A 4 kg block rests between the floor and a 3 kg block. The 3 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 force must be applied horizontally to the 4 kg block to make it move?
To find the force required to make the 4 kg block move, we need to consider the forces acting on it.
1. Weight: The weight of a body is given by the formula W = m * g, where W is the weight, m is the mass, and g is the acceleration due to gravity. Therefore, the weight of the 4 kg block is W = 4 kg * 9.8 m/s^2 = 39.2 N.
2. Normal force: The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the normal force is equal to the weight of the block. So, the normal force on the 4 kg block is N = 39.2 N.
3. Frictional force: The static frictional force can be calculated using the formula F = μ * N, where F is the frictional force, μ is the coefficient of static friction, and N is the normal force. Here, the coefficient of static friction is 0.800, and the normal force is 39.2 N. Therefore, the static frictional force acting on the 4 kg block is F = 0.800 * 39.2 N = 31.36 N.
To make the 4 kg block move, an external force larger than the static frictional force must be applied. So, the horizontal force required to make the block move is 31.36 N or anything larger than that.
To determine the force required to make the 4 kg block move, we need to consider the forces acting on it and evaluate the maximum static friction force. The magnitude of static friction is given by the equation:
fs = μs * N
where fs is the static friction force, μs is the coefficient of static friction, and N is the normal force.
In this case, the 4 kg block is resting on the floor, so the normal force acting on it is equal to its weight:
N = m * g
where m is the mass of the block (4 kg) and g is the acceleration due to gravity (9.8 m/s²).
N = 4 kg * 9.8 m/s² = 39.2 N
We can now calculate the maximum static friction force between the 4 kg block and the floor:
fs1 = μs * N = 0.800 * 39.2 N = 31.36 N
The 3 kg block is tied to a wall with a rope, so it cannot move horizontally. Hence, the maximum static friction force acting between the 4 kg block and the 3 kg block equals the force applied horizontally:
fs2 = force = 31.36 N
Therefore, a horizontal force of 31.36 N must be applied to the 4 kg block to make it move.