A 100 N force is applied to a 50.0 kg crate resting on a level florr. The coeeficient of kinetic friction is 0.15.
a. What is the acceleration of the crate?
a = F(net)/m
F(net) = 100 N - (friction force)
Why did the crate go to the therapist?
Because it was feeling a little too frictional!
To find the acceleration of the crate, we first need to calculate the net force acting on it.
The formula to calculate the net force is:
Net Force = Applied Force - Force of Friction
Given:
Applied Force (F_applied) = 100 N
Coefficient of Kinetic Friction (μ_k) = 0.15
Now, we need to calculate the force of friction using the formula:
Force of Friction (F_friction) = μ_k * Normal Force
To find the normal force, we'll use the equation:
Normal Force (N) = mass * gravity
Given:
Mass (m) = 50.0 kg
Gravity (g) = 9.8 m/s^2
Let's calculate the normal force:
N = m * g
N = 50.0 kg * 9.8 m/s^2
N = 490 N
Now we can calculate the force of friction:
F_friction = μ_k * N
F_friction = 0.15 * 490 N
F_friction = 73.5 N
Finally, we can calculate the net force and the acceleration:
Net Force = F_applied - F_friction
Net Force = 100 N - 73.5 N
Net Force = 26.5 N
To find the acceleration (a), we'll use Newton's second law of motion:
Net Force = mass * acceleration
26.5 N = 50.0 kg * a
Solving for a:
a = 26.5 N / 50.0 kg
a ≈ 0.53 m/s^2
Therefore, the acceleration of the crate is approximately 0.53 m/s^2.
To find the acceleration of the crate, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.
The formula for calculating acceleration is:
acceleration = net force / mass
In this case, the net force is the applied force minus the force of friction.
Step 1: Calculate the force of friction
The force of friction can be calculated using the formula: force of friction = coefficient of friction * normal force
Given:
Coefficient of kinetic friction (μ) = 0.15
Normal force (Fn) = mass * acceleration due to gravity (g)
Since the crate is on a level floor, the normal force is equal to the weight of the crate, which can be calculated as:
Fn = mass * g
Mass (m) = 50.0 kg
Acceleration due to gravity (g) = 9.8 m/s^2 (approximately)
Now, substitute the values into the formula to find the force of friction:
force of friction = 0.15 * (50.0 kg * 9.8 m/s^2)
Step 2: Calculate the acceleration
The net force is equal to the applied force minus the force of friction.
Given:
Applied force (F) = 100 N
Now, substitute the values into the formula to find the acceleration:
net force = applied force - force of friction
Finally,
acceleration = net force / mass
Substitute the values into the formula to calculate the acceleration.
Fk=(0.15)50kg
Fk=7.5 N
100N-7.5N=92.5N/50kg=1.85M/s^2
thanks