Two wooden crates rest on top of one another. the smaller top crate has a mass of m1 = 25 kg and the larger bottom crate has a mass of m2 = 91 kg. there is no friction between the crate and the floor, but the coefficient of static friction between the two crates is µs = 0.79 and the coefficient of kinetic friction between the two crates is µk = 0.62. a massless rope is attached to the lower crate to pull it horizontally to the right (which should be considered the positive direction for this problem).1)the rope is pulled with a tension t = 234 n (which is small enough that the top crate will not slide). what is the acceleration of the small crate? 2)in the previous situation, what is the magnitude of the frictional force the lower crate exerts on the upper crate? 3)what is the maximum tension that the lower crate can be pulled at before the upper crate begins to slide? 4)the tension is increased in the rope to 1187 n causing the boxes to accelerate faster and the top box to begin sliding. what is the acceleration of the upper crate? m/s25)as the upper crate slides, what is the acceleration of the lower crate?

Jason and mia are both running in a race. as they approach the finish line, you being the physicist that you are decide to time how long it takes them to reach the end of the race. when you start your stop watch (you can take this as time t = 0 s) you notice that mia is an unknown distance d ahead of jason and both are moving with the same initial velocity v_0. you also notice that jason is accelerating at a constant rate of a_j, while mia is deaccelerating at a constant rate of -a_m. jason and mia meet each other for the first time at time t = t_1. at this time (t = t_1) jason's velocity is two times that of mia's velocity, meaning v_j (t_1) = 2v_m (t_1). a) draw the position vs. time graph describing mia's and jason's motion from time t = 0 to time t = t_1. clearly label your axes and initial conditions on your graph. b) draw the velocity vs. time graph describing mia and jason's motion from time t = 0s to time t = t_1. clearly label your axes and initial conditions on your graph. c) how long from when the stop watch was started at t = 0s did it take mia and jason to meet? express your answer in terms of know quantities v_0, a_m, and a_j. d) when the stop watch started at time t = 0s, how far apart, d, were mia and jason? express your answer in terms of know quantities v_0, a_m, and a_j.

The heliocentric and the geocentric models of the solar system included these central principles

The two stars in a certain binary star system move in circular orbits. the first star, alpha, has an orbital speed of 36 km/s. the second star, beta, has an orbital speed of 12 km/s. the orbital period is 137 d. a) what is the mass of the star alpha? b) what is the mass of the star beta?