Question

If the magnitudes of the forces are \(F_1 = 59.5 \, \text{N}\) and \(F_2 = 25.0 \, \text{N}\), what are the magnitude (in \(\text{m/s}^2\)) and direction of the acceleration of the block? Let \(m = 8.00 \, \text{kg}\) and \(\theta = 34.0\):

A. Apply Newton's second law to calculate acceleration.
B. Resolve forces into components along and perpendicular to the incline.
C. Analyze the effects of friction on the block's motion.
D. Discuss the role of the angle \(\theta\) in the acceleration calculation.

Answer 1

To calculate the magnitude of the acceleration of the block, you can apply Newton's second law and use the net force and mass of the block. The magnitude of the acceleration is 10.6 m/s^2. The direction of the acceleration is the same as the direction of the forces.

Step-by-step explanation:

In order to calculate the acceleration of the block, we can apply Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.

Fnet = m * a

Here, the net force can be calculated by adding the magnitudes of the two forces:

Fnet = F1 + F2 = 59.5 N + 25.0 N = 84.5 N

Since the mass of the block is given as 8.00 kg, we can rearrange the equation to solve for acceleration:

a = Fnet / m = 84.5 N / 8.00 kg = 10.6 m/s^2

The magnitude of the acceleration of the block is 10.6 m/s^2.

The direction of the acceleration can be determined by analyzing the effects of the forces. Since the magnitudes of both forces are positive, their directions must be the same. Therefore, the acceleration of the block is in the same direction as the forces.

The angle Theta (θ) mentioned in the question does not play a role in calculating the acceleration of the block.