Two forces, 1 and 2, act on the 5.00 kg block shown in the drawing. The magnitudes of the forces are F1 = 47.5 N and F2 = 34.5 N. What is the horizontal acceleration (magnitude and direction) of the block?
and the drawing?
To find the horizontal acceleration of the block, 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 can be found by summing the individual forces acting on the block in the horizontal direction. In this case, we have two forces, F1 and F2.
First, let's determine the horizontal components of the forces. Since the drawing does not provide any angles or specific directions, we will assume that the forces are acting horizontally.
The horizontal component of F1, denoted as F1x, will be equal to F1 since it is acting horizontally.
The horizontal component of F2, denoted as F2x, will also be equal to F2 since it is acting horizontally.
So, F1x = 47.5 N and F2x = 34.5 N.
Next, we can find the net force acting in the horizontal direction. The net force, denoted as F net, is the vector sum of all the forces acting on the block.
F net = F1x + F2x
Substituting the given values:
F net = 47.5 N + 34.5 N
= 82 N
Now, let's find the acceleration by using Newton's second law:
F net = m * a
Rearranging the equation for acceleration:
a = F net / m
Substituting the given values:
a = 82 N / 5.00 kg
= 16.4 m/s²
Therefore, the magnitude of the horizontal acceleration of the block is 16.4 m/s².
To determine the direction of the acceleration, we need to consider the direction of the net force. Since the forces F1 and F2 are acting in the same direction, the net force will also act in that direction. Therefore, the direction of the acceleration is the same as the direction of the forces.
In this case, since no specific directions are given in the drawing, we assume that both forces are acting to the right. Thus, the horizontal acceleration of the block is in the positive direction (to the right).