Two forces F1 and F2 act on the 7.00 kg block in opposite directions. The magnitude of these forces are F1 = -59 N and F2 = +33.0 N. What is the horizontal acceleration (magnitude and direction of the block?)

To find the horizontal acceleration of the block, we need to determine the net force acting on it. The net force is the vector sum of the individual forces acting on the block.

In this case, the individual forces F1 and F2 are acting in opposite directions. Since F1 is negative and F2 is positive, we can interpret them as forces in the left and right directions, respectively.

To calculate the net force, we can add the magnitudes of F1 and F2 and assign a sign based on their directions. Since F1 is negative and F2 is positive, we subtract the magnitude of F1 from F2:

Net force = F2 - F1 = 33.0 N - (-59 N) = 33.0 N + 59 N = 92.0 N

The net force acting on the block is 92.0 N in the direction of F2 (right).

Next, we can use Newton's second law (F = ma) to relate the net force to the acceleration of the block, where F is the net force and m is the mass of the block.

Since the problem states that the mass of the block is 7.00 kg, we can substitute the values into the equation:

92.0 N = 7.00 kg * a

Solving for the acceleration (a):

a = 92.0 N / 7.00 kg
≈ 13.14 m/s²

Therefore, the magnitude of the horizontal acceleration of the block is approximately 13.14 m/s², and the direction of the block's acceleration is to the right.

To find the horizontal acceleration of the block, we need to calculate the net force acting on it.

The net force can be determined by adding the individual forces together. Since F1 and F2 act in opposite directions, we need to consider their signs. Let's assign positive to the right and negative to the left.

F1 = -59 N (opposite direction of motion)
F2 = +33 N (same direction as motion)

Now, let's find the net force:

Net force = F1 + F2

Net force = -59 N + 33 N

Net force = -26 N

The net force is -26 N, which means the resulting force is acting in the left direction.

To find the acceleration, we can use Newton's second law:

Net force = mass × acceleration

Since the mass of the block is given as 7.00 kg, we can rearrange the equation to solve for acceleration:

acceleration = Net force / mass

acceleration = -26 N / 7.00 kg

Using a calculator, we can find the acceleration:

acceleration ≈ -3.71 m/s²

Therefore, the magnitude of the horizontal acceleration of the block is approximately 3.71 m/s², and the direction of acceleration is to the left.

F = ma

so plug in your numbers.