How Does Tension Affect Motion on a Frictionless Surface?

AI Thread Summary
The discussion revolves around a physics problem involving a 10 kg box on a frictionless surface, subjected to a tension force of T = 75 ˆx + 25 ˆz N. Despite initial confusion about whether the box would move due to the tension being less than its weight, it is clarified that the box will indeed accelerate horizontally since the vertical forces are balanced. Using Newton's second law, the acceleration can be calculated, leading to the determination of the box's speed after 0.05 seconds. The participant expresses relief at finding the solution easier than anticipated. The key takeaway is that tension can cause motion on a frictionless surface, independent of the weight of the object.
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Homework Statement


A box of mass M=10 kg is at rest on a frictionless level surface (like an ideally smooth ice
rink). A rope tied to the box is pulled horizontally, such that the tension in the rope is
T = 75 ˆx + 25 ˆz N, where both the x-axis and the z-axis are parallel to the floor. What is the speed of the box after 0.05 seconds?

Homework Equations


Magnitude of T = (75^2 + 25^2)^(1/2) = 79 N
weight of box = 10 kg * 9.8 m/s^2 = 98 N

The Attempt at a Solution


Because the weight of the box is greater than the tension force, the box should not move, right?
 
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The weight of the box is balanced by the normal reaction of the surface.
Using Newton's second law find the acceleration and then the velocity.
 
I got it! Thanks so much! That ended up being much easier than I was making it!
 
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