(a) You pull a box with a constant force across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box increase, decrease, or remain the same? Explain, (b) What if there is friction?
Solution 12Q: We have to analyze the variation in acceleration when a force is applied is at an angle in absence and presence of friction.
Step 1 of 3Concept: Newton’s second law: The force F acts on mass m produces an acceleration a in the object. Mathematically, F=ma
Step 2 of 3</p>
A] Force applied at an angle, in absence of friction
As it is clear from figure (1) that when a constant force F is applied on the box, placed on a frictionless table, with the help of a rope, we find that entire magnitude of force F is responsible for creating acceleration acceleration a in the box of mass m, which can be given by the equation,
Now if the same force of magnitude F is applied at an angle to the horizontal, we find that magnitude of acceleration in horizontal direction decreases, as the same force F get resolve along horizontal and vertical direction as shown in figure (2). Resolving the force F along horizontal and vertical direction, we get,
Only the horizontal component is responsible for pulling the block along horizontal direction while the vertical component of force is balanced by the weight of the box. Therefore, the box moves due to force , corresponding acceleration is given as
Thus, when the box is pulled horizontally at an angle, the acceleration decreases.