A force of 50 N directed 30 degrees above the hoizontal is applied to a 10-kg block at rest on a rough horizontal surface. What is the coefficient of kinetic friction between the block and the horizontal surface if the acceleration of the block is 2.0 m/s2?
To solve this problem, we need to use Newton's second law of motion, which states that the net force on an object is equal to the product of its mass and acceleration.
1. Calculate the horizontal component of the applied force:
The horizontal component of the force can be found using the given angle of 30 degrees. We can use trigonometry to find the horizontal component:
Horizontal force = Force * cos(angle)
Horizontal force = 50 N * cos(30°)
2. Calculate the frictional force:
The frictional force between the block and the surface can be calculated using the formula:
Frictional force = Coefficient of friction * Normal force
The normal force is the force exerted by the surface perpendicular to the block. In this case, the block is on a rough horizontal surface, so the normal force is equal to the weight of the block.
Normal force = mass * gravity
Normal force = 10 kg * 9.8 m/s^2
Now, using the given acceleration and Newton's second law, we can calculate the frictional force:
Frictional force = mass * acceleration
3. Find the coefficient of kinetic friction:
To find the coefficient of kinetic friction, we divide the frictional force by the normal force:
Coefficient of kinetic friction = Frictional force / Normal force
Now, let's plug in the values and calculate.
1. Calculation of the horizontal component of the applied force:
Horizontal force = 50 N * cos(30°)
2. Calculation of the frictional force:
Normal force = 10 kg * 9.8 m/s^2
Frictional force = 10 kg * 2.0 m/s^2
3. Calculation of the coefficient of kinetic friction:
Coefficient of kinetic friction = Frictional force / Normal force
By following these steps, you can find the value of the coefficient of kinetic friction.