A dense particle with mass 5 kg follows the path r(t)=⟨sin(3t),cos(4t),2t9/2⟩r(t)=⟨s in⁡(3t),cos⁡(4t),2t9/2⟩ with units in meters and seconds. What force acts on the mass at t=0t=0?

Therefore the force acts on the the mass is .

Explanation:

Force: Force is the product of mass and acceleration.

F= ma

F is denoted force

m  is denoted mass

a  is denoted acceleration.

The first order derivative of the path gives the velocity of the particle.

The second order derivative of the path gives the acceleration of the particle.

Rule of derivatives:

The path is

r(t)= <sin(3t), cos(4t), >

Differentiating with respect t

Again differentiating with respect t

When t=0

The mass of the object is 5 kg.

Force =

Therefore the force acts on the the mass is .

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation: