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Chapter 3: Problem 105

Reading of the spring scale in figure (B) (A) \(90 \mathrm{~N}\) (B) \(62.5 \mathrm{~N}\) (C) \(55 \mathrm{~N}\) (D) \(75 \mathrm{~N}\)

Short Answer

Expert verified
Unfortunately, we cannot provide a specific short answer due to missing information about the angle, mass, and acceleration due to gravity in the problem. If this information was provided, you would be able to use the equation \(mg = T \cdot \cos \theta\) to calculate the force exerted by the spring scale and compare it to the given options.

Step by step solution

01

Identify the forces acting on the object in figure (B)

In the figure (B), the object is hanging on the spring scale at an angle. Therefore, we have two main forces acting on the object: gravitational force (weight) and tension force exerted by the spring scale. We can represent the weight with W and the tension with T.
02

Resolve the forces

Since the spring scale is at an angle, we need to resolve the forces into their horizontal and vertical components. The vertical component of the tension T will balance the weight W, which is determined by the mass of the object and the acceleration due to gravity. Let's call the angle between the spring scale and the vertical direction as \(胃\). Using trigonometry, we can express the vertical component of the tension force as: \[T_y = T \cdot \cos \theta\]
03

Balance the forces

For the object to be in equilibrium, the vertical component of the tension force must equal the weight, i.e., \(W = T_y\). We can rewrite this equation using the vertical component of the tension force from the previous step: \[W = T \cdot \cos \theta\] Since gravitational force is \(W = mg\), where \(m\) is the mass of the object and \(g\) is the acceleration due to gravity, we can rewrite the equation again as: \[mg = T \cdot \cos \theta\] Now we need to find the angle, mass, and acceleration due to gravity which are required to find the tension T.
04

Find the angle, mass, and acceleration due to gravity

For this step, we will need some information about the specific figure (B). Unfortunately, this information is not provided in the problem statement, so we cannot proceed with the calculations. However, if you were given the angle, mass, and acceleration due to gravity, you could follow these steps to find the correct answer: 1. Substitute the given values of angle, mass, and acceleration due to gravity into the equation \(mg = T \cdot \cos \theta\). 2. Solve the equation for T, which represents the force exerted by the spring scale. 3. Compare the result with the given options and find the correct answer. 4. Make sure that the signs of the forces are considered correctly during the calculation so that no errors occur. Without the required information, we cannot determine the specific answer to this problem. However, you can use this step-by-step guide to solve similar problems in the future where all necessary data is provided.

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