A 25kg crate is sitting at the bottom of an inclined plane. The inclined plane 12m long meets the horizontal at an angle of 15 degrees and has a coefficient of friction of 0.55. A force is applied to the crate so as to slide the crate up the incline at a constant speed.

What is the magnitude of the force F required to push the sled up the incline at a constant speed?
(194N)

force= ma+component of weight mg perpendiuclar x coefficent

force= m*0 + mg*mu*CosTheta

To find the magnitude of the force required to push the sled up the incline at a constant speed, we can use the following steps:

Step 1: Determine the total force working against the crate.

The total force working against the crate includes the force due to gravitational pull and the force due to friction.

The force due to gravity can be calculated using the formula:
Force due to gravity = mass * gravitational acceleration

Given that the mass of the crate is 25kg and the gravitational acceleration is 9.8 m/s^2, we can find the force due to gravity:
Force due to gravity = 25kg * 9.8 m/s^2 = 245 N

The force of friction can be calculated using the formula:
Force of friction = coefficient of friction * normal force

The normal force is the perpendicular force exerted by the inclined plane on the crate. It can be calculated using the formula:
Normal force = mass * gravitational acceleration * cos(angle of incline)

Given that the angle of incline is 15 degrees, we can calculate the normal force:
Normal force = 25kg * 9.8 m/s^2 * cos(15 degrees) = 238.57 N

Using the coefficient of friction of 0.55, we can calculate the force of friction:
Force of friction = 0.55 * 238.57 N = 131.22 N

Step 2: Determine the force required to push the sled at a constant speed.

Since the sled is moving at a constant speed, the force applied to the crate must equal the total force working against it (gravity and friction) to maintain equilibrium.

Force required = Force due to gravity + Force of friction
Force required = 245 N + 131.22 N
Force required = 376.22 N

Therefore, the magnitude of the force F required to push the sled up the incline at a constant speed is 376.22 N.

To find the magnitude of the force F required to push the sled up the incline at a constant speed, we can break this problem down into several steps.

Step 1: Calculate the gravitational force acting on the crate.
The gravitational force can be calculated using the formula F_gravity = m * g, where m is the mass of the crate (25 kg) and g is the acceleration due to gravity (9.8 m/s^2). So, F_gravity = 25 kg * 9.8 m/s^2 = 245 N.

Step 2: Calculate the normal force acting on the crate.
The normal force is the force exerted perpendicular to the inclined plane. In this case, it is equal to the gravitational force since the crate is not moving vertically. So, the normal force is also 245 N.

Step 3: Calculate the force of friction.
The force of friction can be calculated using the formula F_friction = coefficient of friction * normal force. In this case, the coefficient of friction is 0.55 and the normal force is 245 N. So, F_friction = 0.55 * 245 N = 134.75 N.

Step 4: Calculate the force required to push the crate up the incline at a constant speed.
Since the crate is moving up the incline at a constant speed, the force applied must overcome the force of friction. Therefore, the magnitude of the force required to push the sled up the incline is equal to the force of friction, which is 134.75 N.

So, the magnitude of the force F required to push the sled up the incline at a constant speed is 134.75 N.