A 10 kg box is pushed across horizontally to the right with 60N of force. The box accelerates to the right at 2 m/s^2 what is the coefficient of friction
force= mass * acceleration
60 - Ff = 10 * 2
To find the coefficient of friction, we can use the equation:
frictional force = coefficient of friction * normal force
First, let's find the normal force acting on the box. The normal force is equal to the force of gravity acting on the box, which can be calculated using the formula:
force of gravity = mass * gravitational acceleration
where the mass is 10 kg and the gravitational acceleration is approximately 9.8 m/s^2.
force of gravity = 10 kg * 9.8 m/s^2 = 98 N
Next, let's determine the frictional force acting on the box. The frictional force is proportional to the normal force and is given by Newton's second law:
frictional force = mass * acceleration
where the mass is 10 kg and the acceleration is 2 m/s^2.
frictional force = 10 kg * 2 m/s^2 = 20 N
Now we can substitute the values into the first equation to find the coefficient of friction:
20 N = coefficient of friction * 98 N
Dividing both sides of the equation by 98 N gives:
coefficient of friction = 20 N / 98 N
Simplifying this expression gives the value of the coefficient of friction:
coefficient of friction ≈ 0.2041
To find the coefficient of friction, we need to use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the net force is the force applied minus the force of friction.
Given:
Mass (m) = 10 kg
Force applied (F_applied) = 60 N
Acceleration (a) = 2 m/s^2
Step 1: Calculate the net force acting on the box.
The net force (F_net) is equal to the force applied minus the force of friction.
F_net = F_applied - F_friction
Step 2: Calculate the force of friction.
The force of friction (F_friction) can be determined using the formula:
F_friction = μ * N
where μ is the coefficient of friction and N is the normal force.
Step 3: Calculate the normal force.
The normal force (N) is the force exerted by a surface to support the weight of an object resting on it. In this case, since the box is pressed horizontally against the surface, the normal force is equal to the box's weight, which is given by:
N = m * g
where g is the acceleration due to gravity, approximately 9.8 m/s^2.
Step 4: Substitute the known values into the equations.
F_net = F_applied - F_friction
F_friction = μ * N
N = m * g
Substituting for N:
F_friction = μ * (m * g)
Substituting for F_friction in the F_net equation:
F_net = F_applied - μ * (m * g)
Substituting for F_net in Newton's second law equation:
m * a = F_applied - μ * (m * g)
Step 5: Solve for the coefficient of friction (μ).
Rearranging the equation to isolate μ, we get:
μ = (F_applied - m * a) / (m * g)
Substituting the known values:
μ = (60 N - 10 kg * 2 m/s^2) / (10 kg * 9.8 m/s^2)
Simplifying the equation:
μ = (60 N - 20 N) / 98 N
μ = 40 N / 98 N
μ ≈ 0.408 (approximately)
Therefore, the coefficient of friction is approximately 0.408.