1.) A 500 kg roller coaster is pulled to the top of a hill 45 m high and arrives at the top with a zero speed.
a) how much work has done by the vhain to pull the car to the top?
b) how much potential energy does it have at the top?
c)What is the total energy of the system?
d) how much kinetic energy does it have at the bottom?
e) what is the speed at the bottom?
2.) A simple pendelum is 1.5 m long and has 3.0 kg bob attached.
a) how much work was done by the chain to pull the car to the top?
b) how much potential energy does it have to the top?
c) what is the total energy of the system?
d) how much kinetic energy does it have at the bottom?
>> FORMULAS <<
KE= 1/2 v^2 (kinetic energy)
PE=mgh (potential energy)
kg.m/s^2.m
W= Fd (work equals force and distance)
Im sorry I don't know which formula to choose. PLease please please help me!
1)
a) W=mgh
b) PE=mgh
c) E(toral) = PE = mgh
d) KE= PE=mgh
e) mv²/2=mgh
v=sqrt(2gh)
2) pendelum ... car ???
A.) 220500J
B.) 220500
For the first question:
a) To calculate the work done by the chain to pull the roller coaster to the top, you can use the formula: work = force x distance. The force can be found using the formula: force = mass x acceleration. In this case, since the roller coaster is at rest at the top, acceleration is 0. Thus, the force is also 0. So, the work done by the chain is 0 Joules.
b) The potential energy at the top of the hill can be calculated using the formula: potential energy = mass x gravitational acceleration x height. Using the given values, the potential energy at the top is: potential energy = 500 kg x 9.8 m/s² x 45 m = 220,500 Joules.
c) The total energy of the system is the sum of the potential energy and the kinetic energy, which is constant since there is no external force. So, the total energy of the system is equal to the potential energy at the top: 220,500 Joules.
d) At the bottom of the hill, all the potential energy has been converted to kinetic energy. So, the kinetic energy at the bottom is equal to the potential energy at the top: 220,500 Joules.
e) To find the speed at the bottom, you can use the formula: kinetic energy = 1/2 x mass x velocity². Since the kinetic energy at the bottom is 220,500 Joules and the mass is 500 kg, you can rearrange the formula to solve for velocity: velocity = √((2 x kinetic energy) / mass). Plugging in the values, the speed at the bottom is approximately 67.37 m/s.
For the second question:
a) Since a pendulum is not pulled by a chain to the top, no work is done by the chain. So, the work done by the chain is 0 Joules.
b) The potential energy at the highest point of the pendulum's swing can be calculated using the same formula as in the first question: potential energy = mass x gravitational acceleration x height. The height in this case is half the length of the pendulum (since the mass is at the maximum height in the swing), so the potential energy at the top is: potential energy = 3.0 kg x 9.8 m/s² x 1.5 m / 2 = 22.05 Joules.
c) The total energy of the system remains constant, just like in the first question. So, the total energy of the system is 22.05 Joules.
d) At the bottom of the swing, all the potential energy is converted to kinetic energy. So, the kinetic energy at the bottom is also 22.05 Joules.
Again, you can use the formula: kinetic energy = 1/2 x mass x velocity² to find the speed at the bottom, using the given values of kinetic energy and mass.
Sure, I can help you with these questions. Let's answer each question step by step.
1) Work done by the chain to pull the roller coaster to the top:
The work done is given by the formula W = Fd, where W is the work, F is the force applied, and d is the distance. In this case, the force applied is equal to the weight of the roller coaster, which is given by the formula F = mg, where m is the mass of the roller coaster and g is the acceleration due to gravity (approximately 9.8 m/s^2). The distance d is 45 m, the height of the hill. Therefore, the work done is W = mgd.
2) Potential energy of the roller coaster at the top:
The potential energy is given by the formula PE = mgh, where PE is the potential energy, m is the mass of the roller coaster, g is the acceleration due to gravity, and h is the height. Substituting the given values, you can calculate the potential energy.
3) Total energy of the system:
The total energy of the system is the sum of the potential energy and the kinetic energy. Total Energy = PE + KE.
4) Kinetic energy of the roller coaster at the bottom:
The kinetic energy is given by the formula KE = 1/2 mv^2, where KE is the kinetic energy, m is the mass of the roller coaster, and v is the velocity. At the bottom of the hill, the roller coaster will have converted all its potential energy into kinetic energy, so the potential energy at the top is equal to the kinetic energy at the bottom.
5) Speed of the roller coaster at the bottom:
To find the speed at the bottom, you can use the relationship between kinetic energy and speed. Set the calculated kinetic energy equal to 1/2 mv^2 and solve for v.
Now, let's move on to the questions for the simple pendulum.
1) Work done by the chain to pull the pendulum to the top:
Since we are dealing with a simple pendulum, there is no chain involved. Instead, the pendulum is powered by gravitational potential energy. Therefore, no work is done by the chain.
2) Potential energy of the pendulum at the top:
The potential energy is given by the formula PE = mgh, where PE is the potential energy, m is the mass of the bob, g is the acceleration due to gravity, and h is the height. Substituting the given values, you can calculate the potential energy.
3) Total energy of the system:
Just like in the roller coaster case, the total energy of the system is the sum of the potential energy and the kinetic energy. Total Energy = PE + KE.
4) Kinetic energy of the pendulum at the bottom:
The kinetic energy is given by the formula KE = 1/2 mv^2, where KE is the kinetic energy, m is the mass of the bob, and v is the velocity. At the bottom of the swing, all the potential energy is converted to kinetic energy, so the potential energy at the top is equal to the kinetic energy at the bottom.
I hope this explanation helps you in solving the problems! Let me know if you have any further questions.