A particle with mass 1.53 kg oscillates horizontally at the end of a horizontal spring. A student measures an amplitude of 0.987 m and a duration of 121 s for 78 cycles of oscillation. Find the frequency (f), the speed at the equilibrium position (vmax), the spring constant (k), the potential energy at an endpoint (Umax), the potential energy when the particle is located 60.5% of the amplitude away from the equiliibrium position (U), and the kinetic energy (K), and the speed (v), at the same position.

0.645 Hz

38.959 N/m

4.981 m/s

18.976 J

6.495 J

12.031 J

3.965 m/s

Explanation:

k = Spring constant

m = Mass = 1.53 kg

A = Amplitude = 0.987 m

Number of cycles = 78

Time = 121 s

Frequency is given by

The frequency is 0.645 Hz

We have the relation

Spring constant is 38.959 N/m

Energy is conserved

The speed is 4.981 m/s

Potential energy is given by

The energy is 18.976 J

At 60.5%

The energy is 6.495 J

Total energy

The energy is 12.031 J

Speed

The speed is 3.965 m/s

coil wire, increase current, put iron inside the coil

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: