he weight of the block in the drawing is 77.0 N. The coefficient of static friction between the block and the vertical wall is 0.490. (a) What minimum magnitude of the force is required to prevent the block from sliding down the wall? (Hint: The static frictional force exerted by the block is directed upward, parallel to the wall.) (b) What minimum force is required to start the block moving up the wall? (Hint: The static frictional force is now directed down the wall.) Angle is 40 degrees.

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To solve this problem, we need to analyze the forces acting on the block and consider the conditions for equilibrium and motion.

Let's start by drawing a free-body diagram for the block:

1. Weight: The weight of the block acts vertically downward with a magnitude of 77.0 N.

2. Normal force: The block is in contact with the wall, so there is a normal force acting perpendicular to the wall. Since the block is not moving into or away from the wall, the normal force has the same magnitude as the weight and acts in the opposite direction.

3. Frictional force: The static frictional force exerted by the block is directed upward, parallel to the wall. Its magnitude depends on the coefficient of static friction and the normal force.

Now let's address part (a) of the question: What minimum magnitude of the force is required to prevent the block from sliding down the wall?

In order for the block to remain in place (not slide down), the maximum static frictional force must be equal to or greater than the component of the weight of the block acting parallel to the wall.

The component of the weight parallel to the wall can be found by multiplying the weight by the sine of the angle between the wall and the inclined plane (assuming the block is on an incline).

The formula for the magnitude of static friction force is given by:

Friction force = coefficient of static friction * normal force

Since the normal force is equal to the weight, we have:

Friction force = coefficient of static friction * weight

Therefore, the minimum magnitude of the force required to prevent the block from sliding down the wall is:

Force = Friction force = coefficient of static friction * weight

Substituting the values given in the problem:

Force = 0.490 * 77.0 N

Calculating this gives us the minimum magnitude of the force required to prevent the block from sliding down the wall.

Now let's move on to part (b) of the question: What minimum force is required to start the block moving up the wall?

To start the block moving up the wall, we need to overcome the static frictional force acting on the block. The maximum static frictional force is given by the same formula as in part (a).

Therefore, the minimum force required to start the block moving up the wall is equal to the maximum static frictional force:

Force = Friction force = coefficient of static friction * weight

However, in this case, the static frictional force is directed down the wall, opposite to the direction of motion.

Substituting the values given in the problem:

Force = 0.490 * 77.0 N

Calculating this gives us the minimum force required to start the block moving up the wall.

Remember to take into account the direction in which the force is applied, as it affects the direction of the static frictional force.