Question

If the block has a mass of $2\mathrm{kg}$ and the pulling force and the frictional force acting on the block both equal $20\mathrm{N}$, what is the acceleration of the block? (A) $0\mathrm{m}/{\mathrm{s}}^2$ (B) $10\mathrm{m}/{\mathrm{s}}^2$ (C) $40\mathrm{m}/{\mathrm{s}}^2$ (D) The acceleration cannot be determined without additional information.

Short answer

The net force acting on the block is zero since the pulling force and frictional force are equal. Using Newton's second law (F = m*a), we find that the acceleration is $a=\frac{0}{2}=0\mathrm{m}/{\mathrm{s}}^2$. The correct answer is (A) 0 m/s².

Step-by-step solution

Determine the net force acting on the block

According to Newton's second law, the force acting on an object equals its mass times its acceleration (F = m*a). The net force acting on the block is the difference between the pulling force and the frictional force. Since both forces are equal, the net force is zero. $F_{net}=F_{pull}-F_{friction}=20N-20N=0N$

Apply Newton's second law of motion

Now we will apply Newton's second law (F = m*a) to find the acceleration of the block. We know that the net force acting on the block is zero and the mass is 2 kg. Using the equation, we will find the acceleration. $0=2\ast a$

Calculate the acceleration

To find the acceleration, we will now rearrange the equation and solve for "a". $a=\frac{0}{2}$ This gives us an acceleration of 0 m/s². The correct answer is (A) 0 m/s².

Key concepts

Net Force

The net force is the overall force acting on an object when all individual forces are taken into account. In physics, it's essential to understand that the motion of an object is not determined by the individual forces, but by the net force which is the vector sum of all forces. For instance, if two teams are playing tug-of-war and each team is pulling with an equal force, the rope does not move because the net force is zero.

Using the example from the textbook exercise, we have a block being pulled with a force of 20 N, and at the same time, it is opposed by a frictional force of 20 N. Here, the forces are equal and opposite, so they cancel each other out. We can calculate the net force using the formula:
$F_{net}=F_{pull}-F_{friction}$.
In this case, $F_{net}=20N-20N=0N$. Since the net force is zero, there is no change in the motion of the block.

Acceleration

Acceleration is a measure of how quickly the velocity of an object is changing. It is not just about speed, but also about the direction in which the object is moving. If an object speeds up, slows down, or changes direction, it is accelerating. Acceleration can be calculated using Newton's second law of motion when the net force and the mass of an object are known.

In the context of our exercise, acceleration can be found using the formula $a=\frac{F_{net}}{m}$, where $a$ is the acceleration, $F_{net}$ is the net force, and $m$ is the mass of the object. Since the net force is zero (as shown in the Net Force section), no matter the mass, the acceleration will be zero as well, which is confirmed by the equation $a=\frac{0}{2}=0\frac{m}{s^2}$. Therefore, the block does not accelerate.

Frictional Force

Friction is a force that opposes the sliding motion between two surfaces that are in contact. It is the reason why objects eventually stop moving unless a force is continuously applied. The magnitude of frictional force depends on the materials of the contacting surfaces and the force pressing them together. There are different types of friction such as static, kinetic, and rolling friction.

In our exercise, the frictional force is equal to the pulling force, which is 20 N. This indicates that the surfaces have enough friction to completely oppose the applied force. Understanding frictional force is crucial in solving problems related to motion, as it often acts as the opposing force reducing the net force and hence affecting the acceleration of an object.

GED Physics Practice

GED (General Educational Development) tests are a suite of four subject tests which, when passed, certify that the test taker has high school-level academic skills. Physics, being a part of the science test, requires understanding concepts like net force, acceleration, and friction. GED Physics practice involves solving problems that test this knowledge.

In the exercise provided, the practice problem is designed to test the student's grasp of Newton's second law of motion and the related concepts. It's important for GED students to not only know the theoretical aspects but also to apply them in practical scenarios like this textbook exercise. Remember, practice problems like these help solidify your understanding of physics principles and prepare you for the types of questions you may encounter on the actual GED exam.