a 5-kg crate is resting on a horizontal plank. the coefficient of static friction is .5 and the coefficient of kinetic friction is .4. after one end of the plank is raised so the plank makes an angle of 25 degrees with the horizontal, the force of friction is?

Net force down plank if it is stationary:

mgSin25-.5cos25 if this is positive, then the block is moving, and the coeff friction is .4.

However, it is negative, so it is still standing still.

To determine the force of friction on the crate when the plank is raised, we need to consider the forces acting on the crate.

When the plank is horizontal, the force of static friction prevents the crate from moving. The formula for static friction is:

Frictional force (static) = coefficient of static friction * normal force

The normal force is equal to the weight of the crate, which is the mass of the crate multiplied by the acceleration due to gravity:

Weight of the crate = mass * acceleration due to gravity

W = m * g

where m is the mass of the crate (5 kg) and g is the acceleration due to gravity (approximately 9.8 m/s²).

Now, we can calculate the normal force:

Normal force = Weight of the crate = m * g

Next, when the plank is raised at an angle, the force of friction changes to the force of kinetic friction. The formula for kinetic friction is slightly different:

Frictional force (kinetic) = coefficient of kinetic friction * normal force

To find the coefficient of kinetic friction, we need to determine if the crate is actually moving. If the crate is not moving, the static friction force will still be acting. If the crate is moving, the kinetic friction force will be acting.

If we assume that the crate is not moving, the angle of the plank does not affect the force of friction. Therefore, the force of friction remains the same as the static friction force when the plank is horizontal.

Calculating the force of friction:

Frictional force = coefficient of static friction * normal force

Frictional force = 0.5 * (m * g)

Plug in the values:

Frictional force = 0.5 * (5 kg * 9.8 m/s²)

Frictional force = 0.5 * (49 N)

Frictional force = 24.5 N

Therefore, the force of friction on the crate when the plank is raised at an angle of 25 degrees with the horizontal is 24.5 N.