A man is pulling a block with a mass of 6.2 kg across a horizontal surface and accelerates the block at a
rate of 0.50 m/s^2
. The coefficient of kinetic friction between the block and the surface is 0.24. What is
the magnitude of the force with which the man pulls?
To find the magnitude of the force with which the man pulls, we need to consider the forces acting on the block.
The force of friction opposing the motion of the block can be calculated using the formula:
Frictional force = coefficient of kinetic friction * normal force
The normal force can be calculated using the formula:
Normal force = mass * acceleration due to gravity
In this case, the acceleration due to gravity is approximately 9.8 m/s^2.
Normal force = 6.2 kg * 9.8 m/s^2 = 60.76 N
Frictional force = 0.24 * 60.76 N = 14.53 N
To accelerate the block at a rate of 0.50 m/s^2, the man needs to overcome the force of friction and provide an additional force. This additional force can be calculated using Newton's second law:
Force = mass * acceleration
Force = 6.2 kg * 0.50 m/s^2 = 3.1 N
The magnitude of the force with which the man pulls is the sum of the force of friction and the additional force:
Magnitude of force = 14.53 N + 3.1 N = 17.63 N
Therefore, the magnitude of the force with which the man pulls is approximately 17.63 N.
To find the magnitude of the force with which the man pulls the block, we need to consider the forces acting on the block and use Newton's second law of motion.
Newton's second law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. Mathematically, it can be written as:
F_net = m * a
Where:
- F_net is the net force acting on the block
- m is the mass of the block
- a is the acceleration of the block
In this case, the only force acting in the horizontal direction is the force with which the man pulls the block. There is also the force of friction opposing the motion, but since the block is already moving (given the coefficient of kinetic friction), we don't need to consider static friction.
The force of friction can be calculated using the equation:
f_friction = μ * N
Where:
- f_friction is the force of friction
- μ is the coefficient of kinetic friction
- N is the normal force
The normal force is the perpendicular force exerted by the surface on the object and can be calculated as:
N = m * g
Where:
- m is the mass of the block
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
Now, let's calculate the force with which the man pulls the block.
First, calculate the force of friction:
f_friction = 0.24 * (6.2 kg * 9.8 m/s^2)
Next, substitute the force of friction into Newton's second law to solve for the net force:
F_net = m * a
F_net = 6.2 kg * 0.50 m/s^2
Finally, since the force of friction is in the opposite direction of the applied force, the magnitude of the force with which the man pulls the block is equal to the net force, which can be calculated as:
Force = F_net + f_friction
To find the magnitude of the force with which the man pulls the block, we can use Newton's Second Law of Motion. The formula for this law is:
F_net = m * a
Where:
F_net is the net force acting on the object,
m is the mass of the object, and
a is the acceleration of the object.
In this case, the mass of the block is given as 6.2 kg and the acceleration is given as 0.50 m/s^2. We need to find the net force F_net.
The net force can be calculated by considering the forces acting on the block. There are two forces to consider: the force applied by the man (pulling force) and the force of friction.
The force of friction can be calculated using the formula:
f_friction = μ * f_normal
Where:
μ is the coefficient of kinetic friction, and
f_normal is the normal force.
The normal force is equal to the weight of the block, which can be calculated using the formula:
f_normal = m * g
Where:
m is the mass of the block, and
g is the acceleration due to gravity (approximately 9.8 m/s^2).
Now, we can substitute the values into the formulas to find the force of friction and the net force. Let's start with the force of friction:
f_friction = μ * f_normal
= μ * (m * g)
Given that the coefficient of kinetic friction (μ) is 0.24 and the mass (m) is 6.2 kg, we can calculate the normal force:
f_normal = m * g
= 6.2 kg * 9.8 m/s^2
Now, let's substitute the normal force into the formula for the force of friction:
f_friction = 0.24 * (6.2 kg * 9.8 m/s^2)
Next, subtract the force of friction from the net force to find the pulling force applied by the man:
F_net = f_friction - f_normal
Finally, we can find the magnitude of the force with which the man pulls by taking the absolute value of the net force:
|F_net| = |f_friction - f_normal|
Let's calculate the value:
f_normal = 6.2 kg * 9.8 m/s^2 = 60.76 N
f_friction = 0.24 * (6.2 kg * 9.8 m/s^2) = 31.9872 N
F_net = 31.9872 N - 60.76 N = -28.7728 N
|F_net| = |-28.7728 N| = 28.7728 N
Therefore, the magnitude of the force with which the man pulls the block is approximately 28.7728 N.