Problem 14
Question
A \(2.75\) -m-long board is used to slide a compressor a vertical distance of \(0.750 \mathrm{~m}\). What is the MA of the ramp made by the board?
Step-by-Step Solution
Verified Answer
The mechanical advantage of the ramp is approximately 3.67.
1Step 1: Understand the Problem
We need to find the Mechanical Advantage (MA) of a ramp, which is defined as the ratio of the length of the ramp to the vertical height it rises. Here, we have a ramp (the board) with a length of 2.75 meters and a height of 0.750 meters.
2Step 2: Use MA Formula
The formula to calculate the mechanical advantage (MA) of a ramp is: \[MA = \frac{\text{Length of Ramp}}{\text{Height of Ramp}}\] We will use this formula to find the MA.
3Step 3: Substitute Values
Substitute the given values into the formula:\[MA = \frac{2.75 \text{ m}}{0.750 \text{ m}}\]
4Step 4: Calculate
Perform the division:\[MA = \frac{2.75}{0.750} \approx 3.67\]So, the mechanical advantage of the ramp is approximately 3.67.
Key Concepts
Physics ProblemsInclined PlanesSimple Machines
Physics Problems
Physics problems can be fun and rewarding, especially when they involve real-life scenarios like inclined planes. These problems help us understand how the principles of physics, such as force, energy, and motion, apply to everyday activities.
To tackle a physics problem effectively, follow a systematic approach:
To tackle a physics problem effectively, follow a systematic approach:
- **Understand the problem statement:** Read carefully to identify what is given and what needs to be found.
- **Identify relevant formulas:** Look for equations or principles that relate to the problem.
- **Substitute and solve:** Plug in the known values and solve for the unknowns.
- **Check your work:** Verify the result by considering units, estimations, or looking for errors in calculations.
Inclined Planes
Inclined planes are simple machines that make our lives much easier. Think of them as flat surfaces tilted at an angle, like ramps, slides, or even hills.
An inclined plane allows us to move heavy objects over a vertical distance with much less effort than lifting them directly. When you use an inclined plane:
An inclined plane allows us to move heavy objects over a vertical distance with much less effort than lifting them directly. When you use an inclined plane:
- **Less force needed:** The force required is less than lifting the object vertically.
- **Longer distance traveled:** The trade-off is that the object travels a longer distance.
- **Mechanical advantage:** By dividing the length by the vertical height, we calculate the mechanical advantage of the ramp.
Simple Machines
Simple machines are basic devices that alter the direction or magnitude of a force. They are fundamental to our understanding of mechanical advantage. Common examples include levers, pulleys, wheels and axles, screws, wedges, and inclined planes. They help us perform tasks with less effort.
A simple machine like an inclined plane allows for mechanical advantage. This mechanical advantage is a measure of how effectively a simple machine can multiply force. For instance:
A simple machine like an inclined plane allows for mechanical advantage. This mechanical advantage is a measure of how effectively a simple machine can multiply force. For instance:
- If a ramp (or inclined plane) has a higher mechanical advantage, it greatly reduces the force needed to move an object upward.
- Understanding and calculating the mechanical advantage helps in designing efficient machines, like conveyor belts or slides.
- With a calculated MA of 3.67 in our exercise, the ramp allows the force applied to move a heavy compressor to be minimized by over three and a half times.
Other exercises in this chapter
Problem 13
The radius of the axle of a winch is \(3.00\) in. The length of the handle (radius of wheel) is \(1.50 \mathrm{ft}\). (a) What weight will be lifted by an effor
View solution Problem 14
The handle of a jackscrew is \(60.0 \mathrm{~cm}\) long. (a) If the mechanical advantage is \(78.0\), what is the pitch? (b) How much weight can be raised by ap
View solution Problem 15
A resistance of \(325 \mathrm{~N}\) is raised by using a ramp \(5.76 \mathrm{~m}\) long and by applying a force of \(75.0 \mathrm{~N}\). (a) How high can it be
View solution Problem 15
The diameter of the wheel of a wheel-and-axle is \(10.0 \mathrm{~cm} .\) (a) If a force of \(475 \mathrm{~N}\) is raised by applying a force of \(142 \mathrm{~N
View solution