In science, work is defined as the component of force parallel to motion multiplied by displacement. One reason that individuals use ramps, rather than lifting heavy items straight up, is that using a ramp increases total displacement, but reduces the amount of force required to move an object by exactly the same amount as the increase in displacement, provided that the ramp's surface is frictionless. According to the information in the paragraph, using a ramp with a frictionless surface will have which of the following effects? A. The total amount of work required to move an object will decrease. B. The total amount of work required to move an object will increase. C. The total amount of work required to move an object will remain the same. D. The amount of work required to move an object will initially increase, but will later decrease.

Step by step solution

01

The formula for work is \(W = F \cdot d\), where \(W\) is the work, \(F\) is the force, and \(d\) is the displacement. This will be the basis for our solution. #Step 2: Analyze the case of using a frictionless ramp#

When using a frictionless ramp, the total displacement increases, while the force required to move the object decreases. It's important to keep in mind that the force reduction is by exactly the same amount as the increase in displacement, according to the problem statement. #Step 3: Apply the work formula for the frictionless ramp case#

02

Since the force required to move the object on the ramp decreases by the same amount as the increase in displacement, their product remains the same. Therefore, the work remains the same when using a frictionless ramp. This is represented by the equation \(W_r = F_r \cdot d_r\), where \(W_r\) is the work done using the ramp, \(F_r\) is the force needed on the ramp, and \(d_r\) is the displacement on the ramp. Since their product remains the same, \(W_r = W\), where \(W\) is the work done without using the ramp. #Step 4: Choose the correct answer from the options given#

Based on our analysis and the use of the work formula, we can conclude that using a frictionless ramp will keep the total amount of work required to move an object the same. Therefore, the correct answer is: C. The total amount of work required to move an object will remain the same.

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