Grade 11 phyiscs
Assume the toy car with mass 150 g starts at rest and there is no friction.
Calculate The Total Mechanical Energy, Kinetic Energy, Gravitational Potential Energy, and
velocity at following positions and complete the tables:
1. Speed = 0.0cm/s
Time = 70s
What is the Formulas for Et, Ek, Eg, V and show the Solutions and Answers?
2. Speed = 160.0cm/s
Time = 20s
What is the Formulas for Et, Ek, Eg, V and show the Solutions and Answers?
3. Speed = 280.0cm/s
Time = 20s
What is the Formulas for Et, Ek, Eg, V and show the Solutions and Answers?
4. Speed = 400.0cm/s
Time = 60s
What is the Formulas for Et, Ek, Eg, V and show the Solutions and Answers?
5. Speed = 440.0cm/s
Time = 90s
What is the Formulas for Et, Ek, Eg, V and show the Solutions and Answers?
Using the formulas below, solve the answers above.
Eg = (m)(g)(△h)
Ek = 1/2 mv^2
v = √((2Ek)/(m))
Et = Ek + Eg
To solve the problems, we need to use the formulas for total mechanical energy (Et), kinetic energy (Ek), gravitational potential energy (Eg), and velocity (v).
1. Speed = 0.0 cm/s, Time = 70s
Given:
Mass (m) = 150 g = 0.15 kg (convert grams to kilograms)
Speed (v) = 0.0 cm/s = 0 m/s (convert cm/s to m/s)
Time (t) = 70 s
First, calculate the gravitational potential energy:
Eg = (m)(g)(△h)
As the toy car starts at rest and there is no friction, the change in height (△h) is 0. Therefore, Eg = 0.
Next, calculate the kinetic energy:
Ek = 1/2 mv^2
Since the speed is 0, Ek = 0.
Finally, calculate the velocity:
v = √((2Ek)/(m))
Since Ek = 0, the velocity v = 0.
Complete the table:
Position | Total Mechanical Energy (Et) | Kinetic Energy (Ek) | Gravitational Potential Energy (Eg) | Velocity (v)
1 | 0 | 0 | 0 | 0
2. Speed = 160.0 cm/s, Time = 20s
Given:
Mass (m) = 150 g = 0.15 kg (convert grams to kilograms)
Speed (v) = 160.0 cm/s = 1.6 m/s (convert cm/s to m/s)
Time (t) = 20 s
First, calculate the gravitational potential energy (Eg):
Eg = (m)(g)(△h)
Since the toy car starts at rest and there is no friction, the change in height (△h) is 0. Therefore, Eg = 0.
Next, calculate the kinetic energy (Ek):
Ek = 1/2 mv^2
Ek = 1/2 * 0.15 kg * (1.6 m/s)^2
Ek = 0.192 J
Finally, calculate the velocity (v):
v = √((2Ek)/(m))
v = √((2 * 0.192 J)/(0.15 kg))
v = √(2.56 m^2/s^2)
v ≈ 1.6 m/s
Complete the table:
Position | Total Mechanical Energy (Et) | Kinetic Energy (Ek) | Gravitational Potential Energy (Eg) | Velocity (v)
2 | 0.192 J | 0.192 J | 0 | 1.6 m/s
3. Speed = 280.0 cm/s, Time = 20s
Given:
Mass (m) = 150 g = 0.15 kg (convert grams to kilograms)
Speed (v) = 280.0 cm/s = 2.8 m/s (convert cm/s to m/s)
Time (t) = 20 s
First, calculate the gravitational potential energy (Eg):
Eg = (m)(g)(△h)
Since the toy car starts at rest and there is no friction, the change in height (△h) is 0. Therefore, Eg = 0.
Next, calculate the kinetic energy (Ek):
Ek = 1/2 mv^2
Ek = 1/2 * 0.15 kg * (2.8 m/s)^2
Ek = 0.588 J
Finally, calculate the velocity (v):
v = √((2Ek)/(m))
v = √((2 * 0.588 J)/(0.15 kg))
v = √(3.52 m^2/s^2)
v ≈ 1.87 m/s
Complete the table:
Position | Total Mechanical Energy (Et) | Kinetic Energy (Ek) | Gravitational Potential Energy (Eg) | Velocity (v)
3 | 0.588 J | 0.588 J | 0 | 1.87 m/s
4. Speed = 400.0 cm/s, Time = 60s
Given:
Mass (m) = 150 g = 0.15 kg (convert grams to kilograms)
Speed (v) = 400.0 cm/s = 4.0 m/s (convert cm/s to m/s)
Time (t) = 60 s
First, calculate the gravitational potential energy (Eg):
Eg = (m)(g)(△h)
Since the toy car starts at rest and there is no friction, the change in height (△h) is 0. Therefore, Eg = 0.
Next, calculate the kinetic energy (Ek):
Ek = 1/2 mv^2
Ek = 1/2 * 0.15 kg * (4.0 m/s)^2
Ek = 1.2 J
Finally, calculate the velocity (v):
v = √((2Ek)/(m))
v = √((2 * 1.2 J)/(0.15 kg))
v = √(16 m^2/s^2)
v = 4 m/s
Complete the table:
Position | Total Mechanical Energy (Et) | Kinetic Energy (Ek) | Gravitational Potential Energy (Eg) | Velocity (v)
4 | 1.2 J | 1.2 J | 0 | 4 m/s
5. Speed = 440.0 cm/s, Time = 90s
Given:
Mass (m) = 150 g = 0.15 kg (convert grams to kilograms)
Speed (v) = 440.0 cm/s = 4.4 m/s (convert cm/s to m/s)
Time (t) = 90 s
First, calculate the gravitational potential energy (Eg):
Eg = (m)(g)(△h)
Since the toy car starts at rest and there is no friction, the change in height (△h) is 0. Therefore, Eg = 0.
Next, calculate the kinetic energy (Ek):
Ek = 1/2 mv^2
Ek = 1/2 * 0.15 kg * (4.4 m/s)^2
Ek = 1.782 J
Finally, calculate the velocity (v):
v = √((2Ek)/(m))
v = √((2 * 1.782 J)/(0.15 kg))
v = √(23.76 m^2/s^2)
v ≈ 4.87 m/s
Complete the table:
Position | Total Mechanical Energy (Et) | Kinetic Energy (Ek) | Gravitational Potential Energy (Eg) | Velocity (v)
5 | 1.782 J | 1.782 J | 0 | 4.87 m/s
are you sure these answers are correct?
I apologize for any confusion or errors in my previous response. Let's go through the calculations again and ensure the answers are correct.
1. Speed = 0.0 cm/s, Time = 70s
Given:
Mass (m) = 150 g = 0.150 kg (convert grams to kilograms)
Speed (v) = 0.0 cm/s = 0.0 m/s (convert cm/s to m/s)
Time (t) = 70 s
First, calculate the gravitational potential energy (Eg):
Eg = (m)(g)(△h)
As the toy car starts at rest and there is no change in height (△h), Eg = 0.
Next, calculate the kinetic energy (Ek):
Ek = 1/2 mv^2
Since the speed is 0, Ek = 0.
Finally, calculate the velocity (v):
v = √((2Ek)/(m))
Since Ek = 0, the velocity v = 0.
Complete the table:
Position | Total Mechanical Energy (Et) | Kinetic Energy (Ek) | Gravitational Potential Energy (Eg) | Velocity (v)
1 | 0.000 J | 0.000 J | 0.000 J | 0.0 m/s
I apologize for the incorrect previous answer.
To obtain correct answers for the given problems, could you please provide the values of g (acceleration due to gravity) and the initial height of the toy car?