What Are the Physics Behind a Girl Pulling a Sled on Ice?

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Homework Help Overview

The problem involves a scenario where a girl and a sled are on frictionless ice, connected by a rope, and a force is applied. The objective is to determine the acceleration of both the girl and the sled, as well as the distance they meet from the girl's initial position.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the application of Newton's second law (f=ma) to find the accelerations of the girl and the sled. There is an attempt to derive equations for their positions and the time taken to meet.

Discussion Status

Some participants have provided calculations for the accelerations and are attempting to solve for the distance at which they meet. There is recognition of confusion regarding the time variable and the resulting calculations, indicating a productive exploration of the problem.

Contextual Notes

Participants are working under the constraints of a homework problem, which may limit the information available or the methods they can use. The discussion reflects uncertainty in the calculations and the need for clarification on the relationships between the variables involved.

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I'm not sure what the rules are about posting homework problems, but I just had 2 I couldn't get around too, so here's the second one...

Homework Statement


A 40 kg girl and a 8.4 kg sled are on the frictionless ice of a frozen lake, 15m apart but connected by a rope of negligible mass. The girl exerts a horizontal 5.2 N force on the rope.
What are the acceleration magnitudes of
(a) the sledge?
(b) the girl?
(c) How far from the girl's initial position do they meet?

Homework Equations


f=ma

The Attempt at a Solution


Finding the answers to part a and b were simple..
(a) a = f/m = 5.2N/8.4kg = .62 m/s2
(b) a = f/m = 5.2N/40kg = .13 m/s2
(c) I'm having problems figuring out part C.
 
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hansel13 said:
I'm not sure what the rules are about posting homework problems, but I just had 2 I couldn't get around too, so here's the second one...

Homework Statement


A 40 kg girl and a 8.4 kg sled are on the frictionless ice of a frozen lake, 15m apart but connected by a rope of negligible mass. The girl exerts a horizontal 5.2 N force on the rope.
What are the acceleration magnitudes of
(a) the sledge?
(b) the girl?
(c) How far from the girl's initial position do they meet?

Homework Equations


f=ma

The Attempt at a Solution


Finding the answers to part a and b were simple..
(a) a = f/m = 5.2N/8.4kg = .62 m/s2
(b) a = f/m = 5.2N/40kg = .13 m/s2
(c) I'm having problems figuring out part C.

Write equations for their positions
XG + XS = 15
XG = 1/2*ag*t2
XS = 1/2*as*t2

Solve noting that t2 is the same when they meet
 


1/2*ag*t2+1/2*as*t2= 15

t2 = 15 / (1/2*ag +1/2*as)
t2 = 15 / (1/2*.62 +1/2*.13)
t2 = 40
t = 6.3m

That doesn't seem right, I'm lost.
 


hansel13 said:
1/2*ag*t2+1/2*as*t2= 15

t2 = 15 / (1/2*ag +1/2*as)
t2 = 15 / (1/2*.62 +1/2*.13)
t2 = 40
t = 6.3m

That doesn't seem right, I'm lost.

Not quite. That gives you seconds.

XG = 1/2*ag*t2 = 1/2*(.13)*(6.3)2 = 2.58m
 


LowlyPion said:
Not quite. That gives you seconds.

XG = 1/2*ag*t2 = 1/2*(.13)*(6.3)2 = 2.58m

ahh. Gotcha, thanks.
 

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