Three forces are acting on a particle of mass m initially in equilibrium. If the first two forces (R1 and R2) are perpendicular to each other and suddenly the third force (R3) is removed, then the acceleration of the particle is
Given,
Magnitude of Forces on object are R1, R2&R3
Two forces R1 & R2 are normal to each other.
In vector form →R1, →R2&→R3.
Two forces →R1 & →R2 are normal to each other.
Initially object is in equilibrium, mean vector sum of forces is zero.
→R1+ →R2+→R3=0 (at equilibrium)
→R1+ →R2=−→R3(at equilibrium)
In Term of magnitude
∣∣→R1+ →R2∣∣=∣∣→R3∣∣
If force →R3is removed, the remaining forces are →R1, →R2.
→F=→R1+→R2
Acceleration = Force/ Mass =→FM
|a|=∣∣∣→FM∣∣∣=∣∣→F∣∣M=∣∣→R1+ →R2∣∣M=∣∣→R3∣∣M=R3M
Hence, acceleration on mass m is R3M