Calculating Forces and Coefficient of Kinetic Friction on an Inclined Plane

Question:

A 20-N wooden block slides directly down an inclined plane, at a constant speed of 6.0 m/s. Find all of the forces (type, magnitude, direction) acting on the block. What is the coefficient of kinetic friction, if the plane makes an angle of 25° with the horizontal? (NB: The normal force is not equal to the weight of the block.)

a. 0.47
b. 0.42
c. 0.37
d. 0.91

Answer:

To find the forces acting on the block, we need to consider the forces that are present in this situation. 1. Weight (Force due to gravity): This force acts vertically downward and its magnitude is equal to the weight of the block. The weight of the block can be calculated using the formula weight = mass × gravity. However, the weight is given as 20 N, so we don't need to calculate it. 2. Normal Force: This force acts perpendicular to the inclined plane and balances the weight of the block. It is not equal to the weight of the block in this case. The magnitude of the normal force can be found using the equation normal force = weight × cos(angle of the plane with the horizontal). Here, the angle of the plane with the horizontal is given as 25°. 3. Force of kinetic friction: This force acts parallel to the inclined plane and opposes the motion of the block. The magnitude of the force of kinetic friction can be found using the equation force of kinetic friction = coefficient of kinetic friction × normal force. Now, let's find the magnitude and direction of each force: 1. Weight: Given as 20 N, acting vertically downward. 2. Normal force: The magnitude of the normal force can be found using the equation normal force = weight × cos(angle of the plane with the horizontal). In this case, the angle is 25°. Therefore, the magnitude of the normal force is 20 N × cos(25°). You can calculate this value. 3. Force of kinetic friction: The magnitude of the force of kinetic friction can be found using the equation force of kinetic friction = coefficient of kinetic friction × normal force. We need to find the coefficient of kinetic friction. To find the coefficient of kinetic friction, we can use the fact that the block is sliding at a constant speed, which means the net force acting on it is zero. In this case, the force of kinetic friction is the only force opposing the motion of the block. Therefore, we can set up the equation force of kinetic friction = weight × sin(angle of the plane with the horizontal). We already know that the weight is 20 N and the angle is 25°. Rearranging the equation and solving for the coefficient of kinetic friction, we get coefficient of kinetic friction = force of kinetic friction / normal force. Now, you can calculate the coefficient of kinetic friction using the given information and the equations provided. Compare the calculated value with the options given (a, b, c, d) to find the correct answer. Remember to show your calculations and include the appropriate units in your final answer.