a student applies a 100 n force at an angle 55 degrees above the horizontal to a 20 kg box. The coefficient of static friction is 0.43, and the coefficient of kinetic friction is 0.3. Describe the motion of the box.
To describe the motion of the box, we need to compare the applied force to the maximum frictional force that can be exerted on the box. Let's break down the problem step by step:
Step 1: Determine the normal force
The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the weight of the box is equal to its mass multiplied by the acceleration due to gravity (9.8 m/s^2). So, the weight of the box can be calculated as follows:
Weight = mass × acceleration due to gravity
Weight = 20 kg × 9.8 m/s^2
Weight = 196 N
Since the box is on a flat surface and not accelerating vertically, the normal force must counterbalance the weight of the box. Therefore, the normal force is equal to the weight of the box, which is 196 N.
Step 2: Calculate the maximum static frictional force
The maximum static frictional force can be calculated using the equation:
Friction force (static) = coefficient of static friction × normal force
Given that the coefficient of static friction is 0.43, and the normal force is 196 N, the maximum static frictional force can be calculated as follows:
Friction force (static) = 0.43 × 196 N
Friction force (static) ≈ 84.28 N
Step 3: Compare the applied force with the maximum static frictional force
Since the applied force is given as 100 N, we can compare it to the maximum static frictional force to determine the motion of the box.
Case 1: Applied force is less than the maximum static frictional force
If the applied force is less than the maximum static frictional force, i.e., 100 N < 84.28 N, the box will not move since the static frictional force can balance the applied force. So, the box will remain stationary.
Case 2: Applied force is equal to the maximum static frictional force
If the applied force is exactly equal to the maximum static frictional force, i.e., 100 N = 84.28 N, the box will initially remain stationary but will start to move if a slight external force is applied.
Case 3: Applied force is greater than the maximum static frictional force
If the applied force is greater than the maximum static frictional force, i.e., 100 N > 84.28 N, the box will experience a net force in the direction of the applied force. As a result, the box will start to move in the direction specified by the force.
Once the box starts moving, the type of friction acting on it changes from static to kinetic friction.
Step 4: Determine the kinetic frictional force
The kinetic frictional force can be calculated using the equation:
Friction force (kinetic) = coefficient of kinetic friction × normal force
Given that the coefficient of kinetic friction is 0.3, and the normal force is 196 N, the kinetic frictional force can be calculated as follows:
Friction force (kinetic) = 0.3 × 196 N
Friction force (kinetic) = 58.8 N
If the applied force is greater than the kinetic frictional force, i.e., 100 N > 58.8 N, the box will continue to move with a net force equal to the difference between the applied force and the kinetic frictional force.
In summary, if the student applies a 100 N force at an angle of 55 degrees above the horizontal to the box, the box will start moving in the direction specified by the force if the applied force exceeds the maximum static frictional force (84.28 N). Once the box starts moving, it will continue to move with a net force equal to the difference between the applied force and the kinetic frictional force (58.8 N).