To calculate the total mechanical energy (Et), kinetic energy (Ek), gravitational potential energy (Eg), and velocity (v) at each given position, we can use the formulas provided.
Given:
Mass (m) = 150 g = 0.15 kg
Acceleration due to gravity (g) = 9.8 m/s^2
1. At Speed = 0.0 cm/s, Time = 70s:
Since the speed is 0, the kinetic energy (Ek) is also 0.
The potential energy (Eg) at this position can be calculated using the formula:
Eg = (m)(g)(Δh)
Eg = (0.15 kg)(9.8 m/s^2)(0) = 0 J
Therefore, the total mechanical energy (Et) is also 0.
The velocity (v) can be calculated using the formula:
v = √((2Ek)/(m))
v = √((2(0))/(0.15 kg)) = 0 m/s
2. At Speed = 160.0 cm/s, Time = 20s:
The velocity (v) is given as 160 cm/s. Converting it to m/s, we get 1.6 m/s.
The kinetic energy (Ek) can be calculated using the formula:
Ek = 1/2 mv^2
Ek = 1/2 (0.15 kg)(1.6 m/s)^2 ≈ 0.192 J
The potential energy (Eg) at this position is 0, as the height (Δh) is not given.
Therefore, the total mechanical energy (Et) is approximately equal to the kinetic energy:
Et ≈ 0.192 J
The velocity (v) is already provided as 1.6 m/s.
3. At Speed = 280.0 cm/s, Time = 20s:
The velocity (v) is given as 280 cm/s. Converting it to m/s, we get 2.8 m/s.
The kinetic energy (Ek) can be calculated using the formula:
Ek = 1/2 mv^2
Ek = 1/2 (0.15 kg)(2.8 m/s)^2 ≈ 0.588 J
The potential energy (Eg) at this position is 0, as the height (Δh) is not given.
Therefore, the total mechanical energy (Et) is approximately equal to the kinetic energy:
Et ≈ 0.588 J
The velocity (v) is already provided as 2.8 m/s.
4. At Speed = 400.0 cm/s, Time = 60s:
The velocity (v) is given as 400 cm/s. Converting it to m/s, we get 4 m/s.
The kinetic energy (Ek) can be calculated using the formula:
Ek = 1/2 mv^2
Ek = 1/2 (0.15 kg)(4 m/s)^2 = 0.48 J
The potential energy (Eg) at this position is 0, as the height (Δh) is not given.
Therefore, the total mechanical energy (Et) is approximately equal to the kinetic energy:
Et = 0.48 J
The velocity (v) is already provided as 4 m/s.
5. At Speed = 440.0 cm/s, Time = 90s:
The velocity (v) is given as 440 cm/s. Converting it to m/s, we get 4.4 m/s.
The kinetic energy (Ek) can be calculated using the formula:
Ek = 1/2 mv^2
Ek = 1/2 (0.15 kg)(4.4 m/s)^2 ≈ 0.726 J
The potential energy (Eg) at this position is 0, as the height (Δh) is not given.
Therefore, the total mechanical energy (Et) is approximately equal to the kinetic energy:
Et ≈ 0.726 J
The velocity (v) is already provided as 4.4 m/s.
In summary:
1. Total Mechanical Energy (Et) = 0 J, Kinetic Energy (Ek) = 0 J, Gravitational Potential Energy (Eg) = 0 J, Velocity (v) = 0 m/s.
2. Total Mechanical Energy (Et) ≈ 0.192 J, Kinetic Energy (Ek) ≈ 0.192 J, Gravitational Potential Energy (Eg) = 0 J, Velocity (v) = 1.6 m/s.
3. Total Mechanical Energy (Et) ≈ 0.588 J, Kinetic Energy (Ek) ≈ 0.588 J, Gravitational Potential Energy (Eg) = 0 J, Velocity (v) = 2.8 m/s.
4. Total Mechanical Energy (Et) = 0.48 J, Kinetic Energy (Ek) = 0.48 J, Gravitational Potential Energy (Eg) = 0 J, Velocity (v) = 4 m/s.
5. Total Mechanical Energy (Et) ≈ 0.726 J, Kinetic Energy (Ek) ≈ 0.726 J, Gravitational Potential Energy (Eg) = 0 J, Velocity (v) = 4.4 m/s.
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:
1. Speed = 0.0cm/s
Time = 70s
2. Speed = 160.0cm/s
Time = 20s
3. Speed = 280.0cm/s
Time = 20s
4. Speed = 400.0cm/s
Time = 60s
5. Speed = 440.0cm/s
Time = 90s
Using the formulas below, solve the answers above.
Eg = (m)(g)(△h)
Ek = 1/2 mv^2
v = √((2Ek)/(m))
Et = Ek + Eg
1 answer