A window washer uses the chair and pulley arrangement shonw in the figure to lift himself up the side of a building. The window washer's mass is 70 kg and the chair's mass is 10 kg. With what force must he pull down on the rope in order to accelerate upward at
incomplete question.
To determine the force the window washer must pull down on the rope to accelerate upward, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
The forces involved in this scenario are the force exerted by the window washer pulling down on the rope (Tension force) and gravity acting on both the window washer and the chair.
First, let's find the net force acting on the system (window washer + chair):
Net force = Force pulling down (Tension force) - Force due to gravity
The force due to gravity acting on the window washer is given by the formula:
Force due to gravity = mass × acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s².
Force due to gravity (window washer) = (70 kg + 10 kg) × 9.8 m/s²
= 80 kg × 9.8 m/s²
= 784 N
Now, let's substitute the values into the equation for the net force:
Net force = Tension force - 784 N
The window washer wants to accelerate upward, which means the net force must be upward. In other words, the tension force must be greater than the force due to gravity. So, we can rewrite the equation as:
Tension force = Net force + 784 N
Since the window washer wants to accelerate upward, we can assume a desired upward acceleration value. Let's say the desired acceleration is 2 m/s².
Net force = mass × desired upward acceleration
= (70 kg + 10 kg) × 2 m/s²
= 80 kg × 2 m/s²
= 160 N
Finally, substitute this value into the equation for the tension force:
Tension force = 160 N + 784 N
= 944 N
Therefore, the window washer must pull down on the rope with a force of 944 Newtons in order to accelerate upward at 2 m/s².