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Chapter 4: Problem 26

A man lifts a 2.0 -kg stone vertically with his hand at a constant upward acceleration of \(1.5 \mathrm{m} / \mathrm{s}^{2} .\) What is the magnitude of the total force of the man's hand on the stone?

Short Answer

Expert verified
Answer: The magnitude of the total force of the man's hand on the stone is 22.62 N.

Step by step solution

01

Identify the forces acting on the stone

There are two forces acting on the stone: gravitational force (weight) acting downwards and the applied force by the man acting upwards.
02

Calculate the gravitational force (weight)

The gravitational force (weight) acting on the stone can be calculated using the formula: \(W = mg\), where \(m\) is the mass of the stone and \(g\) is the gravitational acceleration (\(9.81 \, \mathrm{m}/\mathrm{s}^{2}\)). Plugging in the values, we have \(W = (2.0\, \mathrm{kg})(9.81 \, \mathrm{m}/\mathrm{s}^{2}) = 19.62 \, \mathrm{N}\)
03

Calculate the net force using Newton's second law of motion

According to Newton's second law of motion, the net force acting on an object is equal to the product of its mass and acceleration (\(F_{net} = ma\)). Using the given values, we have \(F_{net} = (2.0\, \mathrm{kg})(1.5 \, \mathrm{m}/\mathrm{s}^{2}) = 3.0 \, \mathrm{N}\)
04

Determine the applied force by the man

To find the magnitude of the force exerted by the man's hand on the stone, we need to combine the gravitational force and the net force. Since the stone is moving upward and the gravitational force acts downward, the applied force must be greater than the gravitational force. Thus, \(F_{applied} = F_{net} + W = 3.0 \, \mathrm{N} + 19.62 \, \mathrm{N} = 22.62 \, \mathrm{N}\)
05

Report the final answer

The magnitude of the total force of the man's hand on the stone is \(22.62 \, \mathrm{N}\).

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Most popular questions from this chapter

Two blocks are connected by a lightweight, flexible cord that passes over a frictionless pulley. If \(m_{1}=3.6 \mathrm{kg}\) and \(m_{2}=9.2 \mathrm{kg},\) and block 2 is initially at rest \(140 \mathrm{cm}\) above the floor, how long does it take block 2 to reach the floor?
Four separate blocks are placed side by side in a left-toright row on a table. A horizontal force, acting toward the right, is applied to the block on the far left end of the row. Draw FBDs for (a) the second block on the left and for (b) the system of four blocks.
A toy freight train consists of an engine and three identical cars. The train is moving to the right at constant speed along a straight, level track. Three spring scales are used to connect the cars as follows: spring scale \(A\) is located between the engine and the first car; scale \(\mathrm{B}\) is between the first and second cars; scale \(C\) is between the second and third cars. (a) If air resistance and friction are negligible, what are the relative readings on the three spring scales \(\mathrm{A}, \mathrm{B},\) and \(\mathrm{C} ?\) (b) Repeat part (a), taking air resistance and friction into consideration this time. [Hint: Draw an FBD for the car in the middle. \(]\) (c) If air resistance and friction together cause a force of magnitude \(5.5 \mathrm{N}\) on each car, directed toward the left, find the readings of scales $\mathrm{A}, \mathrm{B},\( and \)\mathrm{C}$
A computer weighing \(87 \mathrm{N}\) rests on the horizontal surface of your desk. The coefficient of friction between the computer and the desk is $0.60 .$ (a) Draw an FBD for the computer. (b) What is the magnitude of the frictional force acting on the computer? (c) How hard would you have to push on it to get it to start to slide across the desk?
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