Question

A 50 g particle that can move along the x-axis experiences the net force Fx=2.0t2N, where t is in s. The particle is at rest at t = 0 s.

Answer 1

The momentum of the particle is given by (10Î + 20tĵ) kg m/s, and the net force acting on it is (0Î + 20ĵ) N.

Step-by-step explanation:

The question involves determining the momentum of a 5.0-kg particle as a function of time when it is moving with a velocity given by v(t) = (2.0Î + 4.0tĵ) m/s. Momentum (p) is the product of mass (m) and velocity (v) and is a vector quantity. Here, m = 5.0 kg, so the momentum as a function of time is p(t) = m*v(t) = 5.0 kg * (2.0Î + 4.0tĵ) m/s, which simplifies to (10Î + 20tĵ) kg m/s.

To find the net force acting on the particle, we need to use Newton's second law, which states that net force equals mass times acceleration (F = m*a). Since the velocity function is time-dependent, its derivative concerning time will give us acceleration. Differentiating v(t) = (2.0Î + 4.0tĵ) m/s with respect to time, we get the acceleration a(t) = (0Î + 4.0ĵ) m/s². The net force on the particle is thus F_net = m*a(t) = 5.0 kg * (0Î + 4.0ĵ) m/s², which simplifies to (0Î + 20ĵ) N.

Answer 2

For a 5.0-kg particle moving with a specified velocity, the momentum as a function of time is (10Î + 20tĵ) kg*m/s and the net force acting on the particle is (0Î + 20ĵ) N.

Step-by-step explanation:

The question pertains to the calculation of momentum as a function of time for a particle in motion and the determination of the net force acting on it. Firstly, for a particle with mass 5.0 kg moving with a velocity function v(t) = (2.0Î + 4.0tĵ) m/s, we know that momentum p is the product of mass m and velocity v, given as p(t) = m * v(t). Using this relation, we find that the momentum is p(t) = 5.0 kg * (2.0Î + 4.0tĵ) m/s, which simplifies to (10Î + 20tĵ) kg*m/s. To find the net force, we recall that force is the time derivative of momentum. Therefore, the net force is the derivative of the momentum function with respect to time. Calculating the derivative, we obtain the net force as (0Î + 20ĵ) N, since the derivative of a constant is zero and the derivative of 4.0t with respect to t is 4.0.