A 46.6 kg crate is at rest on a level floor, and te coefficient of kinetic friction is 0.32. The acceleration of gravity is 9.8M/s^2. If the crate is pushed horizontally with a force of 201.67 N, how far does it move in 3.42s? Answer in units of m
First calculate the friction force, Ff.
Ff = (0.32)*M*g = 146.14 Newtons
Then calculate the net horizontal force on the box
Fnet = 211.67 - 146.14 = 65.53 N
Then calculate the acceleration
a = Fnet/M = 1.41 m/s^2
Then use
Distance moved = (1/2) a t^2
(for a starting velocity of zero)
Well, it seems like the crate wants to enjoy a nice slide on the floor! Let's calculate how far it will go.
To figure out the distance, we need to find the net force acting on the crate. The net force is the difference between the applied force and the force of friction.
The force of friction can be found by multiplying the coefficient of kinetic friction (0.32) by the normal force. The normal force is equal to the weight of the crate, which can be calculated by multiplying its mass (46.6 kg) by the acceleration due to gravity (9.8 m/s^2).
Normal force = mass * acceleration due to gravity
Normal force = 46.6 kg * 9.8 m/s^2
Now, the force of friction can be calculated using the formula:
Force of friction = coefficient of kinetic friction * normal force
Alright, but what about the net force? Well, we can subtract the force of friction from the applied force.
Net force = applied force - force of friction
Once we have the net force, we can now calculate the acceleration of the crate using Newton's second law of motion, which states:
Force = mass * acceleration
Rearranging the equation, we get:
Acceleration = net force / mass
Now that we have the acceleration, we can use the following equation to find the distance:
Distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Since the crate is at rest initially, its initial velocity is zero.
So, let's put these steps together and solve the problem:
Step 1: Calculate the normal force.
Normal force = 46.6 kg * 9.8 m/s^2
Step 2: Calculate the force of friction.
Force of friction = 0.32 * normal force
Step 3: Calculate the net force.
Net force = 201.67 N - force of friction
Step 4: Calculate the acceleration.
Acceleration = net force / mass
Step 5: Calculate the distance.
Distance = 0.5 * acceleration * time^2
Plug in the given values and calculate the distance.
To find how far the crate moves, we need to calculate the net force acting on it and apply Newton's second law of motion.
1. Determine the normal force:
The normal force is equal to the weight of the crate, which is given by the formula:
weight = mass * acceleration due to gravity
weight = 46.6 kg * 9.8 m/s^2
weight = 455.48 N
Therefore, the normal force acting on the crate is 455.48 N.
2. Calculate the force of friction:
The force of friction can be found using the equation:
force of friction = coefficient of kinetic friction * normal force
force of friction = 0.32 * 455.48 N
force of friction = 145.7536 N
3. Calculate the net force:
The net force is equal to the applied force minus the force of friction:
net force = applied force - force of friction
net force = 201.67 N - 145.7536 N
net force = 55.9164 N
4. Calculate the acceleration:
The acceleration can be calculated using Newton's second law:
acceleration = net force / mass
acceleration = 55.9164 N / 46.6 kg
acceleration = 1.2 m/s^2
5. Calculate the distance:
The distance can be calculated using the equation of motion:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Since the crate is initially at rest, the initial velocity is 0 m/s.
distance = 0 + (0.5 * 1.2 m/s^2 * (3.42 s)^2)
distance = 0.5 * 1.2 m/s^2 * 11.7364 s^2
distance = 7.0428 m
Therefore, the crate moves approximately 7.04 meters in 3.42 seconds.
To find out how far the crate moves in 3.42 seconds, we can use the equations of motion and the concept of friction.
First, let's calculate the force of friction acting on the crate. The force of friction can be found using the equation:
friction force = coefficient of kinetic friction * normal force
The normal force is equal to the weight of the crate, which can be calculated by multiplying its mass by the acceleration due to gravity:
normal force = mass * acceleration due to gravity
normal force = 46.6 kg * 9.8 m/s^2
Now we can find the friction force:
friction force = 0.32 * (46.6 kg * 9.8 m/s^2)
Next, let's determine the net force acting on the crate. The net force is the difference between the applied force and the force of friction:
net force = applied force - friction force
net force = 201.67 N - friction force
Now, using Newton's second law of motion (F = ma), we can find the acceleration of the crate:
net force = mass * acceleration
acceleration = net force / mass
Finally, we can use the kinematic equation to find the distance traveled by the crate:
distance = initial velocity * time + (1/2) * acceleration * time^2
Since the crate is at rest initially, the initial velocity is zero:
distance = (1/2) * acceleration * time^2
Substituting the values we've calculated:
distance = (1/2) * acceleration * (3.42 s)^2
distance = (1/2) * (net force / mass) * (3.42 s)^2
distance = (1/2) * (201.67 N - friction force) / 46.6 kg * (3.42 s)^2
Calculating the value of the distance will give the final answer in units of meters.