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Chapter 8: Problem 13

A child of mass \(40.0 \mathrm{kg}\) is sitting on a horizontal seesaw at a distance of \(2.0 \mathrm{m}\) from the supporting axis. What is the magnitude of the torque about the axis due to the weight of the child?

Short Answer

Expert verified
Answer: The magnitude of the torque about the supporting axis due to the weight of the child is 784.8 N路m.

Step by step solution

01

Calculate the weight of the child

To calculate the weight of the child, we will use the formula for weight, which is given by \(W = mg\), where \(m\) is the mass of the child, and \(g\) is the acceleration due to gravity (approximately \(9.81 \mathrm{m/s^2}\)). So, for the child with a mass of \(40.0 \mathrm{kg}\), the weight will be: \(W = (40.0 \mathrm{kg})(9.81 \mathrm{m/s^2}) = 392.4 \mathrm{N}\).
02

Calculate the torque

Now that we have the weight of the child, we can calculate the torque using the formula \(\tau = rF\sin\theta\). In this case, the distance from the supporting axis is \(r = 2.0 \mathrm{m}\), the force is the weight of the child \(F = 392.4 \mathrm{N}\), and the angle between the force and the distance is \(\theta = 90^\circ\). So, the torque will be: \(\tau = (2.0 \mathrm{m})(392.4 \mathrm{N})\sin(90^\circ) = (2.0 \mathrm{m})(392.4 \mathrm{N})(1) = 784.8 \mathrm{N \cdot m}\). Thus, the magnitude of the torque about the supporting axis due to the weight of the child is \(784.8 \mathrm{N \cdot m}\).

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Most popular questions from this chapter

A collection of objects is set to rolling, without slipping, down a slope inclined at \(30^{\circ} .\) The objects are a solid sphere, a hollow sphere, a solid cylinder, and a hollow cylinder. A friction less cube is also allowed to slide down the same incline. Which one gets to the bottom first? List the others in the order they arrive at the finish line.
A uniform diving board, of length \(5.0 \mathrm{m}\) and mass \(55 \mathrm{kg}\) is supported at two points; one support is located \(3.4 \mathrm{m}\) from the end of the board and the second is at \(4.6 \mathrm{m}\) from the end (see Fig. 8.19 ). What are the forces acting on the board due to the two supports when a diver of mass \(65 \mathrm{kg}\) stands at the end of the board over the water? Assume that these forces are vertical. (W) tutorial: plank) [Hint: In this problem, consider using two different torque equations about different rotation axes. This may help you determine the directions of the two forces.]
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A hollow cylinder, of radius \(R\) and mass \(M,\) rolls without slipping down a loop-the-loop track of radius \(r .\) The cylinder starts from rest at a height \(h\) above the horizontal section of track. What is the minimum value of \(h\) so that the cylinder remains on the track all the way around the loop? A hollow cylinder, of radius \(R\) and mass \(M,\) rolls without slipping down a loop-the- loop track of radius \(r .\) The cylinder starts from rest at a height \(h\) above the horizontal section of track. What is the minimum value of \(h\) so that the cylinder remains on the track all the way around the loop?
A tower outside the Houses of Parliament in London has a famous clock commonly referred to as Big Ben, the name of its 13 -ton chiming bell. The hour hand of each clock face is \(2.7 \mathrm{m}\) long and has a mass of \(60.0 \mathrm{kg}\) Assume the hour hand to be a uniform rod attached at one end. (a) What is the torque on the clock mechanism due to the weight of one of the four hour hands when the clock strikes noon? The axis of rotation is perpendicular to a clock face and through the center of the clock. (b) What is the torque due to the weight of one hour hand about the same axis when the clock tolls 9: 00 A.M.?
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