Physics Chapter on Static Equilibrium and Torque

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Questions and Answers

What is the expression for the horizontal component of the force on the bar, Fwx?

T cosθ (correct)

T sinθ

mSg - mBg

mBg + mSg

When using the torque equilibrium equation, which term will not appear in the equation when the pivot point is chosen at the right end of the bar?

mSg

T (correct)

Fwy

mBg

What is the derived equation for the vertical component of the force on the bar, Fwy?

Fwy = mBg - T sinθ

Fwy = mSg + mBg

Fwy = (mSg/4) + (mBg/2) (correct)

Fwy = (mSg + mBg) / 2

What is the overall expression for the total force on the bar from the wall, Fw?

Fw = Fwx^2 + Fwy^2 Signup and view all the answers

In the first method to determine Fwx and Fwy, which two equations are utilized?

∑F_x = 0, ∑F_y = 0 Signup and view all the answers

What two conditions must be satisfied for an object to be in static equilibrium?

Net force = 0 and net torque = 0 Signup and view all the answers

Which component of force is responsible for causing torque?

The component of force perpendicular to the lever arm Signup and view all the answers

How is torque (τ) mathematically defined?

τ = r × F Signup and view all the answers

If the net force acting on an object is zero, which of the following statements can still be true?

The object may still rotate if net torque is not zero Signup and view all the answers

What is the unit of torque?

N·m Signup and view all the answers

Which situation illustrates a scenario where the conditions are sufficient for static equilibrium?

Two symmetrical forces are applied equally to a stationary object. Signup and view all the answers

What is the effect of force component F|| on torque?

It has no effect on torque Signup and view all the answers

Which of the following factors increases the amount of torque generated about an axis?

Larger lever arm and larger perpendicular force Signup and view all the answers

What is the correct formula to calculate the torque ( au) when force is applied at an angle?

$\tau = rF\sin(\theta)$ Signup and view all the answers

Under what condition is an object considered to be in rotational equilibrium?

The net torque about any axis is zero. Signup and view all the answers

In the provided example, what is the angle formed between the applied force and the plane of the door?

30° Signup and view all the answers

If m1 represents an unknown mass balancing a uniform plank with mass mp and length L, what is the relation between d and L given in the problem?

$L = 3d$ Signup and view all the answers

How does a uniform plank behave in terms of torque concerning its center of mass?

All its mass is concentrated at the center of mass. Signup and view all the answers

What must be true for a plank to be in static equilibrium regarding torque?

The sum of all torques must equal zero. Signup and view all the answers

Which equation represents the balance of masses on the plank?

mp + 2m2 - m1 = 0 Signup and view all the answers

In the static equilibrium example with two strings, what is the primary unknown being solved for in this scenario?

The tension in the strings. Signup and view all the answers

If the mass m is suspended and requires forces to cancel, what is the relationship established between T3 and mg?

T3 is equal to mg. Signup and view all the answers

Why can the plank achieve balance on the moon as well as on Earth?

Because the gravitational forces cancel out in the torque equation. Signup and view all the answers

Which of the following describes the conditions at the knot in the string system?

There can be no net torque acting on the knot. Signup and view all the answers

Which factor is NOT required for the condition of static equilibrium?

All masses must be equal. Signup and view all the answers

What happens to the forces acting on the mass m if the angle θ changes?

The tension in both strings must adjust to maintain equilibrium. Signup and view all the answers

What is the first condition of static equilibrium for the horizontal forces acting on the knot?

T1 sinα = T2 sinβ Signup and view all the answers

What does the equation ∑Fy = 0 indicate in the context of the knot?

The vertical forces sum up to the weight. Signup and view all the answers

When a sign is hung from a bar, what is the effect of the position of the sign on tension T in the cable?

The farther the sign is from the pivot, the higher the tension. Signup and view all the answers

How is the torque about the pivot calculated when considering the hanging mass?

Torque is determined by the product of T sinθ and the lever arm distance. Signup and view all the answers

What does the term '∑τ = 0' signify in a static equilibrium scenario?

The system is in rotational equilibrium. Signup and view all the answers

In the equation T sin θ = (3/4) L (mS g) + (1/2) L (mB g), what do the terms represent?

The relation between tension and the weight of the sign and bar. Signup and view all the answers

Which statement about the tension T in the cable is correct when balancing the forces in static equilibrium?

T accounts for both the weight of the sign and the bar's contribution. Signup and view all the answers

What is an implication of the wall exerting a force FW on the bar?

It may help balance the forces acting on the bar. Signup and view all the answers

Study Notes

Static Equilibrium

An object is in static equilibrium if it's not moving. This means it's not translating (moving horizontally or vertically) and not rotating.
For an object not to translate, the net force must be zero. This means the vector sum of all forces acting on the object equals zero.
Forces are considered along the x and y axis, such as F₁x + F₂x +…= 0 and F₁y + F₂y +…= 0
Even with zero net force, an object may still be capable of rotating if the torques don't cancel out.
To guarantee static equilibrium, the net force and net torque must be zero.

Torque

Torque is a rotational force, calculated with the formula τ = r × F, where
- τ is the torque
- r is the lever arm (distance from the axis of rotation to the point where the force is applied)
- F is the force
The magnitude of torque is given by τ = r * F * sin θ, where θ is the angle between the force vector and the lever arm.
Torque has a positive or negative sign depending on its direction of rotation (counter-clockwise or clockwise).
Units of torque are measured in Newton-meters (N⋅m).
Only the perpendicular component of a force produces rotation.

Static Equilibrium Examples and Applications

Door Handles: A larger lever arm and a larger perpendicular force makes it easier to rotate an object. Perpendicular force is the force needed at the angle to rotate the door.
Uniform Plank: A uniform plank balanced on a pivot with masses on each end—calculate the unknown mass to keep equilibrium.
Mass Hanging from Strings: A mass hanging from two strings at angles; determine the tensions in each string.
Store Sign: A store sign hung by a plank with a supporting cable – calculate and determine the tension in the cable given the masses
Forces on a Bar: Wall forces exerted on a bar; calculate the force components.

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Description

This quiz covers the principles of static equilibrium and torque as outlined in the physics chapter. Learn how to identify conditions for an object to be in static equilibrium, including the balance of net forces and torques. Dive into the calculation of torque and its significance in rotational motion.