Work Done and Acceleration (Mistaken Answers?)

In summary, "Work Done and Acceleration (Mistaken Answers?)" explores common misconceptions related to the concepts of work and acceleration in physics. It highlights how misunderstandings can arise from incorrect interpretations of the formulas and principles governing these topics. The discussion emphasizes the importance of clarity in definitions and the correct application of equations to avoid errors in problem-solving, particularly in contexts involving forces and motion.
  • #1
amandela
9
3
Homework Statement
Q1) A ball is thrown and follows a parabolic path. Air friction is negligible. Point Q is the highest point on the path. What is the direction of the acceleration there?

Q2) A weightlifter lifts a mass m at constant speed to a height h in time t. How much work is done by the weightlifter?
Relevant Equations
Wnet = ΔKE + ΔPE + Wnc
So for Q1, I answered down (towards Earth) but the solution says there is no acceleration there.

For Q2, I answered mgh, but the solution says it's mgh/t, which is power, right?

I just want to make sure I'm not super confused.

Thank you.
 
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  • #2
You are correct in both cases. Where are you getting the other answers from?
 
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  • #3
PeroK said:
You are correct in both cases. Where are you getting the other answers from?
Agreed, except that if the weight is lifted from rest at speed h/t then it reaches h with KE ##\frac 12mh^2/t^2##.
 
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  • #4
haruspex said:
Agreed, except that if the weight is lifted from rest at speed h/t then it reaches h with KE ##\frac 12mh^2/t^2##.
It says at constant speed.
 
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  • #5
PeroK said:
You are correct in both cases. Where are you getting the other answers from?
Thank you. They're from a test bank for the AP mechanics exam.
 
  • #6
amandela said:
Thank you. They're from a test bank for the AP mechanics exam.
There seems to be a growing problem with dodgy questions and/or dodgy answers. That someone teaching physics might think the acceleration is zero when velocity is zero ought to shock me, but doesn't surprise me.

Note that for any motion you can always change your inertial frame of reference so that an object is instantaneously at rest. But, acceleration is the same across all inertial reference frames. Which is why Newton's laws deal with force and acceleration and not velocity.
 
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FAQ: Work Done and Acceleration (Mistaken Answers?)

What is the relationship between work done and acceleration?

Work done on an object is related to the change in its kinetic energy, which depends on its acceleration. According to the work-energy theorem, the work done on an object is equal to the change in its kinetic energy. Since kinetic energy is given by \( \frac{1}{2}mv^2 \), where \( v \) is velocity, and velocity changes with acceleration, there is a direct connection. However, work done itself is not directly calculated using acceleration but through force and displacement.

Can work be done on an object if there is no acceleration?

Yes, work can be done on an object even if there is no acceleration. For example, if an object is moving at a constant velocity, work can still be done if a force is applied over a distance. In this case, the work done is used to overcome friction or other resistive forces, rather than changing the object's kinetic energy.

Is it possible to have acceleration without work being done?

No, it is not possible to have acceleration without work being done. Acceleration implies a change in velocity, which means there must be a net force acting on the object. This force, when applied over a distance, results in work being done. Thus, whenever there is acceleration, work is being done on the object.

How do you calculate work done if you know the acceleration?

To calculate work done when acceleration is known, you need to use the relationship between force, mass, and acceleration (Newton's Second Law: \( F = ma \)). Once you have the force, you can calculate work done using the formula \( W = Fd \cos(\theta) \), where \( d \) is the displacement and \( \theta \) is the angle between the force and displacement vectors. Therefore, work done can be calculated indirectly using acceleration.

Why do people often confuse work done and acceleration?

People often confuse work done and acceleration because both concepts involve force and motion, but they are related in different ways. Work done is a measure of energy transfer due to force applied over a distance, while acceleration is the rate of change of velocity due to a net force. The confusion arises because both involve forces, but they describe different physical phenomena. Understanding the distinctions and the specific formulas for each can help clarify the differences.

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