PHYS 1070 Lecture Notes - Lecture 1: Friction

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ochreduck86

19 Mar 2018

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Document Summary

Solving force problems: draw a fbd, define x/y axes, apply ne(cid:449)ton"s 1st/2nd law in x/y directions, solve these two equations to find an unknown. Let the motion in the problem guide how you solve. A 1. 30 g spider hangs from a thread. A breeze causes the spider to hang, motionless, with the thread making an angle of 35. 0 degrees to the vertical. What is the tension in the thread and the force exerted by the breeze? y x. Important details: static & kinetic friction fs fs: occurs when an object is not moving, static friction (, (cid:1858) does not have a pre-defined value, kinetic friction () (i. e. f=0) Friction: vary the applied force: (cid:1858) (cid:1858),= (cid:1858)= The friction force response to an increasing applied force. A mass m is suspended as illustrated, from two strings making angles of 60 and 30 with the horizontal.

Related Questions

Two dimensional dynamics often involves solving for two unknown quantities in two separate equations describing the total force. The block in (Figure 1) has a mass m=10kg and is being pulled by a force F on a table with coefficient of static friction

. Four forces act on it:

. The applied force FF (directed

above the horizontal).

. The force of gravity

(directly down, where

. The normal force N (directly up).

. The force of static friction fs (directly left, opposing any potential motion).

If we want to find the size of the necessary to just barely overcome static friction (in which case

, we use the condition that the sum of the forces in both directions must be 0. Using some basic trigonometry, we can write this condition out for the forces in both the horizontal and vertical directions, respectively, as:

In order to find the magnitude of force F, we have to solve a system of two equations with both F and the normal force NN unknown. Use the methods we have learned to find an expression for F in terms of

pucetiger860

This problem introduces the concept of tension. The example is a rope, oriented vertically, that is being pulled from both ends. Let F_u and F_d (with u for up and d for down) represent the magnitude of the forces acting on the top and bottom of the rope, respectively. Assume that the rope is massless so that its weight is negligible compared with the tension. (This is not a ridiculous approximation-modern rope material such as Kevlar can carry tensions thousands of times greater than the weight of tens of meters of such rope.)

Consider the three sections of rope labeled a, b, and c in the figure.

At point 1, a downward force of magnitude F_ad acts on section a.
At point 1, an upward force of magnitude F_bu acts on section b.
At point 1, the tension in the rope is T₁.
At point 2, a downward force of magnitude F_bd acts on section b.
At point 2, an upward force of magnitude F_cu acts on section c.
At point 2, the tension in the rope is T₂.

(A) What is the magnitude F_ad of the downward force on section a?

(B) What is the magnitude F_bu of the upward force on section b?

(C) The magnitude of the upward force on c, F_cu, and the magnitude of the downward force on b, F_bd, are equal because of which of Newton's laws?

(D) The magnitude of the force F_bu is ______ F_bd.

(E) Now consider the forces on the ends of the rope. What is the relationship between the magnitudes of these two forces?

(a) F_u > F_d

(b) F_u = F_d

(F) The ends of a massless rope are attached to two stationary objects (e.g., two trees or two cars) so that the rope makes a straight line. For this situation, which of the following statements are true?

(a) The tension in the rope is everywhere the same.

(b) The magnitudes of the forces exerted on the two objects by the rope are the same.

(d) The forces exerted on the two objects by the rope must be in the direction of the rope.