/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 14 A block with a weight of \(3.0 \... [FREE SOLUTION] | 91Ó°ÊÓ

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A block with a weight of \(3.0 \mathrm{~N}\) is at rest on a horizontal surface. A \(1.0 \mathrm{~N}\) upward force is applied to the block by means of an attached vertical string. What are the (a) magnitude and (b) direction of the force of the block on the horizontal surface?

Short Answer

Expert verified
(a) 2.0 N, (b) downward.

Step by step solution

01

Understand the Forces Involved

The block is affected by two forces: its weight of \(3.0 \mathrm{~N}\) acting downward due to gravity, and an upward force of \(1.0 \mathrm{~N}\) applied by the string. We must find the resultant force of the block on the horizontal surface.
02

Calculate the Net Downward Force

Calculate the net force exerted on the block by subtracting the upward force from the downward gravitational force. The formula is: \( F_{net} = W - F_{upward}\), where \(W = 3.0 \mathrm{~N}\) and \(F_{upward} = 1.0 \mathrm{~N}\).
03

Plug in the Values

Substitute the values into the formula: \[ F_{net} = 3.0 \mathrm{~N} - 1.0 \mathrm{~N} = 2.0 \mathrm{~N} \]This is the net force acting downward on the block and is the force exerted by the block on the horizontal surface.
04

Determine the Direction of the Force

Since the force is calculated as the net downward force on the block, the direction of the force exerted by the block on the horizontal surface is downward.

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Key Concepts

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

Net Force Calculation
When dealing with physics problems, understanding how to calculate the net force acting on an object is key. A net force is basically the total force resulting from all individual forces acting on an object. In this exercise, the block experiences two main forces: the downward gravitational force and an upward force from the string. To find the net force acting on the block, we subtract the upward force from the gravitational force.

  • Gravitational force is given as the weight of the block, which is 3.0 N.
  • Upward force, applied through the string, is 1.0 N.
Using the equation for net force: \[ F_{net} = W - F_{upward} \] where \(W = 3.0 \text{ N}\) and \(F_{upward} = 1.0 \text{ N}\). Plug these values into the equation to find the net force: \[ F_{net} = 3.0 \text{ N} - 1.0 \text{ N} = 2.0 \text{ N}\]

This calculation shows us that the net force acting on the block is 2.0 N directed downward. Net force is crucial in understanding the real impact of multiple forces acting on an object.
Vertical Forces
Vertical forces often come into play when we analyze objects subjected to gravity and structures designed for balancing weight. In this scenario, the vertical forces include both the gravitational force pulling the block downward and the upward force applied by the string.

  • Gravitational force makes sure the block stays pressed against the surface, which is a key concept of Newton's Laws.
  • The upward force attempts to counteract this gravitational pull, albeit only partially.
Understanding vertical forces helps you predict movement (or lack thereof) when forces are balanced or imbalanced. For our exercise, since the gravitational pull is greater than the upward force, the block remains stationary. Its net effect on the surface beneath is the net downward force we calculated earlier at 2.0 N.
Gravitational Force
Gravitational force is a fundamental concept in physics that refers to the attraction between objects with mass. This force is responsible for the block having a weight of 3.0 N in this exercise. The gravitational force is calculated using the mass of the object and the acceleration due to gravity.

The formula for gravitational force is: \[ F_g = m imes g \] where \(m\) is mass and \(g\) is the acceleration due to gravity \(\approx 9.8 \text{ m/s}^2\). In simpler cases like this, the weight is usually provided instead, simplifying our calculations.

  • Here, the gravitational force acting on the block is \(3.0 \text{ N}\), pulling it downward towards Earth.
  • This force forms the basis of our net force calculation since it is only partially countered by the upward string force.
Gravitational force not only helps in keeping objects grounded but also plays a part in how forces interact vertically in many physics problems, like this one.

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Most popular questions from this chapter

An object is hung from a spring balance attached to the ceiling of an elevator cab. The balance reads \(65 \mathrm{~N}\) when the cab is standing still. What is the reading when the cab is moving upward (a) with a constant speed of \(7.6 \mathrm{~m} / \mathrm{s}\) and (b) with a speed of \(7.6 \mathrm{~m} / \mathrm{s}\) while decelerating at a rate of \(2.4 \mathrm{~m} / \mathrm{s}^{2} ?\)

A \(52 \mathrm{~kg}\) circus performer is to slide down a rope that will break if the tension exceeds \(425 \mathrm{~N}\). (a) What happens if the performer hangs stationary on the rope? (b) At what magnitude of acceleration does the performer just avoid breaking the rope?

An \(85 \mathrm{~kg}\) man lowers himself to the ground from a height of \(10.0 \mathrm{~m}\) by holding onto a rope that runs over a frictionless pulley to a \(65 \mathrm{~kg}\) sandbag. With what speed does the man hit the ground if he started from rest?

A customer sits in an amusement park ride in which the compartment is to be pulled downward in the negative direction of a \(y\) axis with an acceleration magnitude of \(1.24 g\), with \(g=\) \(9.80 \mathrm{~m} / \mathrm{s}^{2}\), A \(0.567 \mathrm{~g}\) coin rests on the customer's knee. Once the motion begins and in unit-vector notation, what is the coin's acceleration relative to (a) the ground and (b) the customer? (c) How long does the coin take to reach the compartment ceiling, \(2.20 \mathrm{~m}\) above the knee? In unit-vector notation, what are (d) the actual force on the coin and (c) the apparent force according to the customer's measure of the coin's acceleration?

A \(10 \mathrm{~kg}\) monkey climbs up a massless rope that runs over a frictionless tree limb and back down to a \(15 \mathrm{~kg}\) package on the ground (Fig. 5-54). (a) What is the magnitude of the least acceleration the monkey must have if it is to lift the package off the ground? If, after the package has been lifted, the monkey stops its climb and holds onto the rope, what are the (b) mag. nitude and (c) direction of the monkey's acceleration and (d) the tension in the rope?

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