A 33.5 kg person stands on a 67 kg platform.
He pulls on the rope that is attached to the
platform via the frictionless lower-right pul-
ley. He pulls the rope at an angle of 35◦ to the
horizontal, as shown in the figure below.
Assume: g = 9.8 m/s2 . Ignore friction.
The platform remains level.
(a) If he pulls the platform up at a steady rate,
how much force is he pulling on the rope?
(b) In Part 1 we assumed that the platform re-
mains level. This is a bad assumption.
However, if the man were pulling straight
up on the rope, the forces will be balanced
and the platform should remain level.
1. This is a good assumption.
2. Cannot be determined.
3. This also is a bad assumption.
Find the tension in the system(F=Ma)the divide this by the number of pulleys that have shortened the y distance. the angle is just there to throw you off.
This is a bad assumption.
To solve this problem, we can break it down into two parts: determining the force exerted by the person on the rope (part a), and evaluating the assumption about the platform remaining level (part b).
(a) To find the force exerted by the person on the rope, we need to analyze the forces acting on the system. Considering the system consisting of the person and the platform, the only external force acting is the force exerted by the person on the rope. This force can be separated into horizontal and vertical components.
The vertical component of the force is responsible for counteracting the gravitational force on the system, which equals the combined weight of the person and the platform:
Weight of person = mass of person × gravitational acceleration
= 33.5 kg × 9.8 m/s²
Weight of platform = mass of platform × gravitational acceleration
= 67 kg × 9.8 m/s²
The total vertical force exerted by the person on the rope is the sum of the weights:
Total vertical force = Weight of person + Weight of platform
The horizontal component of the force is responsible for accelerating the system horizontally. We can find this force by multiplying the total vertical force by the tangent of the angle at which the rope is pulled:
Horizontal force = Total vertical force × tan(angle)
(b) Regarding the assumption about the platform remaining level, we need to consider the forces acting on the platform. When the person pulls straight up on the rope, the force is balanced vertically and the platform should remain level. This is because the vertical force exerted by the person is equal in magnitude and opposite in direction to the gravitational force on the system. Therefore, assumption 1 ("This is a good assumption") is correct.
To summarize:
(a) To find the force exerted by the person on the rope:
- Calculate the weight of the person and the platform separately.
- Determine the total vertical force by summing the weights.
- Calculate the horizontal force using the total vertical force and the angle at which the rope is pulled.
(b) The assumption that the platform remains level when the person pulls straight up on the rope is correct.