Our 10kg mystery box rests on a horizontal floor. The
coefficient of static friction is 0.4 and the coefficient
of kinetic friction is 0.3. Determine the force of
friction acting on the box if a horizontal external
applied force is exerted on it of magnitude:
• (a) 0, (b) 10 N, (c) 20 N, (d) 38 N, and (e) 40 N.
To determine the force of friction acting on the box, we need to consider the different scenarios where a horizontal external force is exerted on it.
Given:
Mass of the box (m) = 10 kg
Coefficient of static friction (μs) = 0.4
Coefficient of kinetic friction (μk) = 0.3
Let's analyze each scenario step-by-step:
(a) When the applied force is 0 (F_applied = 0):
In this case, the box is at rest, and the force of friction is due to static friction.
The formula for calculating static friction is:
F_friction_static = μs * N
Where N is the normal force, which is equal to the weight of the box (m * g), where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Substituting the values:
F_friction_static = 0.4 * (10 kg * 9.8 m/s^2)
F_friction_static = 39.2 N
Therefore, the force of friction when no external force is applied is 39.2 N.
(b) When the applied force is 10 N (F_applied = 10 N):
In this case, the box is being pushed with a force of 10 N, but it is still at rest because the applied force is not enough to overcome static friction.
Thus, the force of friction remains at 39.2 N.
(c) When the applied force is 20 N (F_applied = 20 N):
In this case, the applied force is greater than the maximum force of static friction to keep the box at rest. Therefore, the box will start moving, and the force of friction will transition from static to kinetic.
The formula for calculating kinetic friction is:
F_friction_kinetic = μk * N
Substituting the values:
F_friction_kinetic = 0.3 * (10 kg * 9.8 m/s^2)
F_friction_kinetic = 29.4 N
Therefore, the force of friction when an external force of 20 N is applied is 29.4 N.
(d) When the applied force is 38 N (F_applied = 38 N):
In this case, the applied force is just enough to overcome static friction and keep the box at rest.
Thus, the force of friction will be equal to the applied force, which is 38 N.
(e) When the applied force is 40 N (F_applied = 40 N):
In this case, the applied force is greater than the maximum force of static friction. The box will start moving, and the force of friction will transition to kinetic.
The formula for calculating kinetic friction is:
F_friction_kinetic = μk * N
Substituting the values:
F_friction_kinetic = 0.3 * (10 kg * 9.8 m/s^2)
F_friction_kinetic = 29.4 N
Therefore, the force of friction when an external force of 40 N is applied is 29.4 N.
To summarize:
(a) F_friction = 39.2 N
(b) F_friction = 39.2 N
(c) F_friction = 29.4 N
(d) F_friction = 38 N
(e) F_friction = 29.4 N
To determine the force of friction acting on the box, we need to consider the two scenarios: when the box is at rest (static friction) and when the box is moving (kinetic friction).
1. When the box is at rest (static friction):
The maximum force of static friction can be calculated using the equation:
\(F_{\text{static friction}} = \mu_s \cdot N\)
where \(F_{\text{static friction}}\) is the force of static friction, \(\mu_s\) is the coefficient of static friction, and \(N\) is the normal force.
The normal force, in this case, is equal to the weight of the box, which can be calculated using the equation:
\(N = m \cdot g\)
where \(m\) is the mass of the box and \(g\) is the acceleration due to gravity.
Given that the mass of the box is 10 kg and the acceleration due to gravity is approximately 9.8 m/s\(^2\), we can calculate the normal force:
\(N = 10 \, \text{kg} \cdot 9.8 \, \text{m/s}^2\)
Next, we can calculate the force of static friction for each scenario: a) 0 N, b) 10 N, c) 20 N, d) 38 N, and e) 40 N.
2. When the box is moving (kinetic friction):
The force of kinetic friction is given by the equation:
\(F_{\text{kinetic friction}} = \mu_k \cdot N\)
where \(F_{\text{kinetic friction}}\) is the force of kinetic friction, \(\mu_k\) is the coefficient of kinetic friction, and \(N\) is the normal force.
We can now calculate the force of kinetic friction for each scenario: a) 0 N, b) 10 N, c) 20 N, d) 38 N, and e) 40 N.
By following these steps, we can determine the force of friction acting on the box in each scenario.