a horizontal force of 95 N is applied to 60 kg crate on rough , level surface. if crate accelerates at 1.20 m/s2 , what is magnitude of the force of kinetic friction acting on the crate?
Friction = (95 N) - (60 kg)(1.20 m/s2) = 57 N
To find the magnitude of the force of kinetic friction acting on the crate, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
Here's how you can calculate it step by step:
Step 1: Identify the given values:
- Applied horizontal force (F) = 95 N
- Mass of the crate (m) = 60 kg
- Acceleration of the crate (a) = 1.20 m/s²
Step 2: Calculate the net force acting on the crate:
- Net force (F_net) = m * a
Substituting the values:
F_net = 60 kg * 1.20 m/s²
F_net = 72 N
Step 3: Determine the force of kinetic friction:
The force of kinetic friction can be found using the equation:
F_friction = μ * N
where μ is the coefficient of kinetic friction, and N is the normal force.
The normal force (N) is equal to the weight of the crate, which is given by:
N = m * g
where g is the acceleration due to gravity, approximately 9.8 m/s².
N = 60 kg * 9.8 m/s²
N = 588 N
Step 4: Substitute the known values to calculate the force of kinetic friction:
F_friction = μ * 588 N
Since the crate is already accelerating, it implies that the applied force is greater than the force of kinetic friction. Therefore, the maximum force of kinetic friction (F_friction) can be calculated as follows:
F_friction = F_net
72 N = μ * 588 N
Step 5: Solve for the coefficient of kinetic friction (μ):
μ = 72 N / 588 N
μ ≈ 0.1224
Step 6: Finally, calculate the magnitude of the force of kinetic friction:
F_friction = μ * N
F_friction = 0.1224 * 588 N
F_friction ≈ 72 N
Therefore, the magnitude of the force of kinetic friction acting on the crate is approximately 72 N.
To find the magnitude of the force of kinetic friction acting on the crate, you can use Newton's second law of motion.
Newton's second law of motion states that the net force on an object is equal to the product of its mass and acceleration:
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 horizontal force applied to the crate is causing it to accelerate. Since the crate is on a rough, level surface, the force of kinetic friction opposes the applied force, resulting in net force.
The formula for the force of kinetic friction is given by:
f_kinetic = μ * N
where:
f_kinetic is the force of kinetic friction,
μ is the coefficient of kinetic friction, and
N is the normal force exerted on the object.
The normal force can be calculated as:
N = m * g
where:
g is the acceleration due to gravity (approximately 9.8 m/s^2).
Now let's put all the values into the equations:
Given:
Applied force (F_net) = 95 N
Mass of the crate (m) = 60 kg
Acceleration (a) = 1.20 m/s^2
Coefficient of kinetic friction (μ) = unknown
Net force (F_net) = m * a
95 N = 60 kg * 1.20 m/s^2
95 N = 72 N
From here, we can determine the coefficient of kinetic friction.
f_kinetic = μ * N
f_kinetic = μ * (m * g)
Substituting the given values:
72 N = μ * (60 kg * 9.8 m/s^2)
Simplifying the equation:
72 N = μ * 588 N
Dividing both sides by 588 N:
μ = 72 N / 588 N
μ ≈ 0.122
Therefore, the magnitude of the force of kinetic friction acting on the crate is approximately 0.122.