A 22-N force, parallel to the incline, is required to push a certain crate at a velocity of 6.1 up a frictionless incline that is 55° above the horizontal. The mass of the crate is:

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To find the mass of the crate, we can use Newton's second law:

F = m * a.

In this case, the net force acting on the crate is the force parallel to the incline, which is 22 N. We also know that the acceleration of the crate is the component of acceleration parallel to the incline.

To find the component of acceleration parallel to the incline, we need to resolve the force applied and gravitational force into components. The force applied, 22 N, can be decomposed into two perpendicular components: a component parallel to the incline and a component perpendicular to the incline.

The component of the force acting parallel to the incline is given by F_parallel = F * sin(θ), where θ is the angle of the incline. Therefore, F_parallel = 22 N * sin(55°).

Next, we need to consider the gravitational force acting on the crate. The gravitational force can be decomposed into a component parallel to the incline and a component perpendicular to the incline as well. The component of the gravitational force acting parallel to the incline is given by F_gravity_parallel = m * g * sin(θ), where m is the mass of the crate and g is the acceleration due to gravity.

Since we are told that the incline is frictionless, there is no force opposing the motion, and the component of acceleration parallel to the incline equals F_parallel/m = F_gravity_parallel/m. Therefore, we can set these two expressions equal to each other:

F_parallel/m = F_gravity_parallel/m

22 N * sin(55°) = m * g * sin(θ)

The angle θ is given as 55° and the acceleration due to gravity g is approximately 9.8 m/s^2.

Now we can solve for the mass of the crate:

m = (22 N * sin(55°)) / (9.8 m/s^2 * sin(55°)).

By plugging in the values and performing the calculation, we can find the mass of the crate.