A 1200 lb sleigh is pulled along a horizontal surface at uniform speed by means of a rope that makes an angle of 30 degrees above the horizontal. If the tension in the rope is 100 lb., what is the coefficient of friction?
Ws = 1200 Lbs.
Fp = 100*Cos30 = 86.6 Lbs. = Force parallel with the surface.
Fn = 1200-100*sin30 = 1150 Lbs. = Normal force.
Fk = u*Fn = u*1150 Lbs.
Fp-u*Fn = Ws*a.
u*Fn = Fp-Ws*0,
u*Fn = Fp, u = Fp/Fn = 86.6/1150 = 0.075.
0.075
A ladder has a weight of 30-lbs and a length of 26-ft. Determine the maximum distance D it can be
placed from the smooth wall and not slip. The coefficient of static friction between the floor and the
pole is 0.3.
Well, well, well, it seems we have a sleigh ride with some math involved, how exciting! Let's get to it, then.
First things first, we need to find the force of friction acting on the sleigh. The force of friction can be found using the equation:
Frictional force = coefficient of friction * normal force
Now, the normal force is the force exerted by the surface perpendicular to it. Since the sleigh is being pulled horizontally, the normal force is equal to the vertical force exerted by the sleigh, which in this case is its weight.
Therefore, the normal force is equal to 1200 lb. Simple enough, right?
Now, we can plug in the value for the tension in the rope (100 lb) into the equation. The tension in the rope acts as the horizontal force that counteracts the frictional force.
Given that the tension in the rope is equal to the horizontal force, we have:
Frictional force = Tension in the rope = 100 lb.
Now comes the part where we need to find the coefficient of friction. We can rewrite the equation to solve for the coefficient of friction:
Coefficient of friction = Frictional force / normal force
Plugging in the values we know, we get:
Coefficient of friction = 100 lb / 1200 lb
Time for some good old-fashioned division:
Coefficient of friction = 0.083333 (approximately)
So, my friend, the coefficient of friction for this ride is approximately 0.083333. Just remember, while you're enjoying your sleigh ride, no skidding allowed!
To find the coefficient of friction, we first need to understand the forces acting on the sleigh.
First, let's draw a free-body diagram of the sleigh:
```
------------ <-- Force of tension in the rope (100 lb)
| /|
| / |
| / |
| / |
------------
```
The force of tension in the rope is acting upwards at an angle of 30 degrees with respect to the horizontal.
The other force acting on the sleigh is the force of friction, which opposes the motion of the sleigh. We can represent it as:
```
------------
| /|
| / | <---- Force of friction
| / |
| / |
------------
```
Since the sleigh is moving at a uniform speed, the net force acting on it must be zero. This means that the magnitude of the force of friction is equal to the magnitude of the force of tension.
Now, we can use trigonometry to find the horizontal and vertical components of the force of tension:
Vertical component of force of tension = 100 lb * sin(30 degrees) = 100 lb * 0.5 = 50 lb
Horizontal component of force of tension = 100 lb * cos(30 degrees) = 100 lb * 0.866 = 86.6 lb
The force of friction acts in the opposite direction of the horizontal component of the force of tension, so its magnitude is 86.6 lb.
Finally, we can calculate the coefficient of friction using the formula:
Coefficient of friction = Force of friction / Normal force
The normal force is equal to the weight of the sleigh, which is given as 1200 lb.
Coefficient of friction = 86.6 lb / 1200 lb = 0.072
Therefore, the coefficient of friction is approximately 0.072.