1. A 20 kg block is pulled along a horizontal surface by a 50 N force exerted along an attached rope making a 35° angle with the horizontal. What is the normal force exerted by the surface to support the box? If the block in number one is pulled at a constant speed, what is the coefficient of friction between the surfaces? Ans: 167.32 N; 0.24
2. What is the normal force and the coefficient of friction if the block in number one is now pushed at constant speed? Ans: 224.68 N; 0.18
3. If the coefficient of friction between the two surfaces in number one was 0.15, what would be the acceleration of the block? Ans: 0.79 m/s²
4. Find the normal and the parallel forces for the following: a) a 14 N object rests on a 28° slope and b) a 1.4 kg object rests on a 28° slope. Ans: a) 12.36 N, 6.57 N; b) 12.11 N, 6.44 N
5. A 30 N block slides down a 35° incline with constant speed. What is the frictional force? What is the coefficient of friction between the surfaces? Ans: 17.21 N; 0.70
6. A 6 N object is pushed up a 22° incline at constant speed by a 6 N force. What is the frictional force? What is the coefficient of friction? Ans: 3.75 N; 0.67
7. An 8 N object is pushed up a 23° slope with an acceleration of 1 m/s² by a 10 N force. What is the coefficient of friction between the surfaces? Ans: .82
8. A 12 N object slides down a 15° incline with an acceleration of 1.8 m/s². What is the coefficient of friction between the surfaces? Ans: 0.08
9. A picture weighing 1000 N hangs suspended from a two wires. At the point of attachment to the picture, each wire makes a 70° angle with the vertical. What is the tension in each wire? Ans: 1461.90 N
10. A 1000 N traffic sign is held by two wires connected to two poles. One wire forms an angle of 30° with the horizontal and the other an angle of 60° with the horizontal. What is the tension in each wire? Ans: 500 N; 866 N
11. The compass of an aircraft indicates that it is heading due north and its airspeed indicator shows that it is moving through the air at 120 mph. An observer on the ground measures its velocity to be 130 mph 22° east of north. What is the speed and the direction of the wind that is blowing? Ans: 50 mph, east
12. A 500 N sign is held by two wires connected to two poles. One wire is attached horizontally (in other words, it makes an angle of 0° with the horizontal). The other makes an angle of 40° with the horizontal. What is the tension in each wire? Ans: 596 N; 778 N

Vector Applications Notes

Vector Applications Sample Problems