What is the deceleration of the ball?

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Homework Help Overview

The problem involves a metal ball dropped from rest that impacts sand, creating an impression. The objective is to determine the average deceleration of the ball as it hits the sand, with specific parameters provided, including the time of fall and the depth of the impression.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the initial conditions of the ball's motion, questioning the use of time and initial velocity at the moment of impact. There is an exploration of the necessary parameters for calculating deceleration, including the velocity upon impact and the distance over which deceleration occurs.

Discussion Status

There is an ongoing examination of the assumptions made in the problem, particularly regarding the timing of the deceleration and the initial velocity of the ball. Some participants suggest that the question may be flawed due to insufficient information to determine average deceleration accurately.

Contextual Notes

Participants note that the time given in the problem refers to the fall duration, not the deceleration phase, and question the implications of assuming constant deceleration without adequate data.

Hussain
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Homework Statement


The question didn't fit there.
*A boy drops a metal ball from rest on sand. It hits the sand bed in one second and makes an impression of maximum depth 8mm in the sand. What is the average deceleration of the ball as it hits the sand? Assume air resistance is negligible.

vi= 0m/s
t= 1 sec
S= 8 mm or 0.008 m
a=?

Homework Equations



I used S=vit+1/2(at^2)

The Attempt at a Solution


By using that formula I got the answer 0.016 m/s^2 is it correct? Please tell me how to do it
 
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You are using 1 second as the time, but that is the time the ball is falling - not the time that the ball is decelerated by the sand.
 
Hussain said:
vi= 0m/s
This isn't correct: The ball is dropped from rest, but by the time it hits the sand, it already has a certain speed, as it is accelerated by gravity. So, what is ##v_i## when the ball reaches the ground?
 
TomHart said:
Welcome to Physics Forums.
You are using 1 second as the time, but that is the time the ball is falling - not the time that the ball is decelerated by the sand.
Which formula should I use now?
 
The deceleration starts when the ball touches the sand. You need to know 3 things to solve. What is the velocity when the ball first touches the sand? What is the distance over which the deceleration occurs? What is the final velocity of the ball? You should use a formula which utilizes those 3 knowns and allows you to find the unknown (acceleration).
 
TomHart said:
The deceleration starts when the ball touches the sand. You need to know 3 things to solve. What is the velocity when the ball first touches the sand? What is the distance over which the deceleration occurs? What is the final velocity of the ball? You should use a formula which utilizes those 3 knowns and allows you to find the unknown (acceleration).
That is surely what the question intends, but the question is flawed. Average acceleration is Δv/Δt, so it would have to be possible to find the deceleration time. But there is not enough information in the question to find that.
We could find it by pretending the deceleration is constant from the instant of touching the sand to that of coming to rest, but that is clearly not the case, and the question would not need to ask for average deceleration.
A better wording would be "what is the deceleration as it presses into the sand, pretending it is constant?"
 
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