Physics Solution

Question

Problem:

A block of mass m=2.5kg is placed on a frictionless inclined plane that makes an angle of θ=30∘ with the horizontal.

(a) Draw a free-body diagram showing all the forces acting on the block. Label each force clearly.

(b) Determine the component of the gravitational force acting parallel to the inclined plane.

(c) Determine the magnitude of the normal force exerted by the inclined plane on the block.

(d) Calculate the acceleration of the block down the inclined plane.

(e) If the block starts from rest at the top of the incline and travels a distance of d=1.8m along the plane, what will its speed be at the bottom?

Use g=9.8m/s2 for the acceleration due to gravity.

Escape Road

Answer 1

Answer 2

N = Mg Cos ∅ = 2.5*9.8*Cos 30 = Normal force

Force parallel to plane

= Mg Sin ∅= 2.5*9.8*Sin 30

Force = 12.25 N

Acceleration = Force /Mass = 4.9 m/s2

V= sqrt ( 17.64) = 4.2m/s

Answer 3

Hi Elise!

According to the guidelines here I don't think I can solve the whole thing out for you, but I can certainly help walk you through it!

Free body diagrams are an awesome and very useful way to breakdown the individual forces acting on an object. In this problem we have 2 forces: The force of gravity always pointing downwards and the normal force. The normal force always points perpendicular to the surface. On an incline plane, that means that even though the force of gravity is straight downward, the normal force is NOT straight upwards. It shoots out at an angle depending on the angle of the incline plane.

Your job here is to break up the gravitational force(directed downwards) into a component directed down the incline(parallel direction) and component directly opposite the normal force.

Now you use the angle you are given to calculate the Force in the direction of the incline.

Since F = ma, you can solve for the acceleration down the incline using the force you calculate in the direction of the incline as F.

You can also calculate the magnitude of the normal force, as it is equal to the component of gravity in the opposite direction: which we know from Newton's Third Law.

For the last part, this is just a kinematics problem now. You have solved for the acceleration and you are given a distance. Sometimes these problems get people because they forget that an object beginning at rest gives them an initial velocity of 0!

Please feel free to reach out with any questions. I hope this helped!