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Chapter 4: Problem 25

A man lifts a 2.0 -kg stone vertically with his hand at a constant upward velocity of \(1.5 \mathrm{m} / \mathrm{s} .\) 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 exerted by the man's hand on the stone is 19.62 N.

Step by step solution

01

Calculate gravitational force

To calculate the gravitational force acting on the stone, we can use the formula: \(F_g = m \times g\) where \(F_g\) is the gravitational force, \(m\) is the mass of the stone, and \(g\) is the acceleration due to gravity (approximately \(9.81 \mathrm{m} / \mathrm{s}^2\)). Given the mass of the stone as 2.0 kg, we can plug in the values and find the gravitational force. \(F_g = 2.0 \, \text{kg} \times 9.81 \, \frac{\text{m}}{\text{s}^2} = 19.62 \, \text{N}\)
02

Determine net force

Since the stone is moving upward with a constant velocity, the net force acting on it must be zero (according to Newton's first law). So, we have: \(\Sigma F_y = 0\)
03

Calculate the magnitude of the total force exerted by the man's hand

To find the magnitude of the total force exerted by the man's hand (\(F_h\)) on the stone, we can use the net force equation we wrote in Step 2: \(\Sigma F_y = F_h - F_g = 0\) Now we can solve for the force exerted by the man's hand: \(F_h = F_g = 19.62 \, \text{N}\) So, the magnitude of the total force of the man's hand on the stone is \(19.62 \, \text{N}\).

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Most popular questions from this chapter

The coefficient of static friction between block \(\mathrm{A}\) and a horizontal floor is 0.45 and the coefficient of static friction between block \(\mathrm{B}\) and the floor is \(0.30 .\) The mass of each block is $2.0 \mathrm{kg}$ and they are connected together by a cord. (a) If a horizontal force \(\overrightarrow{\mathbf{F}}\) pulling on block \(\mathrm{B}\) is slowly increased, in a direction parallel to the connecting cord, until it is barely enough to make the two blocks start moving, what is the magnitude of \(\overrightarrow{\mathbf{F}}\) at the instant that they start to slide? (b) What is the tension in the cord connecting blocks \(A\) and \(B\) at that same instant?
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