A block weighing 70.0 N rests on a plane inclined at 25.0° to the horizontal. A force F is applied to the object at 50.0° to the horizontal, pushing it upward on the plane. The coefficients of static and kinetic friction between the block and the plane are, respectively, 0.373 and 0.156.

There are facts here, but no question

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To determine the force F required to push the block upward on the inclined plane, we need to analyze the forces acting on the block.

First, let's resolve the weight of the block into components parallel and perpendicular to the plane:

F_weight_parallel = weight * sin(angle of inclination)
F_weight_perpendicular = weight * cos(angle of inclination)

Given that the weight of the block is 70.0 N and the angle of inclination is 25.0°, the values are:

F_weight_parallel = 70.0 N * sin(25.0°)
F_weight_perpendicular = 70.0 N * cos(25.0°)

Next, let's calculate the force of static friction. The maximum static friction force can be found by multiplying the coefficient of static friction by the perpendicular force:

F_static_friction = coefficient of static friction * F_weight_perpendicular

Given that the coefficient of static friction is 0.373, the force of static friction is:

F_static_friction = 0.373 * F_weight_perpendicular

Now, let's calculate the force of kinetic friction. The force of kinetic friction is given by:

F_kinetic_friction = coefficient of kinetic friction * F_weight_perpendicular

Given that the coefficient of kinetic friction is 0.156, the force of kinetic friction is:

F_kinetic_friction = 0.156 * F_weight_perpendicular

Finally, we can determine the force F required to push the block upward on the inclined plane. Since we are considering an inclined plane, we need to take into account both the force parallel to the plane and the force perpendicular to the plane.

The net force parallel to the plane is given by:

F_parallel = F_weight_parallel - F_static_friction

Now, we can resolve the force F and find its components parallel and perpendicular to the plane:

F_parallel = F * cos(50.0°)
F_perpendicular = F * sin(50.0°)

We can set up a system of equations using the forces parallel and perpendicular to the plane:

F_parallel = F_perpendicular * tan(angle of inclination) + F_kinetic_friction

Substituting the values we found earlier, we can solve for the force F:

F * cos(50.0°) = F * sin(50.0°) * tan(25.0°) + 0.156 * F * cos(25.0°)

Now, we can isolate F:

F * (cos(50.0°) - sin(50.0°) * tan(25.0°)) = 0.156 * F * cos(25.0°)

Dividing both sides by F * cos(25.0°), we get:

cos(50.0°) - sin(50.0°) * tan(25.0°) = 0.156

Now, we can solve this equation numerically using a calculator or mathematical software to find the value of F.