A box weighting 200N is pushed on a horizontal floor. What acceleration will result if a horizontal force of 100N is applied to the box.? coefficient of friction is 0.4
The friction force in the reverse direction is 200*0.4 = 80 N.
The net forward force acting on the box is therefore
Fnet = 100 - 80 = 20 N
Acceleration = Fnet/Mass = Fnet*g/(Weight)
= 20*9.8/200 = 0.98 m/s^2
Thanks. I have also done the same solution. Just confirming it. Thanks!
To find the acceleration of the box, we need to consider the forces acting on it and use Newton's second law of motion.
1. Identify the forces acting on the box:
- The force applied horizontally, F_applied = 100N
- The weight of the box, W = 200N
- The force of friction, F_friction
2. Calculate the force of friction:
The force of friction can be determined using the formula: F_friction = coefficient of friction * normal force.
The normal force (N) is equal to the weight of the box (W). So, N = 200N.
F_friction = 0.4 * 200N
F_friction = 80N
3. Determine the net force acting on the box:
The net force acting on the box is the difference between the applied force and the force of friction:
Net force = F_applied - F_friction
Net force = 100N - 80N
Net force = 20N
4. Apply Newton's second law of motion:
Newton's second law states that the net force on an object is equal to the product of its mass and acceleration:
Net force = mass * acceleration
Since we're given the weight of the box, we can use the equation: W = mass * gravity
200N = mass * 9.8m/s^2
mass = 200N / 9.8m/s^2
mass ≈ 20.41 kg
Now plug in the values into the equation:
20N = (20.41 kg) * acceleration
5. Solve for acceleration:
acceleration = 20N / 20.41 kg
acceleration ≈ 0.98 m/s^2
Therefore, the acceleration of the box when a horizontal force of 100N is applied to it is approximately 0.98 m/s^2.
To find the acceleration of the box, we first need to calculate the net force acting on it. The net force is the vector sum of all the forces acting on the box.
In this case, we have two forces acting on the box:
1. The applied force of 100N pushing the box forward.
2. The force of friction opposing the motion.
The force of friction can be calculated using the equation: friction force = coefficient of friction * normal force
The normal force is the force exerted by the surface on the box, which is equal to the weight of the box on a horizontal surface. Therefore, normal force = weight of the box = 200N.
Now, let's calculate the force of friction:
friction force = 0.4 * 200N
friction force = 80N
Since the applied force and the force of friction act in opposite directions, we need to subtract the force of friction from the applied force to find the net force:
net force = applied force - force of friction
net force = 100N - 80N
net force = 20N
Finally, we can use Newton's second law of motion to find the acceleration of the box:
acceleration = net force / mass
Since we are not given the mass of the box, we can use the equation weight = mass * gravity to find the mass. The weight is given as 200N, and the acceleration due to gravity is approximately 9.8 m/s^2.
mass = weight / gravity
mass = 200N / 9.8 m/s^2
mass ≈ 20.41 kg
Now, we can calculate the acceleration:
acceleration = net force / mass
acceleration = 20N / 20.41 kg
acceleration ≈ 0.98 m/s^2
So, the acceleration of the box will be approximately 0.98 m/s^2 when a horizontal force of 100N is applied to it.