Question

1. calculate the net force on the rope.
2. calculate the net force to determine which team will win the tug of war.
3. michael and andrew are pushing a desk across the room. to be funny, michael decides to push against andrew instead of with him. michael can push with a force of 30 n. andrew can only push with a force of 28 n. in which direction will the desk move?
4. greg, matt, and stephen work together to hold the door shut to keep out the zombies. greg pushes with a force of 15 n, matt with 12 n, and stephen with 22 n. what is their net force on the door?
5. calculate the net force acting on the box below.

Explanation:

Step1: Determine the direction of forces

For problem 6:
Let the left - acting force be negative and the right - acting force be positive. The forces are \(F_1=- 30N\) and \(F_2 = 30N\).

Step2: Calculate the net force

The net force \(F_{net}=F_1 + F_2\). Substitute the values: \(F_{net}=-30N + 30N=0N\).

For problem 7:
Left - side forces: \(F_{left}=38N+15N + 40N=93N\) (left - direction is negative, so \(F_{left}=-93N\)).
Right - side forces: \(F_{right}=35N+20N + 5N=60N\) (right - direction is positive).
Net force \(F_{net}=F_{left}+F_{right}=-93N + 60N=-33N\). The negative sign means the left - side team wins.

For problem 8:
Let Andrew's pushing direction (say to the right) be positive (\(F_{Andrew}=28N\)) and Michael's pushing direction (to the left) be negative (\(F_{Michael}=-30N\)).
Net force \(F_{net}=F_{Andrew}+F_{Michael}=28N-30N=-2N\). The negative sign means the desk moves in Michael's pushing direction (to the left).

For problem 9:
Assume all forces are in the same direction (holding the door shut, say in the positive direction).
Net force \(F_{net}=F_{Greg}+F_{Matt}+F_{Stephen}=15N + 12N+22N=49N\).

For problem 10:
Horizontal forces:
Right - acting forces \(F_{right}=6N + 7N+8N=21N\).
Left - acting forces \(F_{left}=5N + 5N=10N\).
Vertical forces: \(F_{up}=2N\) and \(F_{down}=2N\).
Horizontal net force \(F_{x}=F_{right}-F_{left}=21N - 10N = 11N\).
Vertical net force \(F_{y}=F_{up}-F_{down}=2N - 2N=0N\).
Net force \(F_{net}=\sqrt{F_{x}^{2}+F_{y}^{2}}=\sqrt{11^{2}+0^{2}} = 11N\) (in the horizontal right - direction).

Answer:

1. \(0N\)
2. The net force is \(-33N\), and the left - side team wins.
3. The desk moves in Michael's pushing direction (to the left).
4. \(49N\)
5. \(11N\) (in the horizontal right - direction)