What Speed Does the Man Hit the Ground?

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Homework Help Overview

The problem involves an 81 kg man lowering himself from a height of 10.6 m using a rope over a frictionless pulley connected to a 60 kg sandbag. The questions focus on determining the speed at which the man hits the ground and exploring methods to reduce that speed.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss drawing free body diagrams and labeling forces, with one participant expressing uncertainty about progressing beyond that point. Another suggests using Newton's laws to deduce the man's acceleration and questions the relationship between the man's and sandbag's accelerations. There is also a discussion about calculating impact velocity using kinematic equations.

Discussion Status

The discussion includes attempts to clarify the relationship between the forces acting on the man and the sandbag. Some participants have provided hints and guidance on using Newton's laws and kinematics, while others are exploring the implications of their calculations. There is no explicit consensus on the final solution yet.

Contextual Notes

Participants note discrepancies in mass values used in calculations and the need to ensure consistency in problem statements. The discussion reflects an ongoing exploration of assumptions related to the setup of the problem.

sacsac
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Homework Statement



An 81 kg man lowers himself to the ground from a height of 10.6 m by holding onto a rope that runs over a frictionless pulley to a 60 kg sandbag.
(a) With what speed does the man hit the ground if he started from rest?

(b) What can he do to make him hit the ground slower?

Homework Equations


The Attempt at a Solution



attempt for part a: no idea... i drew diagram, labeled forces, but can't seem to go beyond that.
attempt for part b: hold the string attached to the sandbag and pull down as he is going downward.
 
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sacsac said:
1attempt for part a: no idea... i drew diagram, labeled forces, but can't seem to go beyond that.

If you drew your free body diagram and labeled all the forces, the next step should be to write down Newton's laws. Ultimately, you want to deduce the man's acceleration.

Hint: What must be the relationship between the man's acceleration and the sandbag's acceleration?
 
both accelerations should be the same shouldn't it? so this is what i have so far...

Sum of forces for m1: Ft - m1g

Sum of forces for m2: m2g - Ft

m1a = Ft - m1g

m2a = m2g - Ft

Ft = m2g - m2a

m1a = ( m2g - m2a ) - m1g

m1a + m2a = m2g - m1g

80a + 60a = 60*9.8 - 80*9.8

140a = -196

a = -1.4 m/s^2? but since the man is going down, and my reference frame for going down for a is positive, should it be 1.4? and if a = 1.4 or -1.4, how do i find the impact velocity? V^2 = Vo^2 + 2ax?...
 
sacsac said:
how do i find the impact velocity? V^2 = Vo^2 + 2ax?...

Your original statement of the problem says the man's mass is 81kg, yet you use 80 in your work. Typo? Either way, your work is correct. That equation will do nicely to find velocity. Remember, having acceleration (which is constant in this problem), it's just a kinematics question!
 
Oh sorry about that. Yes, it forgot it was supposed to be 81. But I redid it and got the right answer! Thank You very much!
 

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