1.) A car (m=1200 kg) moves form 2.0 m/s to 15.0 m/s in 100 m.
a) What is the initial kinetic energy of the car?
b) What is the final kinetic energy of the car?
c) what is the net work applied to the car?
d) what force is applied to the car?
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)
~please help me!
a) (1/2) m v^2 = .5 * 1200 * 4 = 2,400 Joules
b) (1/2) m v^2 = .5 * 1200 *225 = 135,000 Joules
c) 135,000 - 2,400 = 132,600 Joules
d) Force * distance = 132,600
100 F = 132,600
F = 1,326 Newtons
how far do you lift the bob, up to horizontal? up to top ?
Sure! I'd be happy to help you with these questions.
1) Let's start with the first question:
a) To find the initial kinetic energy of the car, we'll use the formula KE = 1/2 * m * v^2, where KE is the kinetic energy, m is the mass, and v is the velocity.
Given:
Mass of the car (m) = 1200 kg
Initial velocity (u) = 2.0 m/s
Plugging these values into the formula:
KE = 1/2 * (1200 kg) * (2.0 m/s)^2
= 1/2 * 1200 kg * 4.0 m^2/s^2
= 2400 Joules (J)
So, the initial kinetic energy of the car is 2400 J.
b) To find the final kinetic energy of the car, we'll use the same formula as before but with the final velocity (v) instead of the initial velocity.
Given:
Final velocity (v) = 15.0 m/s
Using the formula:
KE = 1/2 * (1200 kg) * (15.0 m/s)^2
= 1/2 * 1200 kg * 225.0 m^2/s^2
= 135000 Joules (J)
Therefore, the final kinetic energy of the car is 135000 J.
c) To find the net work applied to the car, we can use the work-energy theorem, which states that the net work done on an object is equal to the change in its kinetic energy. So, the net work (W) is equal to the change in kinetic energy (ΔKE).
ΔKE = KE_final - KE_initial
Plugging in the values we calculated earlier:
ΔKE = 135000 J - 2400 J
= 132600 Joules (J)
Therefore, the net work applied to the car is 132600 J.
d) To find the force applied to the car, we'll use the work formula: W = Fd, where W is the work done, F is the force applied, and d is the distance traveled.
Given:
Distance (d) = 100 m
Rearranging the formula to solve for force:
F = W/d
Plugging in the values:
F = 132600 J / 100 m
= 1326 Newtons (N)
Thus, the force applied to the car is 1326 N.
Now, let's move on to the second question about the simple pendulum.
2) a) To find the work done by the chain to pull the car to the top, we'll use the formula W = Fd, where W is the work done, F is the force applied, and d is the distance traveled.
Unfortunately, the question doesn't provide any information about the force applied or distance traveled. Please provide that information to proceed with the calculation.
b) To find the potential energy of the pendulum at the top, we'll use the formula PE = mgh, where PE is the potential energy, m is the mass, g is the acceleration due to gravity, and h is the height.
Given:
Length of the pendulum (h) = 1.5 m
Mass of the bob (m) = 3.0 kg
Acceleration due to gravity (g) ≈ 9.8 m/s^2
Using the formula:
PE = (3.0 kg) * (9.8 m/s^2) * (1.5 m)
= 44.1 Joules (J)
Therefore, the potential energy of the pendulum at the top is 44.1 J.
c) The total energy of the system is the sum of the kinetic energy and potential energy. To find the total energy, we'll add the kinetic energy and potential energy together.
Using the values we calculated earlier:
Total energy = KE + PE
= 135000 J + 44.1 J
= 135044.1 Joules (J)
Hence, the total energy of the system is 135044.1 J.
d) At the bottom of the pendulum swing, all of the potential energy is converted into kinetic energy. Therefore, the kinetic energy at the bottom is equal to the potential energy at the top.
Hence, the kinetic energy at the bottom is 44.1 Joules (J).
I hope that helps! Let me know if you have any further questions.