What Went Wrong in My Free-Body Diagram?

In summary, the conversation discusses a problem involving a 40.0 kg crate being lowered by a rope with a downward acceleration of 2.00 m/s2. The question asks for the force exerted by the rope on the crate. The correct answer is 312 N, but the person initially got a different answer due to a mistake in their free-body diagram. They eventually realize their mistake and thank the person for their help.
  • #1
oceanflavored
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Homework Statement


A 40.0 kg crate is being lowered by means of a rope. Its downward acceleration is 2.00 m/s2. What is the force exerted by the rope on the crate?

Homework Equations


Weight = mass(gravity)
Force = mass(acceleration)

The Attempt at a Solution


I solved it (look at attached picture), but my answer is wrong, because the book says the answer is: 312 N. I think that I may have drawn the free-body diagram wrong; would someone please tell me where I went wrong in my free-body diagram?

Thank you so much :) I have a test in six days & this problem will more than likely, be on it :/
 

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  • #2
Well You know the the acceleration from gravity is -9.8. The actual acceleration is -2. The tension force has to account for this difference.

I can't see the free body diagram yet but the book's answer is correct.
 
  • #3
Ahhh! Stupid mistake...I was forgetting to make the acceleration caused by gravity negative! :O
Thank you so much! :)

Also, I have no idea how to mark this thread "SOLVED!" I even looked in "Thread Tools" & didn't see anything ://
 
Last edited:

1. What is normal force?

Normal force is the force that a surface exerts on an object in contact with it. It is always perpendicular to the surface and acts in the opposite direction of the force applied by the object on the surface.

2. How is normal force different from weight?

Normal force and weight are two different forces. Weight is the force of gravity acting on an object, while normal force is the force of the surface pushing back on the object. Weight always acts vertically downwards, while normal force can act in any direction perpendicular to the surface.

3. What factors affect the magnitude of normal force?

The magnitude of normal force depends on the weight of the object and the angle at which it is placed on the surface. It also depends on the type of surface and any other forces acting on the object.

4. Can normal force ever be greater than weight?

Yes, in certain situations, normal force can be greater than weight. This can happen when the object is accelerating upwards or when it is on an incline. In these cases, the surface has to exert a greater force to prevent the object from falling or sliding.

5. How is normal force important in understanding the motion of objects?

Normal force plays an important role in understanding the motion of objects, especially in situations where the object is in contact with a surface. It helps to determine the direction and magnitude of the force needed to keep the object in equilibrium or to cause it to accelerate. Additionally, it is crucial in determining the normal force and frictional force relationship, which affects an object's motion.

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