A 136-kg crate is at rest on the floor. A worker attempts to push it across the floor by applying a 412-N force horizon- tally. (a) Take the coefficient of static friction between the crate and floor to be 0.37 and show that the crate does not move. (b) A second worker helps by pulling up on the crate. What minimum vertical force must this worker apply so that the crate starts to move across the floor? (c) If the second worker applies a horizontal rather than a vertical force, what minimum force, in addition to the original 412-N force, must be exerted to get the crate started?

A 136-kg crate is at rest on the floor. A worker attempts to push it across the floor by applying a 412-N force horizon- tally. (a) Take the coefficient of static friction between the crate and floor to be 0.37 and show that the crate does not move. (b) A second worker helps by pulling up on the crate. What minimum vertical force must this worker apply so that the crate starts to move across the floor? (c) If the second worker applies a horizontal rather than a vertical force, what minimum force, in addition to the original 412-N force, must be exerted to get the crate started?