Suppose two children push horizontally, but in exactly opposite directions, on a third child in a wagon. The first child exerts a force of 73.0 N, the second a force of 95.0 N, friction is 14.0 N, and the mass of the third child plus wagon is 23.0 kg. Calculate the acceleration in m/s2. (Enter the magnitude.)
net force is ... 95.0 - 73.0 - 14.0 ... in the direction of the 95.0 force
acceleration = net force / mass
To calculate the acceleration, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
First, we need to find the net force acting on the third child and the wagon. The net force is the sum of all the forces acting on the object. In this case, we have two forces pushing in opposite directions (73.0 N and 95.0 N) and friction opposing the motion (-14.0 N).
Net force = Force 1 + Force 2 + Force of friction
Net force = 73.0 N - 95.0 N - 14.0 N
Net force = -36.0 N
Since the forces are opposing each other, we consider the net force to be negative.
Now, we can calculate the acceleration using Newton's second law:
Acceleration = Net force / mass
Acceleration = -36.0 N / 23.0 kg
Acceleration ≈ -1.57 m/s^2
The negative sign indicates that the wagon and third child will accelerate in the opposite direction of the total force.
To calculate the acceleration, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
The net force is the difference between the two forces applied by the children, minus the friction force:
Net Force = 73.0 N - 95.0 N - 14.0 N
= -36.0 N
Since the forces are opposite in direction, we take the negative sign.
Now, we can calculate the acceleration using the formula:
Net Force = Mass * Acceleration
Rearranging the formula to solve for acceleration:
Acceleration = Net Force / Mass
Acceleration = -36.0 N / 23.0 kg
Acceleration = -1.57 m/s^2
Therefore, the acceleration is approximately -1.57 m/s^2.