Question

A 4.00-kg block rests between the floor and a 3.00-kg block as shown in the figure. The 3.00-kg block is tied to a wall by a horizontal rope. If the coefficient of static friction is 0.800 between each pair of surfaces in contact, what horizontal force F must be applied to the 4.00-kg block to make it move

Answer 1

To move the 4.00-kg block, calculate the total weight of both blocks to find the normal force, then multiply by the coefficient of static friction to find the maximum static frictional force. The required force F must exceed this value to initiate movement.

Step-by-step explanation:

The question involves finding the horizontal force F required to move a 4.00-kg block when it is resting between the floor and a 3.00-kg block, with a coefficient of static friction of 0.800 between each pair of surfaces.

To calculate this force, we first need to determine the maximum static frictional force that can act on the 4.00-kg block. The static frictional force (fs) is given by the equation fs = μs × N, where μs is the coefficient of static friction and N is the normal force.

The normal force in this case is the weight of the 3.00-kg block plus the weight of the 4.00-kg block, which is (3.00 kg + 4.00 kg) × 9.8 m/s2. After calculating the normal force, we can then multiply it by the coefficient of static friction to find the maximum static frictional force.

The applied force F must be greater than this maximum static frictional force to initiate movement of the 4.00-kg block.

Answer 2

To make the 4.00-kg block move, the force applied needs to overcome the force of static friction between the surfaces.

Step-by-step explanation:

To make the 4.00-kg block move, the force applied needs to overcome the force of static friction between the surfaces.

Static friction is given by the equation:

fs = μs * N

where fs is the force of static friction, μs is the coefficient of static friction, and N is the normal force.

Since the 4.00-kg block is resting on the floor, the normal force on it is equal to its weight:

N = m * g

where m is the mass of the block and g is the acceleration due to gravity.

Once the force applied is greater than the force of static friction, the block will start to move.