 617.4 N to raise herself slowly at constant speed.