# Force F on Mass m at Angle Θ: Acceleration Calculations

• dreamz25
In summary, the conversation discusses the effects of a force F acting on a block of mass m at an angle Θ on a horizontal smooth surface. The resulting acceleration can be calculated using different equations depending on the relationship between F, Θ, and mg. One of the options mentioned (D) is incorrect due to a possible typo, and the vector components ax and ay cannot be simply added as they have different directions.
dreamz25

q) A force F acts on a block of mass m placed on a horizontal smooth surface at an angle Θ with horizontal. Then

(A) If F sinΘ < mg then a = (F + mg) / m

(B) Acceleration = FcosΘ/m where, F > mg cosecΘ

(C) Acceleration = F/m if FsinΘ > mg

(D) If F SinΘ > mg then a = (F + mg) / m

my work
--------

on drawing the F.B.D we we get..

clearly there will be linear and vertical acceleration as well...
Now if F sinΘ > mg then the Normal force will be 0
=> F sinΘ - mg = may ---- (i)

and, F cosΘ = max ------ (ii)

Adding the two eqns. we get,

F sinΘ + F cosΘ - mg = m (ax + ay)

or, ax + ay = (F - mg) / m

but the correct option is d.

couldn't represent vectors with their notations so please understand
it urselves.

Am i wrong? if yes then where and why?

Thanks in advance...!

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None of those answers look right. Are you sure there's not a typo in there? (Check the orientation of the > signs.)

And you can't just add perpendicular vector components, such as ax + ay.

why not...?

dreamz25 said:
why not...?
They are vectors. Direction counts.

Your work is correct. The correct option is (D) because when F sinΘ > mg, the normal force will be greater than mg, resulting in a positive acceleration in the x-direction. This means that the net force in the x-direction is F + mg, and dividing by the mass gives the correct expression for acceleration. Option (A) is incorrect because it does not take into account the normal force. Option (B) is incorrect because it assumes that F is greater than mg, which may not always be the case. Option (C) is incorrect because it assumes that the normal force is equal to mg, which is not always true. Overall, your explanation and calculations are correct.

## 1. What is the formula for calculating acceleration using force and mass at an angle?

The formula for calculating acceleration using force and mass at an angle is a = Fsin(Θ)/m, where a is the acceleration, F is the applied force, Θ is the angle between the force and the horizontal axis, and m is the mass of the object.

## 2. Can the acceleration of an object be negative?

Yes, the acceleration of an object can be negative. A negative acceleration means that the object is slowing down or moving in the opposite direction of the applied force.

## 3. How does the angle affect the acceleration of an object?

The angle affects the acceleration of an object by changing the direction of the force and therefore, the direction of the acceleration. A larger angle will result in a smaller acceleration, while a smaller angle will result in a larger acceleration.

## 4. What is the unit of measurement for force and mass?

The unit of measurement for force is Newtons (N), and the unit of measurement for mass is kilograms (kg). When using these units in the acceleration formula, the resulting unit will be meters per second squared (m/s²).

## 5. Can the acceleration of an object be greater than the applied force?

No, the acceleration of an object cannot be greater than the applied force. The acceleration is directly proportional to the applied force and inversely proportional to the mass of the object. Therefore, the acceleration can never exceed the applied force.

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