Answer :
Final answer:
After calculating the horizontal and vertical components of the applied force, we used the coefficient of static friction to find the mass at the threshold of movement. The calculated mass is 123.61 kg, which does not match any of the provided options.
Explanation:
To determine the most massive trunk you will be able to move, we first need to calculate the maximum force of static friction. The coefficient of static friction (μs) is given as 0.76, and the force you apply is at an angle 25° below horizontal.
Firstly, let's calculate the component of the applied force that acts in the horizontal direction:
F_horizontal = 750N * cos(25°)
= 750N * 0.9063
= 679.725N.
Now let's find the vertical component, which adds to the normal force:
F_vertical = 750N * sin(25°)
= 750N * 0.4226
= 316.95N.
Next, we find the normal force (N). The normal force is equal to the weight of the trunk (mg) minus the vertical component of the applied force (since it acts upward against the weight):
N = mg - F_vertical
We are searching for the mass (m) at the threshold of motion, which happens when the applied horizontal force equals the force of static friction (μs * N). So we'll set up the equation:
F_horizontal = μs * N
679.725N = 0.76 * (mg - 316.95N)
Now we can calculate the mass (m), using g = 9.8 m/s²:
679.725N = 0.76 * (m * 9.8 m/s² - 316.95N)
679.725N = 7.448 m - 240.842N
920.567N = 7.448m
m = 920.567N / 7.448
m = 123.61 kg
However, none of the provided options match this mass.
