you find it takes 200N of horizontal force to move an empty pickup truck along a level road at a speed of 2.4m/s. you then load the pickup truck and pump 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.
original friction= 200N
reduce by .19%: 162N
weight increased by 42%, increases friction by 1.42
new horizontal force: 200*.81*1.41
i don't quite understand how you reduced 200N to 162N ?
81% of 200 N is 162 N, the new rolling friction force if the weight stayed the same. You must also account for the higher weight.
The 1.41 in Mr. Pursley's final formula should be 1.42
thank you so much this really helps :)
To determine the horizontal force required to move the loaded pickup truck at the same speed, we can follow these steps:
Step 1: Calculate the change in weight of the pickup truck.
The problem states that the total weight of the pickup truck increases by 42%. Let's denote the initial weight of the pickup truck as W1. To find the increased weight (W2), we can express it as follows:
W2 = W1 + W1 * 42% = W1 * (1 + 0.42) = 1.42 * W1
Step 2: Calculate the change in the coefficient of rolling friction.
The coefficient of rolling friction is stated to decrease by 19%. Let's denote the initial coefficient as μ1. To find the new coefficient (μ2), we can express it as follows:
μ2 = μ1 - μ1 * 19% = μ1 * (1 - 0.19) = 0.81 * μ1
Step 3: Calculate the force required to move the loaded pickup truck.
We know that the horizontal force required to move the empty pickup truck is 200N. Let's denote the force required to move the loaded pickup truck as F2.
The force equation for the pickup truck is:
F2 = μ2 * (W2 + Fg)
Where Fg is the force due to gravity or weight.
Step 4: Calculate the force due to gravity.
The force due to gravity on the loaded pickup truck can be expressed as:
Fg = W2 * g
Where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Step 5: Substitute the values into the force equation.
Substituting the known values into the force equation, we get:
F2 = μ2 * (W2 + Fg)
F2 = 0.81 * μ1 * (1.42 * W1 + W1 * g)
Step 6: Simplify the equation.
F2 = 0.81 * μ1 * W1 * (1.42 + g)
Step 7: Calculate the horizontal force required to move the loaded pickup truck.
Substituting the known values into the simplified equation, we get:
F2 = 0.81 * μ1 * W1 * (1.42 + 9.8)
Now, plug in the values of μ1, W1, and calculate the force F2 required to move the loaded truck.