When a horizontal force of magnitude 14.7 Newton is applied to a body of mass 4 kg which is resting on a rough horizontal plane, the body is found to be in limiting equilibrium.
Calculate the resultant reaction P (Newton) acting on the body.
To find the resultant reaction force acting on the body, we need to consider the forces involved in the system.
1. Weight (mg): The weight of the body can be calculated using the formula:
Weight = mass × gravitational acceleration
In this case, the mass is 4 kg and the standard gravitational acceleration is approximately 9.8 m/s². Therefore,
Weight = 4 kg × 9.8 m/s² = 39.2 N (acting vertically downward)
2. Applied force (F): The applied force is given as 14.7 N, acting horizontally.
3. Frictional force (Ff): The frictional force acts in the opposite direction to the applied force. Since the body is in limiting equilibrium, the frictional force must be equal in magnitude and opposite in direction to the applied force, meaning:
Frictional force (Ff) = -14.7 N
To determine the resultant reaction force (P), we need to find the net force acting vertically. In limiting equilibrium, the net force in the vertical direction must be zero.
Net force in the vertical direction = Reaction force (P) - Weight
Since the body is in limiting equilibrium, the net force in the vertical direction must be zero. Therefore, the reaction force equals the weight:
P = Weight = 39.2 N
Hence, the resultant reaction force (P) acting on the body is 39.2 Newtons, vertically upward.
To calculate the resultant reaction force P acting on the body, we need to consider the forces acting on the body and the condition of limiting equilibrium.
In this scenario, we have a horizontal force (F) applied to the body and a reaction force (R) acting on it in the opposite direction. Since the body is in limiting equilibrium, the net force acting on it will be zero.
The weight of the body (W) can be calculated using the formula W = m * g, where m is the mass of the body (4 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
W = 4 kg * 9.8 m/s^2 = 39.2 N
In order for the body to be in limiting equilibrium, the reaction force R must have the same magnitude as the applied force F but act in the opposite direction.
Since the net force acting on the body is zero, we can write:
F - R = 0
Given that F = 14.7 N, we can rearrange the equation to solve for R:
R = F = 14.7 N
Therefore, the resultant reaction force P acting on the body is 14.7 N.