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?
To determine how hard each player must pull to drag the coach at a steady 2.0 m/s, we need to calculate the total force required to overcome the friction force.
Step 1: Drawing a diagram
Let's start by drawing a diagram to visualize the forces involved. We have a sled being pulled by two players with ropes, and the friction force acting against the sled.
Step 2: Resolving forces
We can resolve the forces into horizontal and vertical components. The horizontal component of force will determine the sled's motion.
Step 3: Calculating the force required
The horizontal component of force required to overcome the friction force can be calculated using trigonometry. The formula for the horizontal component of force is:
Force(horizontal) = Force(total) * cos(angle)
Given that the friction force is 800 N and the angle between the ropes is 20°, we can calculate the total force required:
Force(horizontal) = 800 N * cos(20°)
Force(horizontal) = 800 N * 0.9397
Force(horizontal) ≈ 751.76 N
Step 4: Determining the force each player must pull
Since there are two players, each player will pull with half of the total required force:
Force(player) = Force(horizontal) / 2
Force(player) = 751.76 N / 2
Force(player) ≈ 375.88 N
Therefore, each player must pull with a force of approximately 375.88 N to drag the coach at a steady 2.0 m/s.
To find the force required for each player to drag the coach at a steady speed, we can start by analyzing the forces acting on the sled.
The forces acting on the sled are:
1. The force applied by the players, which we need to find.
2. The friction force opposing the motion and given as 800 N.
3. The force of gravity acting vertically downwards.
Let's assume that the force applied by each player is F, and since there are two players, the total force applied by both players is 2F.
Since the sled is moving at a steady speed, the net force acting on the sled must be zero. This means that the force applied by the players must balance out the friction force.
Now, let's break down the force applied by each player into its components. Since the angle between the ropes is given as 20°, the vertical component of the force (Fv) would contribute to balancing the force of gravity, while the horizontal component of the force (Fh) would contribute to overcoming the friction force.
The vertical component of the force (Fv) can be found using trigonometry:
Fv = F * sin(20°)
The horizontal component of the force (Fh) can be found using trigonometry as well:
Fh = F * cos(20°)
Since the friction force is acting in the horizontal direction opposite to the motion, we can equate the horizontal component of the force to the friction force to find F:
Fh = 800 N
Now, we have an equation for the horizontal component of the force:
F * cos(20°) = 800 N
Solving for F:
F = 800 N / cos(20°)
To find the force required for each player, we divide the force by 2:
Force per player = F / 2
Finally, let's substitute the value of F into the equation and calculate the force required for each player:
Force per player = (800 N / cos(20°)) / 2
Using a calculator, we can find that the force per player is approximately 933.18 N.
does it tell u how much coach weighs
The net total force on the sled through the ropes is
F=2T cos(10°), where T is the tension on each rope.
Let m be the mass of the coach + the sled.
Then F-800=ma
where 800 = frictional force
m=total mass of coach and sled
a=acceleration = 2 m/s.
Solve for T.