A man is standing on a platform that is connected to a pulley arrangement, as the drawing shows. By pulling upward on the rope with a force the man can raise the platform and himself. The total mass of the man plus the platform is 94.7 kg. What pulling force should the man apply to create an upward acceleration of 1.20 m/s2?
To find the pulling force the man should apply, we can use Newton's second law of motion which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
In this case, the force applied by the man on the rope is equal to the force required to overcome the downward force of gravity acting on the man and the platform, plus the force required to accelerate them upwards.
Step 1: Calculate the downward force of gravity
The downward force of gravity can be calculated using the formula:
Force of gravity = mass * acceleration due to gravity
The mass of the man plus the platform is given as 94.7 kg. The acceleration due to gravity on Earth is approximately 9.8 m/s^2.
Force of gravity = 94.7 kg * 9.8 m/s^2
Step 2: Calculate the total force required
The total force required is the sum of the force of gravity and the force required to create an upward acceleration of 1.20 m/s^2.
Total force required = Force of gravity + Force for acceleration
Step 3: Calculate the pulling force
The pulling force applied by the man on the rope is equal to the total force required.
Pulling force = Total force required
Now, let's calculate the values:
Force of gravity = 94.7 kg * 9.8 m/s^2
Total force required = Force of gravity + (94.7 kg * 1.20 m/s^2)
Pulling force = Total force required
Plug in the values and calculate the pulling force.