Please do 1-6 on paper clear with work (explaining)

1. A girl pushes horizontally on a 100-kg crate, as shown in the two figures below. The coeffi- cient of kinetic friction between the crate and the floor is 0.2; the coefficient of static friction is 0.4. a) For each of the two situations described in the figures, indicate whether the frictional force is static or kinetic. b) In each case, find the magnitude of the frictional force. Case 1: The girl is pushing with a force of 300 N, Case 2: The girl is pushing with a force of 300 N, and the crate does not move. and the crate is moving along the floor. 2 Ron pulls with a string on a wooden block of mass m = 80 kg. The tension in the string is 300 N and the string makes an angle of 37 with respect to the String horizontal, as shown. The floor is very rough (#* = 0.35 and #s = 0.75) and the block does not move. a) Draw a free-body diagram for the block. b) Find the magnitude of the normal force exerted by the floor on the block. c) Find the magnitude of the frictional force exerted by the floor on the block. 3. Two identical blocks of mass 5 kg are connected by a massless string that passes over a massless frictionless pulley, as shown at left. The kinetic coefficient of friction between the blocks and each of the surfaces they sit on is exactly My = 0.4. What will be the acceleration of 530 the two blocks? 4. Ron is speeding down a steep mountain pass out of Butte, going 30 m/s (about 67 mi/hr). He suddenly sees an elk on the road ahead and slams on his brakes, locking all the wheels while the car slides to a stop. The mass of the car (with Ron in it) is 1000 kg. The coef- ficient of kinetic friction between the tires and the road is uk = 0.80. The road makes an angle _20 of 20 with the horizontal. a) What is the weight of the car (including Ron)? b) Find the total friction force acting on the car. (You may treat the car as if it is a block sliding down a ramp, i.e., don't treat the four wheels separately.) c) Find the acceleration (magnitude and direction) of the car after the wheels lock. d) How far will the car slide before it comes to a stop? 5 A box is placed atop a spring of spring constant k = 250 N/m, compressing the spring by 2 cm. What is the mass of the box? 6. The earth has a mass mearth = 5.97 x 1024 kg and the moon's mass is mmoon = 7.35 x 1022 kg. The earth-moon distance is 3.84 x 105 m. a) Find the gravity force acting between the earth and the moon. b) What is the resulting gravitational acceleration of the moon toward the earth? c) What is the acceleration of the earth due to the moon's gravity