A ball of mass 2.00-kg is dropped from a height of 1.5 m (from the ground) onto a massless spring (the spring has an equilibrium length of 0.50 m). The ball compresses the spring by an amount of 0.20 m by the time it comes to a stop. Calculate the spring constant of the spring.

653.3 N/m

Explanation:

From the question,

Potential energy of the falling ball = elastic energy stored in the spring.

mgh = 1/2ke² Equation 1

Where m = mass of the ball, h = height from which the ball was dropped, g = acceleration due to gravity, k = spring constant, e = extension.

make k the subject of the equation

k = 2mgh/e² Equation 2

Given: m = 2 kg, h = 1.5 m, g = 9.8 m/s², e = 0.5-0.2 = 0.3 m

Substitute these values into equation 2

k = 2(2)(9.8)(1.5)/0.3²

k = 653.3 N/m

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: