A 60 kg is pushed 12m across a horizontal floor by a horizontal force of 200N. The coefficient of kinetic friction is 0.3. How much work went into overcoming friction and how much work went into accelerating the box.
Wc = M*g = 60 * 9.8 = 588 N. = Normal force, Fn.
Fk = u*Fn = 0.3 * 588 = 176.4 N.
Work = Fk*d = 176.4 * 12 = 2117 J.
Fap-Fk = M*a.
200-176.4 = 60*a.
60a = 23.6.
a = 0.393 m/s^2.
Work = M*a * d = 60*0.393 * 12 = 283 J.
A 60kg box is pushed 12M acrosse horizontal floor by a horizontal force of 200N. The coefficient of kinetie friction is 0.3. How much work went in to over coming friction. How much in to acceleration the box.
To calculate the work done in different ways, we need to first calculate the force of kinetic friction acting on the box and the acceleration of the box.
1. Calculating the force of kinetic friction:
We can use the equation for friction force: F_friction = μ * F_normal, where F_friction is the force of kinetic friction, μ is the coefficient of kinetic friction, and F_normal is the normal force.
The normal force acting on the box is equal to the weight of the box, which can be calculated as F_normal = m * g, where m is the mass of the box and g is the acceleration due to gravity.
Given that the mass of the box is 60 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate:
F_normal = 60 kg * 9.8 m/s^2 = 588 N
Now we can calculate the force of kinetic friction:
F_friction = 0.3 * 588 N = 176.4 N
2. Calculating the acceleration of the box:
We can use Newton's second law of motion: F_net = m * a, where F_net is the net force acting on the box, m is the mass of the box, and a is the acceleration.
The net force acting on the box is equal to the applied force minus the force of friction:
F_net = F_applied - F_friction
Given that the applied force is 200 N, we can substitute the values to find the net force:
F_net = 200 N - 176.4 N = 23.6 N
Now we can calculate the acceleration:
23.6 N = 60 kg * a
a = 23.6 N / 60 kg
a ≈ 0.39 m/s^2
3. Calculating the work done to overcome friction:
The work done to overcome friction can be calculated using the equation: W_friction = F_friction * d, where W_friction is the work done to overcome friction, F_friction is the force of kinetic friction, and d is the displacement.
Given that the force of kinetic friction is 176.4 N and the displacement is 12 m, we can calculate:
W_friction = 176.4 N * 12 m = 2116.8 J
4. Calculating the work done to accelerate the box:
The work done to accelerate the box can be calculated using the equation: W_acceleration = F_net * d, where W_acceleration is the work done to accelerate the box, F_net is the net force, and d is the displacement.
Given that the net force is 23.6 N and the displacement is 12 m, we can calculate:
W_acceleration = 23.6 N * 12 m = 283.2 J
Therefore, the work done to overcome friction is 2116.8 J and the work done to accelerate the box is 283.2 J.
To find the work done in overcoming friction and the work done in accelerating the box, we need to use the equations for work and the concept of net force.
Work (W) is defined as the product of force (F) and the displacement (d) in the direction of the force. Mathematically, it can be represented by the equation:
W = F * d
First, let's calculate the work done in accelerating the box:
The net force (F_net) on an object is the vector sum of all the individual forces acting on it. In this case, we have a force applied horizontally and the force of friction opposing the motion. The equation for the net force is:
F_net = F_applied - F_friction
Given:
Applied force (F_applied) = 200 N
Coefficient of kinetic friction (μ) = 0.3
To calculate the frictional force (F_friction), we use the equation:
F_friction = μ * normal force
The normal force (N) is equal to the weight of the object, which can be calculated by multiplying the mass (m) by the acceleration due to gravity (g):
N = m * g
Given:
Mass (m) = 60 kg
Acceleration due to gravity (g) = 9.8 m/s^2
Now, let's calculate the work done in overcoming friction:
Using the frictional force (F_friction) and the displacement (d) of 12 m, we can substitute the values into the equation for work:
W_friction = F_friction * d
Finally, we can calculate the work done in accelerating the box:
Since the applied force (F_applied) is the net force, we can use the equation for work to find the work done in accelerating the box:
W_acceleration = F_applied * d
Now, let's substitute the values into the equations and calculate the work done:
First, calculate the normal force:
N = m * g
N = 60 kg * 9.8 m/s^2
N = 588 N
Next, calculate the frictional force:
F_friction = μ * N
F_friction = 0.3 * 588 N
F_friction = 176.4 N
Now, calculate the work done in overcoming friction:
W_friction = F_friction * d
W_friction = 176.4 N * 12 m
W_friction = 2116.8 J (Joules)
Finally, calculate the work done in accelerating the box:
W_acceleration = F_applied * d
W_acceleration = 200 N * 12 m
W_acceleration = 2400 J (Joules)
Therefore, the work done in overcoming friction is 2116.8 Joules, and the work done in accelerating the box is 2400 Joules.