Question

Consider the following 3 cases. (1) A block initially at rest on a floor is given a quick push by a hand. (2) The hand does not touch the block after the quick push. The block slides across the floor, gradually slows down, then comes to rest. In (3), the block is at rest.

In (1), while the hand is pushing the block, but while the block is still at rest, what is the direction of the net force on the block?

In (1), while the hand is pushing the block, but while the block is still at rest, what is the direction of the block’s acceleration?

In (2), after the hand has let go but while the block moves, what is the direction of the net force on the block?

In (2), after the hand has let go but while the block moves to the right before it stops, what is the direction of the block’s acceleration?

In (3), after the block has stopped moving and is at rest, what is the direction of the net force on the block?

In (3), after the block has stopped moving and is at rest, what is the direction of the block’s acceleration?

Answer 1

In case (1), the net force and acceleration are in the same direction as the force applied by the hand. In case (2), the net force is in the opposite direction of the block's motion, while the acceleration is zero when the block stops. In case (3), both the net force and acceleration are zero.

Step-by-step explanation:

In case (1), while the hand is pushing the block but the block is still at rest, the direction of the net force on the block is in the same direction as the force applied by the hand. Since the hand is pushing the block forward, the net force on the block is also in the forward direction.

The direction of the block's acceleration in case (1) is also in the same direction as the net force applied by the hand. Therefore, the block's acceleration is in the forward direction.

In case (2), after the hand has let go but while the block is still moving, the direction of the net force on the block is in the opposite direction of the block's motion. Friction between the block and the floor opposes the motion, so the net force is in the opposite direction.

After the block moves to the right and stops in case (2), the direction of the block's acceleration is zero. The block comes to rest, so there is no acceleration.

In case (3), after the block has stopped moving and is at rest, there is no net force on the block. The forces acting on the block are balanced, resulting in a net force of zero.

Since the block is at rest and not accelerating in case (3), the direction of the block's acceleration is also zero.

Answer 2

(1) The block isn't moving, despite the hand's force on it.

• The net force on the block is zero.
• The acceleration of the block is also zero.

(2) The block is gradually slowing down as it slides across the floor.

• The acceleration of the block points in the opposite direction of the block's movement (i.e., the opposite direction of the block's velocity.)
• The net force on the block points in the opposite direction of the block's movement. (Same direction as the block's acceleration.)

(3) Once again, the block is not moving.

• The net force on the block is zero.
• The acceleration of the block is also zero.

Step-by-step explanation:

By Newton's Second Law, the net force on an object is in the same direction as its acceleration. Since this question said a lot about the object's motion, the direction of the object's acceleration might be easier to find than its net force.

(1)

The acceleration of an object is the rate of change of its velocity over time.

In this situation, the velocity of the object is zero, which is itself a constant. As a result, the rate of change of the object's velocity over time would be zero. Hence, the acceleration of the object would also be equal to zero. The zero vector doesn't have a specific direction.

By Newton's Second Law, the net force on the object is proportional to its acceleration. As a result, the net force on the object in this case would also be equal to zero. What about the hand's force on the block? The friction and normal force from the ground balances that force while the block hasn't yet started to move.

(2)

The object is slowing down over time. In other words, its velocity is decreasing over time. When a scalar value is decreasing, its rate of change would be negative. However, since velocity and acceleration are vectors, the acceleration of the object would be in the opposite direction of its velocity.

The net force on an object is in the same direction as its acceleration. As a result, the net force on this block in this case would also be in the opposite direction of the block's velocity.

(3)

Similar to the first situation, since the velocity of the block is zero (a constant,) its acceleration would be equal to zero. Since the net force on an object is proportional to its acceleration, the net force on this block would also be equal to zero.