A single frictionless roller coaster car of mass m=750 kg tops the first hill with speed v=15 m/s ar height h =40m as shown 1) Find the speed of the car at B and C

2) if mass m were doubled, would the speed at B increase, decrease, or remain the same?

1. The speed of the roller coaster car at point B and C: are 19.8 m/s and 0 m/s respectively.

2. If mass (m) of the roller coaster car were doubled, the speed at B would increase because energy is dependent on  the mass of an object.

Given the following data:

1. To find the speed of the roller coaster car at point B and C:

First of all, we would determine the potential energy of the roller coaster car by using the formula:

Where:

From the diagram, height at point B = meters

P.E = 147000 Joules.

Next, we would determine the speed by applying the law of conservation of energy.

Substituting the values, we have;

Speed, v = 19.8 m/s

From the diagram, at point C, the speed is equal to zero (0) meters per seconds.

2. If mass (m) of the roller coaster car were doubled, the speed at B would increase because energy is dependent on  the mass of an object.

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1.) 19.8 m/s

2.) The speed will remain the same

Explanation:

Given that a single frictionless roller coaster car of mass m = 750 kg tops the first hill with speed v = 15 m/s at height h = 40m.

To Find the speed of the car at B and C, the height = 40/2 = 20m

Let us first calculate the potential energy P. E = mgh

P.E = 750 × 9.8 × 20

P.E = 147000 J

According to conservative of energy

K.E = P.E at the bottom of the hill

1/2mV^2 = 147000

750 × V^2 = 294000

V^2 = 294000/750

V^2 = 392

V = sqrt ( 392 )

V = 19.8 m/s

Therefore, the speed of the car at point B and C will be 19.8 m/s approximately.

2) if mass m were doubled, would the speed at B increase, decrease, or remain the same?

From the conservative of energy, the energy will not depend on mass. Therefore, the speed will remain the same.

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:

double the distance = divide strength by 4