What will be the acceleration of a 10kg block w.r.t. the ground frame?

In summary, the conversation is discussing the calculation of the acceleration produced by a 10 kg block on a 5 kg block with respect to the ground. The equations of f=ma and g=10m/s are mentioned. The attempt at a solution involves finding the effective force at play on each block and calculating the acceleration using the equation 25N=10kg*a. However, the correct answer is 5 m/s2. The conversation also discusses the acceleration of the system in different reference frames and the need to consider the tension in the cable.
  • #1
prakhargupta3301
58
1

Homework Statement


upload_2018-7-1_20-57-28.png
[/B]We have to find acceleration produced by 10 kg block on 5 kg block with respect to the ground.
Downward acceleration of life is 5m/s-2

Homework Equations


f=ma
g=10m/s

The Attempt at a Solution


Effective force at play on 10 kg block: mg- ma
= 100N-50N
= 50 Newtons
Effective force at play on 5 kg block: mg-ma
= (50-25)N
= 25 Newtons
The 10 kg block outmatched its nemesis (5kg block) by +25 Newtons. It's the heavier one.
25N=10kg*a
2.5m/s2

But this isn't the correct answer. The correct is 5 m/s2.
I'm at sea. Please help
Thanks for reading.
 

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  • #2
If the 10kg mass had fallen as was resting on the elevator floor, or the pulley jammed and the mass was hanging from the ceiling, then its acceleration w.r.t. ground would be ##5m/s^2##, as would be the entire elevator. Otherwise, it will be accelerating downward at a rate greater than ##5m/s^2##.
 
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  • #3
.Scott said:
Otherwise, it will be accelerating downward at a rate greater than ##5m/s^2##.
Will it be 15m/s2?
Or 12.5 m/s2?
Or something else?
 
  • #4
No free answers. Do the math.
That said, I would work out the acceleration w.r.t. the elevator. Then add in the elevator acceleration.
 
  • #5
I did the math. But with respect to keeping the elevator as my reference and got 5m/s2 as acceleration of the system of the pulley in downward direction.
What I need help is with knowing, whether the acceleration would seem different from the inertial frame?
i.e would it still be 5m/s2, or 2.5m/s2 as I have already found?
Thank you.
 
  • #6
prakhargupta3301 said:
What I need help is with knowing, whether the acceleration would seem different from the inertial frame?
i.e would it still be 5m/s2, or 2.5m/s2 as I have already found?
Thank you.
The apparent "G force" in the elevator will be ##G-5m/s^2## or ##5m/s^2##.
If the 10kg mass was entirely free, it would fall ##5m/s^2## w.r.t. to the elevator and ##10m/s^2## w.r.t. the ground.
Attaching it to the 5kg mass through the pulley system will only slow it down - so the correct answer will be less than ##10m/s^2##.
 
  • #7
prakhargupta3301 said:
Effective force at play on 10 kg block: mg- ma
= 100N-50N
You seem to have assumed, wrongly, that the acceleration of the 10kg block inthe ground frame is 5m/s2.
Create unknowns for the tension in the cable and the acceleration of the 10kg block (either in the ground frame or relative to the lift - your choice).
Write the ΣF=ma equation for each block.
prakhargupta3301 said:
Downward acceleration of life is 5m/s-2
It can seem like that some days.
prakhargupta3301 said:
The correct is 5 m/s2.
It isn't that either.
 

Related to What will be the acceleration of a 10kg block w.r.t. the ground frame?

1. What is acceleration in physics?

Acceleration is defined as the rate of change of velocity with respect to time. It is a vector quantity, meaning it has both magnitude and direction. In simpler terms, acceleration is the measure of how much an object's velocity changes over a period of time.

2. How is acceleration calculated?

The formula for acceleration is a = ∆v/∆t, where a is acceleration, ∆v is the change in velocity, and ∆t is the change in time. This means that acceleration is equal to the change in velocity divided by the change in time.

3. How do you find the acceleration of an object?

The acceleration of an object can be found by dividing the change in its velocity by the change in time. This can be done using data from a motion graph, or by using equations of motion such as a = v-u/t, where v is final velocity, u is initial velocity, and t is time.

4. What is the acceleration of a 10kg block w.r.t. the ground frame?

The acceleration of a 10kg block w.r.t. the ground frame would depend on the forces acting on the block. If there is no net force acting on the block, it would have zero acceleration. However, if there is a net force, the acceleration can be calculated using Newton's second law, F = ma, where F is the net force, m is the mass of the block, and a is the acceleration.

5. Does the acceleration of an object depend on its mass?

Yes, the acceleration of an object does depend on its mass. The greater the mass of an object, the greater the force needed to accelerate it. This can be seen in the equation F = ma, where a is directly proportional to the force and inversely proportional to the mass. Therefore, a heavier object would have a smaller acceleration compared to a lighter object when the same force is applied.

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