A 40-kg block is dragged along a horizonatl surface by an applied force as shown. The coefficient of kinetic friction is µk = 0.4 and the block moves at constant velocity. What is the magnitude of F ?
M*g = 40 * 9.8 = 392 N. = Wt. of block = normal force(Fn).
u*Fn = 0.4 * 392 = 157 N. = Force of kinetic friction.
F - uFn = M*a
F - 157 = 40*0
F =
To find the magnitude of the applied force F, we can use the equation for the force of kinetic friction:
F_friction = µ * N
where F_friction is the force of kinetic friction, µ is the coefficient of kinetic friction, and N is the normal force.
In this case, the block is moving at a constant velocity, which means that the net force on the block is zero. The applied force F is opposing the force of kinetic friction. Therefore, the magnitude of F is equal to the force of kinetic friction F_friction.
To find the normal force N, we can use the equation:
N = m * g
where m is the mass of the block and g is the acceleration due to gravity.
Given:
Mass of the block (m) = 40 kg
Coefficient of kinetic friction (µk) = 0.4
Acceleration due to gravity (g) is approximately 9.8 m/s².
First, calculate the normal force N:
N = m * g
N = 40 kg * 9.8 m/s²
N = 392 N
Next, calculate the force of kinetic friction F_friction:
F_friction = µk * N
F_friction = 0.4 * 392 N
F_friction = 156.8 N
Finally, F (the magnitude of the applied force) is equal to F_friction, so the magnitude of F is 156.8 N.
To find the magnitude of the force F, we need to understand the forces acting on the block.
In this scenario, there are two main forces at play:
1. Applied force (F)
2. Kinetic friction force (Fk)
The applied force (F) is the force being exerted on the block to make it move. The kinetic friction force (Fk) is the opposing force generated due to the contact between the block and the surface it is being dragged on.
Since the block is moving at a constant velocity, we can conclude that the applied force (F) is equal in magnitude and opposite in direction to the kinetic friction force (Fk). Therefore, we have the equation:
F = Fk
The formula for kinetic friction force is given by:
Fk = µk * N
where µk is the coefficient of kinetic friction and N is the normal force.
In this case, the normal force (N) is equal in magnitude and opposite in direction to the gravitational force acting on the block.
The formula for gravitational force is:
Weight (W) = m * g
where m is the mass of the block and g is the acceleration due to gravity.
In this scenario, the weight (W) is equal and opposite to the normal force (N). Therefore, we have:
N = W = m * g
Now, substituting the value of N into the formula for kinetic friction force:
Fk = µk * N = µk * m * g
Since F = Fk, the magnitude of the applied force in this scenario is:
F = µk * m * g
Plugging in the given values:
µk = 0.4 (coefficient of kinetic friction)
m = 40 kg (mass of the block)
g = 9.8 m/s² (acceleration due to gravity)
F = 0.4 * 40 kg * 9.8 m/s²
F = 156.8 N
Therefore, the magnitude of the force F required to drag the 40-kg block at a constant velocity is 156.8 Newtons.