A football coach sits on a sled while two of his players build their strength by dragging the sled across the field with ropes. The friction force on the sled is 800 N and the angle between the two ropes is 20°. How hard must each player pull to drag the coach at a steady 2.0 m/s?
well, 400=forcepulling*cos20
draw a diagram and confirm that.
9. A train is on its way from Chicago, IL to Madison, WI. The trip is said to last 3.15 hours. When the train arrives in Madison, the conductor notices the trip took 3.26 hours. The train company prides itself on always having its trains arrive within a 3% error of the expected time. Will the train company live up to its reputation on this trip?
To find out how hard each player must pull to drag the coach at a steady 2.0 m/s, we need to consider the forces acting on the sled.
First, let's analyze the forces in the horizontal direction. Since the sled is moving at a steady pace, the net force in the horizontal direction must be zero. The only force in the horizontal direction is the force exerted by the players.
Let's call the force exerted by player 1 F1 and the force exerted by player 2 F2. The horizontal component of each force can be calculated using trigonometry.
The horizontal component of F1 is F1 * cos(20°), and the horizontal component of F2 is F2 * cos(20°).
Since the net force in the horizontal direction is zero, we have:
F1 * cos(20°) + F2 * cos(20°) = 0
Now, let's analyze the forces in the vertical direction. The force due to friction exerted on the sled opposes its motion. So, the vertical component of the force due to friction is equal to the weight of the coach.
The vertical component of the force due to friction is F_friction * sin(20°) = 800 N * sin(20°).
The vertical component of the force exerted by player 1 is F1 * sin(20°).
The vertical component of the force exerted by player 2 is F2 * sin(20°).
Since the sled is moving at a steady pace, the net force in the vertical direction must be zero. Therefore, we have:
F1 * sin(20°) + F2 * sin(20°) = 800 N * sin(20°)
Now, we have a system of two equations with two unknowns (F1 and F2). We can solve these equations to find the values of F1 and F2.
Dividing both equations above by the common term of sin(20°), we get:
F1 * cos(20°) + F2 * cos(20°) = 0
F1 + F2 = 800 N
Rearranging the second equation, we have:
F1 = 800 N - F2
Substituting this expression for F1 into the first equation, we get:
(800 N - F2) * cos(20°) + F2 * cos(20°) = 0
Now, we can solve this equation for F2:
800 N * cos(20°) - F2 * cos(20°) + F2 * cos(20°) = 0
800 N * cos(20°) = F2 * cos(20°)
F2 = (800 N * cos(20°)) / cos(20°)
F2 = 800 N
Since F1 + F2 = 800 N, we can conclude that F1 = 0 N.
Therefore, player 1 doesn't need to exert any force to drag the sled while player 2 needs to exert a force of 800 N.