Tensions in Two Dimensions

[wilso119]

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?

 

[rl.bhat]

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.

 

[wilso119]

I got it! Thanks so much! That ended up being much easier than I was making it!