A man pulls a 300N object across a horizontal surface using a 100 N force applied at a 35 degree angle. What is the normal force? If the object is pulled at constant speed, what is the coefficient of friction?
weight minus vertical pulling component
... Fn = 300 - 100 sin(35º)
horizontal pulling component divided by normal force
... [100 cos(35º)] / Fn
200
To find the normal force, we first need to understand what it represents. The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the object is being pulled horizontally, so the normal force will be equal in magnitude and opposite in direction to the force of gravity acting on the object.
To calculate the normal force, we need to know the weight of the object. We can use the formula: weight = mass x acceleration due to gravity. However, the weight is given to us in Newtons as 300N. Since weight is a force, we can equate it to the product of mass and the acceleration due to gravity (9.8 m/s^2). Therefore, we can write:
300N = mass x 9.8 m/s^2
Solving for mass gives us:
mass = 300N / 9.8 m/s^2 ≈ 30.61 kg
Now that we know the mass, we can find the normal force. The normal force is equal to the weight, so the normal force is also 300N in this case.
Next, let's determine the coefficient of friction. The coefficient of friction is a measure of how "sticky" or "slippery" a surface is when two objects are in contact. In this case, we have a force of 100N being applied at a 35-degree angle. The component of this force that is parallel to the surface will be used to overcome the force of friction opposing the motion.
To find the parallel component of the applied force, we will use the formula:
Force parallel = Applied force x cos(angle)
In this case:
Force parallel = 100N x cos(35°) ≈ 81.62N
Since the object is being pulled at a constant speed, the applied force of 100N must be equal in magnitude and opposite in direction to the force of friction. Therefore, the force of friction is also 81.62N.
Finally, to find the coefficient of friction, we can use the formula:
coefficient of friction = force of friction / normal force
coefficient of friction = 81.62N / 300N ≈ 0.272
Therefore, the coefficient of friction is approximately 0.272.