two workers push horizontally in the same direction on a wooden 250 kg wooden crate that is on a wooden floor. (a) what total force must they exert to start the crate moving? (b) once moving , one worker exerts a force of 500N and the other exerts a force of 600N . Calculate the acceleration of crate
(a) Well, it seems that these workers have some serious determination, but unfortunately, I don't know their secret for sure. What I can tell you is that in order to get that stubborn wooden crate moving, they have to exert a force greater than the force of static friction. So, let's just say they'd need to pull harder than a mighty ox trying to escape a dreadful clown.
(b) Ah, once that crate is in motion, things get a bit more interesting. The net force acting on the crate would be the difference between the 600N force and the 500N force. That's like having a tug of war between a juggling chicken and a unicycling elephant.
Now, to calculate the acceleration, we can use Newton's second law, which states that force equals mass times acceleration (F = ma). Since we know the mass of the crate is 250 kg, we can rearrange the formula to find acceleration.
The difference between the two forces is 600N - 500N, which gives us 100N as the net force. Plugging this into the formula, we get:
100N = 250 kg * a
Solving for a, we find that the acceleration of the crate is a whopping 0.4 m/s². That's like a clown trying to sprint wearing big floppy shoes – not the quickest, but it's certainly something!
(a) To start the crate moving, the total force they must exert should overcome the static friction between the crate and the wooden floor. The static friction can be calculated using the formula:
Frictional force (Ff) = coefficient of static friction (μs) × normal force (Fn)
Since the crate is on a horizontal surface, the normal force is equal to the weight of the crate:
Fn = mass × gravitational acceleration = 250 kg × 9.8 m/s² = 2450 N
The coefficient of static friction depends on the materials involved. Let's assume it is μs = 0.3.
Ff = 0.3 × 2450 N = 735 N
Therefore, they must exert a total force of 735 N to start the crate moving.
(b) Once the crate is moving, the friction acting on it changes to kinetic friction. The kinetic frictional force can be calculated using the formula:
Ff = coefficient of kinetic friction (μk) × normal force (Fn)
Again, Fn = 2450 N. Let's assume the coefficient of kinetic friction is μk = 0.2.
Ff = 0.2 × 2450 N = 490 N
The net force on the crate is the difference between the force exerted by one worker (500 N) and the force exerted by the other worker (600 N):
Net force (Fnet) = 600 N - 500 N = 100 N
Since Fnet is smaller than Ff (100 N < 490 N), we can use Newton's second law of motion:
Fnet = mass × acceleration
Rearranging the equation to find acceleration (a):
a = Fnet / mass
a = 100 N / 250 kg
a = 0.4 m/s²
Therefore, the acceleration of the crate is 0.4 m/s².
To answer these questions, we need to apply Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass.
(a) To start the crate moving, the workers must overcome the static friction between the crate and the floor. The force required to do this is the maximum static friction force.
The formula to calculate the maximum static friction force is given by:
F_static = μ_s * N
Where:
F_static is the maximum static friction force,
μ_s is the coefficient of static friction between the crate and the floor, and
N is the normal force exerted by the crate on the floor.
Since the crate is on a horizontal floor, the normal force is equal to the weight of the crate, which is given by:
N = m * g
Where:
m is the mass of the crate, and
g is the acceleration due to gravity.
Plugging in the values:
m = 250 kg
g = 9.8 m/s^2 (approximate value)
N = 250 kg * 9.8 m/s^2
N = 2450 N
Assuming the coefficient of static friction between the crate and the floor is μ_s = 0.5 (hypothetical value):
F_static = 0.5 * 2450 N
F_static = 1225 N
Therefore, the total force the workers must exert to start the crate moving is 1225 N.
(b) Once the crate is moving, the static friction is replaced by kinetic friction, which is typically lower in magnitude. In this case, one worker exerts a force of 500N and the other exerts a force of 600N.
To calculate the acceleration, 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 kinetic friction:
Net force = (500N + 600N) - F_kinetic
Where:
F_kinetic is the force of kinetic friction.
Using the same formula as before, we can calculate the force of kinetic friction:
F_kinetic = μ_k * N
Assuming the coefficient of kinetic friction is μ_k = 0.4 (hypothetical value):
F_kinetic = 0.4 * 2450 N
F_kinetic = 980 N
Plugging in the values:
Net force = (500N + 600N) - 980 N
Net force = 1120 N - 980 N
Net force = 140 N
Finally, we can calculate the acceleration using Newton's second law:
acceleration = Net force / m
acceleration = 140 N / 250 kg
acceleration = 0.56 m/s²
Therefore, the acceleration of the crate is 0.56 m/s².