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Chapter 7: Problem 1

Find the sum of each set of forces acting at the same point in a straight line. \(355 \mathrm{~N}\) (right); \(475 \mathrm{~N}\) (right); \(245 \mathrm{~N}\) (left); \(555 \mathrm{~N}\) (left)

Short Answer

Expert verified
The net force is 30 N to the right.

Step by step solution

01

Identify the Direction of Each Force

First, identify which forces are acting to the right and which are acting to the left. We have forces of 355 N and 475 N acting to the right, and forces of 245 N and 555 N acting to the left.
02

Sum the Rightward Forces

Add together the forces acting to the right. This is calculated as follows: \[ 355 \, \text{N} + 475 \, \text{N} = 830 \, \text{N} \]
03

Sum the Leftward Forces

Add together the forces acting to the left. This is calculated as follows: \[ 245 \, \text{N} + 555 \, \text{N} = 800 \, \text{N} \]
04

Calculate the Net Force

Find the net force by subtracting the total leftward force from the total rightward force. \[ 830 \, \text{N} - 800 \, \text{N} = 30 \, \text{N} \]
05

Determine the Direction of the Net Force

Since the net force is positive, it indicates that the resulting force acts to the right direction.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Vector Addition
When we talk about vector addition in physics, we're discussing how to combine multiple forces, or vectors, acting on an object. Vector addition is crucial when determining how different forces affect an object. Let's break it down:
  • Vectors and their Direction: Forces are vectors, which means they have both a size (magnitude) and a direction. In the provided exercise, each force is given a magnitude in Newtons (N) and a direction either to the right or left.
  • Summing Forces: When we add vectors, direction matters. Forces acting in the same direction reinforce each other, so you sum their magnitudes. Forces in opposite directions counteract one another. Therefore, you subtract the smaller total from the larger one to find the resultant force.
  • Net Result: The result of vector addition tells us the net force acting on the object, indicating how these combined forces affect its motion.
Calculating Net Force
The net force is the overall force acting on an object when all individual forces are considered. Here's how you calculate it:
  • Same Direction Forces: First, add up all forces that are acting in the same direction. In our case, the forces of 355 N and 475 N act to the right, yielding a total of 830 N.
  • Opposite Direction Forces: Do the same for forces acting in the opposite direction. Here, 245 N and 555 N act to the left, so they sum to 800 N.
  • Net Force Calculation: Subtract the total force in the opposite direction from the total force in the initial direction to find the net force. For this exercise, 830 N - 800 N gives us a net force of 30 N. It鈥檚 this net force that determines how the object will move.
Determining Force Direction
The direction of the net force is key to understanding how forces influence an object's movement. Here's why:
  • Resulting Movement: If the net force is positive (greater than zero), it means the dominant force and direction is the one causing movement. In our exercise, the remaining force after vector addition is 30 N to the right, indicating motion in that direction.
  • Importance of Direction: Recognizing force direction allows us to predict the future motion of the object correctly. This is essential in solving real-world physics problems, like determining the trajectory of a moving car or tension in ropes.
Understanding force direction helps you make sense of how objects will behave under different conditions, providing a clearer insight into the dynamics involved.

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Most popular questions from this chapter

Assume that each force is applied perpendicular to the torque arm. Given: \(\tau=35.7\) lb \(\mathrm{ft}\) \(r=0.0240 \mathrm{ft}\) \(F=?\)

If the torque required to loosen a nut on the wheel of a pickup truck is \(40.0 \mathrm{~N} \mathrm{~m}\), what minimum force must be applied to the end of a wrench \(30.0 \mathrm{~cm}\) long to loosen the nut?

If two forces of \(100 \mathrm{~N}\) and \(50.0 \mathrm{~N}\), respectively, act in a westerly direction on a point and a force of \(175 \mathrm{~N}\) acts in a northerly direction on the same point, what is the resultant force?

Two painters, each of mass \(75.0 \mathrm{~kg}\), stand on a \(12.0-\mathrm{m}\) scaffold, \(6.00 \mathrm{~m}\) apart and \(3.00 \mathrm{~m}\) from each end. They share a paint container of mass \(21.0 \mathrm{~kg}\) in the middle of the scaffold. What weight must be supported by each of the ropes secured to the ends of the scaffold?

A torque wrench reads \(14.5 \mathrm{~N} \mathrm{~m}\). If its length is \(25.0 \mathrm{~cm}\), what force is being applied to the handle?
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