AP Physics 1 Exam Question:

A block of mass 2 kg is placed on a frictionless surface. A string is attached to the block and a force of 10 N is applied horizontally to the string. Draw a free-body diagram for the block and determine the acceleration of the block.

Answer:

The free-body diagram for the block is as follows:

The forces acting on the block are:

1. Force of gravity (mg) acting downward: This force can be calculated using the formula Fg = mg, where m is the mass of the block and g is the acceleration due to gravity. In this case, since the block has a mass of 2 kg, the force of gravity is 2 kg * 9.8 m/s^2 = 19.6 N.

2. Tension force of the string acting upward: This is the force applied to the block through the string. In this case, the applied force is 10 N, which is the tension force acting upward.

Since there are no other forces acting on the block in the horizontal direction, the tension force is the net force acting on the block. According to Newton's second law, the net force equals mass times acceleration (F = ma).

Therefore, we can write the following equation:

$F = ma$

$10 \, \text{N} = 2 \, \text{kg} \cdot a$

To find the acceleration of the block, we divide both sides of the equation by the mass:

$a = \frac{10 \, \text{N}}{2 \, \text{kg}}$

$a = 5 \, \text{m/s}^2$

Hence, the acceleration of the block is 5 m/s^2.

Note: The acceleration of the block is the same as the acceleration due to the applied force because there is no horizontal force opposing the motion.