An object of mass M = 649 g is pushed at a constant speed up a frictionless inclined surface which forms an angle θ = 50o with the horizontal. What is the magnitude of the force that is exerted by the inclined surface on the object?

from what direction is the force acting?

The force is parallel to the horizontal(ground) and is drawn as going into the plane of the inclined surface.

To find the magnitude of the force exerted by the inclined surface on the object, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, since the object is moving at a constant speed, its acceleration is zero. Therefore, the net force acting on the object is also zero.

Now, let's consider the forces acting on the object. There are two forces to consider: the force of gravity pulling the object downwards and the force exerted by the inclined surface pushing the object upwards. The force of gravity can be calculated using the formula:

F_gravity = mass * acceleration due to gravity

where the mass is given as M = 649 g and the acceleration due to gravity is approximately 9.8 m/s^2.

F_gravity = 649 g * 9.8 m/s^2

Next, we need to break down the force of gravity into its components parallel and perpendicular to the inclined surface. The force parallel to the inclined surface is responsible for slowing down the object, while the force perpendicular to the inclined surface is responsible for pushing the object into the inclined surface.

The force parallel to the inclined surface can be calculated using the formula:

F_parallel = F_gravity * sin(θ)

where θ is the angle between the inclined surface and the horizontal.

Similarly, the force perpendicular to the inclined surface, which is the force exerted by the inclined surface on the object, can be calculated using the formula:

F_perpendicular = F_gravity * cos(θ)

Now, substituting the values into the equations, we get:

F_gravity = 649 g * 9.8 m/s^2

F_parallel = F_gravity * sin(θ)

F_perpendicular = F_gravity * cos(θ)

Finally, to find the magnitude of the force exerted by the inclined surface on the object, we need to calculate F_perpendicular.