When a constant force is applied to a body, it moves with uniform
From Newton's second law of motion, F= m.a
if force is constant acceleration remains constant.
A particle is moving with a constant speed along a straight line path. A force is not required to
As the particle moves with constant speed in straight line its velocity is constant i.e accleration is zero. From Newton's second law of motion
F=m.a
Force required to keep moving with uniform velocity is zero.
The linear momentum of a particle is given by P = a + bt², where t is time and a & b are constants. The force acting on the body is directly proportional to :
Given momentum of the object is P = a + bt²;
Force is defined as rate of change of momentum F= dP/dt= 2bt. so Force is proportional to t.
A body of mass 1 kg moving on a smooth horizontal surface with velocity 5m/s is to be brought to rest in 5 sec. How much force need to be applied :
Force is defined as rate of change of momentum ie. F= dP/dt= change in momentum / time
Here Force = (mv-mu)/t= m(v-u)/t= 1 kg (0- 5)/ 5 = 1 N
The momentum of a particle is P = 2cos tˆi + 2sin t ˆj. What is the angle between the force F acting on the particle and the momentum P ?
Momentum of object is given as, P = 2cos tˆi + 2sin t ˆj ,
From Newtons Second law, F = dP/dt = -2 sin t î + 2 cos t ˆj.
Taking Dot product of P and F we get = -4 sint . cos t + 4 sint .cost =0 .
So, force and momentum are perpendicular to each other.
A body moving with uniform velocity is stopped in 0.25 sec by applying a force of 200 N. What is the impulse :
Impulse is change in momentum so, J = F.dt = 200 × 0.25 =50 N-s
Figure shows an estimated force-time graph for a base ball struck by a bat from this curve determine impulse delivered to the ball.
Area bounded by force time graph with time axis represents impulse. Area of triangle in the figure is ⇒Impulse = ½×2 ×1800 = 1800 kg m/sec
Acceleration of the block is
Net force acting on the object is 10 N.
so, acceleration a = F/m = 10 N/10 kg= 1 m/s²
A force F = (3ˆi + 4ˆj +12kˆ ) N produces an acceleration of 1 m/sec² in a body, find the mass of the body :
Given force is F = (3ˆi + 4ˆj +12kˆ ) N , magnitude of force is
⇒F²= (3²+4²+12²) so, F = 13 N
From Newton's second law of motion F= m.a
⇒ 13 N = m.1 so, m=13 kg
Sand is poured on a conveyor belt at the rate of 2 kg/s. If belt is moving horizontally with velocity 4 m/s, then additional force required by engine to keep the belt moving with same constant velocity
The force required to keep the conveyor belt moving at a constant velocity is given by the rate of change of momentum.
Momentum of sand per second:
Given kg/s and m/s,
Thus, the additional force required is 8 N.