Acceleration on an Inclined Plane?

• haengbon
In summary, on an inclined plane with an angle of 30 degrees and a coefficient of friction of 0.3, a box weighing 20 kg has an acceleration of -2.36 m/s^2. The parallel force is 100 N and the normal force is 30 N. The error in the solution was switching the sine and cosine functions.
haengbon

Homework Statement

A box weighing 20 kg is on an inclined plane with an angle of 30$$\circ$$.The coefficient of friction is 0.3. What is the acceleration of the box?

Homework Equations

Newton's Second law ( I think? )

g= 10 m/s2

The Attempt at a Solution

$$\sum$$y = 0
NF - Wysin30$$\circ$$ = 0
NF = Wysin30$$\circ$$
NF = [(20)(10)]sin30$$\circ$$
NF = 100 N

f = $$\mu$$NF
f = (0.3)(100)
f = 30

$$\sum$$x = ma

Wcos30$$\circ$$ + f = m(-a)
20cos30$$\circ$$ + 30 = -20a
$$47.32/-20$$ = $$-20a/-20$$
a = -2.36 m/s2

Is this correct? :D

You have your sines and cosines mixed up. The normal force is Wcos(theta); the parallel force is Wsin(theta).

ideasrule said:
You have your sines and cosines mixed up. The normal force is Wcos(theta); the parallel force is Wsin(theta).

so that's the only problem ? :D so If I switched/corrected the two, then my answer would immediately be correct? :D

1. What is acceleration on an inclined plane?

Acceleration on an inclined plane refers to the rate of change of velocity of an object as it moves along an inclined surface. It is affected by both gravity and the angle of the incline.

2. How is acceleration calculated on an inclined plane?

The formula for acceleration on an inclined plane is a = gsinθ, where a is the acceleration, g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle of the incline.

3. Does the mass of the object affect acceleration on an inclined plane?

Yes, the mass of the object does affect acceleration on an inclined plane. The greater the mass of the object, the greater the force of gravity acting on it, leading to a larger acceleration.

4. How does the angle of the incline affect acceleration on an inclined plane?

The angle of the incline affects acceleration on an inclined plane by changing the component of gravity that acts parallel to the incline. The steeper the incline, the greater the force of gravity acting on the object and thus the greater the acceleration.

5. Can acceleration on an inclined plane ever be negative?

Yes, acceleration on an inclined plane can be negative. This occurs when the object is moving in the opposite direction of the incline, causing a decrease in velocity and a negative acceleration value.

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