Conservation of energy (true or false)

AI Thread Summary
The discussion revolves around the conservation of energy and the validity of several statements related to work and energy. The first statement about the train and wagon is deemed false, as the work done by the train is not zero due to the wagon's movement. The second statement is also false because negative net work does not always reduce kinetic energy, especially in conservative force scenarios. The third statement is clarified as true, emphasizing that both balls will have the same speed at the bottom due to gravitational potential energy being conserved, regardless of the slope's angle. Overall, the conversation highlights misconceptions about work and energy in physics, particularly regarding the effects of forces and motion.
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Homework Statement



1.Consider a train that pulls a wagon. By Newton's third law, the wagon pulls on the train with an equal opposite force, therefore the work done by the train must be zero.

2.Negative net work done on an object always reduces the object's kinetic energy.

3.Two identical masses are placed on frictionless slopes at identical heights. The first slope makes an angle of 30deg with respect to the horizontal; the second slope makes an angle of 40deg. Both balls are released simultaneously. At the bottom of the slope, both balls have the same speed.

4.If the work done on an object by a force is zero, then either the force or the displacement must have zero magnitude.

5.The formula W=F d cos theta can be used only if the force is constant over the distance d.

Homework Equations



Conservation of Energy

The Attempt at a Solution



At least one of these are wrong. I don't know which one(s)
Please check and correct me. Thanks

1.False
2.False
3.False, (because mgx changes due to the difference in angle. Since f=ma, accleration will not be the same.)
4.False, (it may be the direction that makes the W=0, for example an object falling where force nor displacement is zero but W=0.)
5.True
 
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jumptheair said:
At least one of these are wrong. I don't know which one(s)
Please check and correct me. Thanks

1.False
2.False
3.False, (because mgx changes due to the difference in angle. Since f=ma, accleration will not be the same.)
4.False, (it may be the direction that makes the W=0, for example an object falling where force nor displacement is zero but W=0.)
5.True

3 is True. Gravity is a conservative force. All that matters is the change in height, not how you get there. So slope one will make the ball travel longer, but it will still have the same speed as ball 2. Now, the two balls will NOT get there at the same time, but when they do get there, they will have the same speed.

4 is True. Work is done by the Earth to pull the object in. W = F * D. F = gravity, D is how much it falls by.
 
Arr.. still wrong.. help is still needed
 
Last edited:
Why would 1. and 2. be false? Or are they true? HELP!
 
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Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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