Show that the acceleration of any object down a frictionless incline that makes an angle theta...

Show that the acceleration of any object down a frictionless incline that makes an angle theta with the horizontal is a= g sin theta (note that the acceleration is independent of mass.

Expert Solution

This is a very general question and has no certain answer because you don't tell us which direction the force is directed.

I will solve one solution in which the force you mention is the weight of the object

Let
F = the force
m = mass of object (unknown)
g = gravity
a = acceleration down slope
? = angle of slope from horizontal
Fn = normal force of slope on mass
Ff = friction force of slope on mass
Fg = Force of weight (gravity) acting parallel to the slope
? = coefficient of kinetic friction

as stated, the force is the weight of the mass
F = mg

If we draw a free body diagram
The normal force of the slope on the mass is
Fn = Fcos?
Fn = mgcos?

and the weight force acting parallel to the slope is
Fg = Fsin?
Fg = mgsin?

Then the friction force of the slope on the mass is
Ff = ?Fn
Ff = ?mgcos?

So the net force accelerating the mass will be the gravity force parallel to the slope minus the friction force

Fnet = Fg - Ff
Fnet = mgsin? - ?mgcos?
Fnet = mg(sin? - ?cos?)

If we then compare this equation to the basic equation
F = ma
we can see that
a = g(sin? - ?cos?)

which is the acceleration of the mass down the slope with no other external forces acting on it.

If friction is negligable, ? ? 0, and this reduces to

a = gsin?

genius_generous answered 5 days ago

A) Determine the acceleration of a 25.0 kg mass down a frictionless incline plane (angle of...

A) Determine the acceleration of a 25.0 kg mass down a frictionless incline plane (angle of incline=30 degrees) B) Repeat the above problem for an incline with a coefficient of friction of 0.15.

Consider an object sliding down a frictionless incline. 1. Would you expect the object to move...

Consider an object sliding down a frictionless incline. 1. Would you expect the object to move at a constant velocity or would you expect the object to accelerate as it moves down the incline? 2. If the angle of inclination increased, would you expect your answer to the previous question to change? If not, why not? If so, why and how? 3. How could you experimentally show that the velocity changed as the object slid down the incline? What measurements...

A 1.6 kg breadbox on a frictionless incline of angle ? = 38 ? is connected,...

A 1.6 kg breadbox on a frictionless incline of angle ? = 38 ? is connected, by a cord that runs over a pulley, to a light spring of spring constant k = 100 N/m, as shown in the figure. The box is released from rest when the spring is unstretched. Assume that the pulley is massless and frictionless. (a) What is the speed of the box when it has moved 10.6 cm down the incline? (b) How far down...

1. Ball rolling down an incline :Later you will be measuring the acceleration of the rolling...

1. Ball rolling down an incline :Later you will be measuring the acceleration of the rolling ball down the incline for several different incline angles, and we want to compare with the theoretical expected value. The best way to show this is to plot the acceleration on the vertical axis, and the value of sin(θ) on the horizontal axis, as shown on the plot below. Draw in the expected theoretical variation of the acceleration on this plot. 2. A 0.200...

In lab you will roll a cart down a nearly frictionless incline set at a small...

In lab you will roll a cart down a nearly frictionless incline set at a small angle. The cart will start at rest and travel a distance of 30.0cm±0.2cm. After travelling, the flag will pass through the photogate in order to measure the speed, vf or v30 (the speed at the end of the 30.0cm trip). Size of flag: d(flag width)=1.50cm±0.10cm Time through photogate t(blocked) = 0.02095s±0.00010s You know the initial speed, final speed, and distance the cart travels (not...

A box slides down a frictionless incline and a hoop, uniform disk and a solid sphere...

A box slides down a frictionless incline and a hoop, uniform disk and a solid sphere all roll down another incline of exactly the same length and height. They all have the same mass and start out from rest at the same time. Rank the objects: box, hoop, disk and sphere in the order they reach the bottom of the ramp. If any reach the bottom at the same time, state that explicitly. Reaches first ______ ______ ______ ______ Reaches bottom last

A cube with mass M slides down a frictionless curved incline as shown in the figure...

A cube with mass M slides down a frictionless curved incline as shown in the figure below. It has a completely inelastic collision with another cube m at the bottom that is

8. A cart slides down an inclined plane with the angle of the incline θ starting...

8. A cart slides down an inclined plane with the angle of the incline θ starting from rest. At the moment the cart begins to move, a ball is launched from the cart perpendicularly to the incline. (a) Choosing an x-y-coordinate system with the x-axis along the incline and the origin at the initial location of the cart, derive the equation of the trajectory that the ball assumes from the perspective of this coordinate system. (b) Determine where the maximum...

A crate of mass 50.0 kg slides down a 60.0o incline. The crates acceleration is 4.00...

A crate of mass 50.0 kg slides down a 60.0o incline. The crates acceleration is 4.00 m/s2, and the incline is 10.0 meter long. a) What is the kinetic energy of the crate as it reaches the bottom of the incline? b) How much work is spent in overcoming friction? c) What is the magnitude of friction force that acts on the crate as it slides down the incline? An advertisement claims that a certain 1200kg car can accelerate from...

a block slides down a frictionless inclined plane of height h=1m, making theta with the horizontal....

a block slides down a frictionless inclined plane of height h=1m, making theta with the horizontal. At the bottom of the plane, the block continues to move on a flat surface with a coefficient of friction u = 0.30. How far does the mass move on the flat surface?

Question