I need help with this question dealing with motion: \"A box of books weighing 30
ID: 1737861 • Letter: I
Question
I need help with this question dealing with motion: "A box of books weighing 300 N is shoved across the floor ofan apartment by a force of 400 N exerted downward at an angleof 35.2 degrees below the horizontal. If the coefficient of kineticfriction between box and floor is 0.570, how long does it take tomove the box 4.00 m, starting from rest?" Thanks! I need help with this question dealing with motion: "A box of books weighing 300 N is shoved across the floor ofan apartment by a force of 400 N exerted downward at an angleof 35.2 degrees below the horizontal. If the coefficient of kineticfriction between box and floor is 0.570, how long does it take tomove the box 4.00 m, starting from rest?" Thanks!Explanation / Answer
first you need to find the horizontal component of the exertedforce: cos(35.2)*400 = 326.858 N in the x direction now you need to find the resistive force due to friction Ff = mu * Fg however, since the exerted force has a negative Y component, it iscontributing to the downward force of the box as well, affectingthe force of friction. we know that Fg = 300N, but we need the exerted force's Y componentin addition to that: sin(35.2)*400 = 230.573 N 300N + 230.573N = 530.573N so now, Force of Friction = .570 * 530.573N = 302.4N So the net force acting on the box is going to be 400N - 302.4N =97.6N now use kinematics to find the time required to reach 4 meters The mass of the box is 300N / 9.8m/s^2 = 30.61kg With the mass, and net force, we can find the acceleration of thebox: 97.6N / 30.61kg = 3.188 m/s^2 now find the time: D = 1/2 * a * t^2 4 = .5*3.188*t^2 t^2 = 2.509 s t = 1.584 seconds The box will take 1.584 seconds to reach 4m