A 5 kg block is being held against the wall. What is the minimum force needed to keep the block from moving if the force is applied at an angle that is 15 degrees above the horizontal. The coefficient of static friction between the wall and the block is 0.275.

force = F

F sin 15 = F up

F cos 15 = F horizontal = F normal to wall

friction = mu F cos 15 up

total up= F sin 15 + .275 F cos 15

Fdown = m g = 5*9.81 = 49 Newtons

so
F (sin 15 + 0.275 cos 15) = 49

To find the minimum force needed to keep the block from moving, we need to consider both the gravitational force and the frictional force acting on the block.

First, let's calculate the gravitational force acting on the block. The weight of the block can be determined using the formula:

Weight = mass × acceleration due to gravity

Since the mass of the block is 5 kg and the acceleration due to gravity is approximately 9.8 m/s², we can calculate:

Weight = 5 kg × 9.8 m/s² = 49 N

Now, let's determine the frictional force. The frictional force can be calculated using the formula:

Frictional force = coefficient of friction × normal force

The normal force is the force exerted by the wall perpendicular to the contact surface. In this case, it is equal to the weight of the block, which is 49 N.

Frictional force = 0.275 × 49 N = 13.475 N (approximately)

Now, we need to find the horizontal component of the force applied at an angle of 15 degrees. This component will counteract the frictional force.

Horizontal component = force × cos(angle)

The angle given is 15 degrees, so we can calculate:

Horizontal component = F × cos(15°) = F × (cos(15°))

Finally, set up the equation for equilibrium:

Force applied = gravitational force + frictional force

Force applied = Weight + Frictional force

F × (cos(15°)) = 49 N + 13.475 N

Now, solve the equation:

F × (cos(15°)) = 49 N + 13.475 N
F × (cos(15°)) = 62.475 N

Therefore, the minimum force needed to keep the block from moving is approximately 62.475 N.