An object of mass M = 924 g is pushed at a constant speed up a frictionless inclined surface which forms an angle è = 50 degrees with the horizontal as shown in the figure below. What is the magnitude of the force that is exerted by the inclined surface on the object?
There is an F shown, at an angle in the figure.
Students are less likely to get help when the name changes with questions of the same type, posted so close together. Please do not use name changes to get more of your questions answered. It doesn't work with me
I'm sorry I don't understand what you mean. I didn't do any name changes. You might be confusing me with someone else.
Just plug in the numbers likewise:
N= mg/ cos (theda)
That will give you your answer!
To find the magnitude of the force exerted by the inclined surface on the object, we can use trigonometry and Newton's second law.
First, let's draw a free-body diagram of the object on the inclined surface. We have the force applied to the object, F, which forms an angle with the horizontal. There is also the force of gravity acting vertically downward and the normal force exerted by the inclined surface perpendicular to it.
Since the object is moving at a constant speed, we know that the sum of the forces in the vertical direction is equal to zero. The vertical component of the force of gravity is balanced by the normal force. Therefore, we can write the equation:
N - mg*cos(θ) = 0
Where N is the normal force, mg is the weight of the object, and θ is the angle of inclination.
Next, we can find the magnitude of the force applied by the inclined surface by considering the horizontal component of the force applied. The force applied can be broken down into two components: one parallel to the incline and one perpendicular to it.
Using trigonometry, we can find the horizontal component of the force:
F_parallel = F*sin(θ)
We also know that the horizontal component of the force applied is equal to the horizontal component of the normal force:
F_parallel = N*sin(90° - θ) = N*cos(θ)
Setting these two equal, we have:
N*cos(θ) = F*sin(θ)
Now, we can substitute the expression for N from the previous equation into this equation:
mg*cos(θ) = F*sin(θ)
Solving for F, we get:
F = (mg*cos(θ))/sin(θ)
Plugging in the given values (mass M = 924 g, angle θ = 50°, and acceleration due to gravity g ≈ 9.8 m/s²), we can calculate the magnitude of the force exerted by the inclined surface on the object.