Two crates, one with mass 4.00 kg and the other with mass 6.00 kg, sit on the frictionless surface of a frozen pond, connected by a light rope (?Fig. P4.39?). A woman wearing golf shoes (for traction) pulls horizontally on the 6.00-kg crate with a force F that gives the crate an acceleration of 2.50 m/s2. (a) What is the acceleration of the 4.00-kg crate? (b) Draw a free-body diagram for the 4.00-kg crate. Use that diagram and Newton’s second law to find the tension T in the rope that connects the two crates. (c) Draw a free-body diagram for the 6.00-kg crate. What is the direction of the net force on the 6.00-kg crate? Which is larger in magnitude, T or F? (d) Use part (c) and Newton’s second law to calculate the magnitude of F.
Solution 43P Step 1: 2 a) acceleration of the 4 kg crate will be 2.5 m/s itself since, the acceleration due to the 2 force is 2.5 m/s Step 2: b) This is the free body diagram of 4 kg crate. The normal force is exerted by the surface in which the crate is residing with. Therefore, the gravitational force and the normal force are balanced here. Therefore, the only force will be acting through the rope as the tension. Since, the acceleration, a = 2.5 m/s and mass of the cratem m = 4 kg, F = 4 kg × 2.5 m/s = 10 N So, the tension on the 4 kg crate’s rope is, 10 N