What is the deceleration of the ball?

In summary, the ball decelerates as it hits the sand and the deceleration lasts for a certain length of time.
  • #1
Hussain
2
0

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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  • #2
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.
 
  • #3
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?
 
  • #4
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?
 
  • #5
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).
 
  • #6
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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1. What is deceleration?

Deceleration is the rate at which an object slows down. It is the opposite of acceleration, which is the rate at which an object speeds up.

2. How is deceleration measured?

Deceleration is usually measured in meters per second squared (m/s²) in the metric system. In the imperial system, it is measured in feet per second squared (ft/s²).

3. What factors affect the deceleration of a ball?

The deceleration of a ball can be affected by factors such as air resistance, friction, and the surface it is rolling on. The mass and shape of the ball can also play a role in its deceleration.

4. How is deceleration different from negative acceleration?

Deceleration is simply a term used to describe a decrease in speed, while negative acceleration is a specific type of deceleration where the object is speeding up in the opposite direction it was previously moving. In other words, negative acceleration involves a change in direction along with a decrease in speed.

5. How can deceleration be calculated?

Deceleration can be calculated by dividing the change in velocity by the time it took for that change to occur. It can also be calculated by dividing the negative of the final velocity by the time it took for that velocity to be reached. The formula for deceleration is: a = (vf - vi)/t or a = -vf/t.

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