Problem 981 Find the force required to preve... [FREE SOLUTION]

Chapter 31: Problem 981

Find the force required to prevent a 500 -pound object from sliding down a \(40^{\circ}\) incline, disregarding friction.

Short Answer

Expert verified

The force required (F) to prevent a 500-pound object from sliding down a \(40^{\circ}\) incline, disregarding friction, is approximately \(321.4\) pounds.

Step by step solution

1. Determine the weight of the object

Since the object weighs 500 pounds, we can represent the weight (force due to gravity) as a vector pointing straight down with a magnitude of 500 pounds.

2. Resolve the weight vector into components

To determine the force needed to counteract the force due to gravity (weight) acting on the object, we need to resolve the weight vector into its components: one parallel to the incline (the force causing the object to slide), and one perpendicular to the incline (the force pushing the object into the incline). To resolve the weight vector into components, we can use the following equations: \( F_{parallel} = F_{weight} \sin{\theta} \) \( F_{perpendicular} = F_{weight} \cos{\theta} \) where \( F_{weight} = 500\) pounds and \( \theta = 40^{\circ} \).

3. Calculate the force parallel to the incline

Using the equation for the parallel force, plug in the weight and angle values: \( F_{parallel} = 500 \sin{40^{\circ}} \) \( F_{parallel} = 500 * 0.6428 \) \( F_{parallel} \approx 321.4\) pounds

4. Determine the force required to prevent sliding

The force required to prevent the object from sliding down the incline is equal to the force acting on the object parallel to the incline. The force required (F) to prevent the object from sliding is approximately 321.4 pounds.

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91影视

Find the force required to prevent a 500 -pound object from sliding down a \(40^{\circ}\) incline, disregarding friction.

Short Answer

Step by step solution

1. Determine the weight of the object

2. Resolve the weight vector into components

3. Calculate the force parallel to the incline

4. Determine the force required to prevent sliding

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