Karen and Bill are rearranging furniture in their house, but they don’t always agree on where all the items should go. At one instant, Karen pushes a large chest of drawers (mass of 20kg) horizontally to the right with a force of 35N, while Bill pushes horizontally to the left with a force of 45N. The chest is on a slippery marble floor, so it slides with essentially no friction. (Karen and Bill are both wearing rubber-soled shoes, so they get good traction.) What is the magnitude of the acceleration of the chest?

Question

Karen and Bill are rearranging furniture in their house, but they don’t always agree on where all the items should go. At one instant, Karen pushes a large chest of drawers (mass of 20kg) horizontally to the right with a force of 35N, while Bill pushes horizontally to the left with a force of 45N. The chest is on a slippery marble floor, so it slides with essentially no friction. (Karen and Bill are both wearing rubber-soled shoes, so they get good traction.) What is the magnitude of the acceleration of the chest?

Answer 1

F1 = 35 N.

F2 = -45 N.

a=(F1+F2)/m = (35 + (-45))/20=-0.5m/s^2=
0.5 m/s^2 To the left.

Answer 2

To find the magnitude of the acceleration of the chest, 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. Mathematically, this can be written as:

a = net force / mass

In this case, the net force acting on the chest can be calculated by finding the vector sum of Karen's force and Bill's force. Since Karen pushes to the right with a force of 35N and Bill pushes to the left with a force of 45N, we can subtract the magnitudes:

net force = 35N - 45N = -10N

Note that we have the negative sign because the forces are in opposite directions.

Now, we can substitute the values into the formula to find the acceleration:

a = (-10N) / 20kg = -0.5 m/s^2

The magnitude of the acceleration of the chest is 0.5 m/s^2. Since both Karen and Bill are pushing horizontally in opposite directions, the chest will experience a deceleration of 0.5 m/s^2.

Answer 3

To find the magnitude of the acceleration of the chest, we can 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.

In this case, there are two forces acting on the chest: Karen is pushing to the right with a force of 35N, and Bill is pushing to the left with a force of 45N. The net force is the difference between these two forces:

Net force = 35N - 45N
= -10N (since Karen's force is in the opposite direction to Bill's force)

Now, we can use Newton's second law of motion to find the acceleration:

Net force = mass x acceleration

-10N = 20kg x acceleration

Dividing both sides by 20kg:

acceleration = -10N / 20kg
= -0.5 m/s^2

So, the magnitude of the acceleration of the chest is 0.5 m/s^2.