You find it takes 230 N of horizontal force to move an unloaded pickup truck along a level road at a speed of 2.4 m/s. You then load up the pickup and pump up its tires so that its total weight increases by 42% while the coefficient of rolling friction decreases by 19%.
Now what horizontal force will you need to move the pickup along the same road at the same speed? The speed is low enough that you can ignore air resistance.
Would I have to find the coefficient for the rolling friction for this problem? I'm really not sure how to start it.
To find the horizontal force needed to move the loaded pickup truck at the same speed, we first need to calculate the new total weight of the truck.
Let's denote the original weight of the truck as W. Adding 42% to the original weight gives us a new weight of W + 0.42W.
Now, let's consider the coefficient of rolling friction. The original coefficient of rolling friction is denoted as μ. Since the coefficient of rolling friction decreases by 19%, the new coefficient of rolling friction is μ - 0.19μ = 0.81μ.
To find the new horizontal force required to move the truck at the same speed, we can use the equation:
Force = (Total Weight) * (Coefficient of Rolling Friction)
Substituting the values, we get:
Force_new = (W + 0.42W) * 0.81μ
Simplifying this equation, we find:
Force_new = 1.42W * 0.81μ
Since we know that the original horizontal force required was 230 N, we can set up the following equation:
Force_original = W * μ
Substituting the given values, we get:
230 = W * μ
Now, we can rearrange this equation to solve for W:
W = 230 / μ
Plugging this value of W into the equation for the new horizontal force, we get:
Force_new = 1.42 * (230 / μ) * 0.81μ
Simplifying this expression, we find:
Force_new = 292.62 N
Therefore, you would need a horizontal force of approximately 292.62 N to move the loaded pickup truck along the same road at the same speed.
Increasing the load by 42% caused the
force of friction to increase by 42%.But the addition of air to the tires caused a 19% decrease in force of
friction:
F = (100%+42%-19%)*Fo,
Change % to decimal:
F = (1+0.42-0.19)*230 = 283N.