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.
Et = Ek + Eg
Ek = 1/2 mv^2
Eg = (m)(g)(△h)
v = √((2Ek)/(m))
To solve the above problems, we will use the given formulas for calculating total mechanical energy (Et), kinetic energy (Ek), gravitational potential energy (Eg), and velocity (v). Here are the steps to solve each problem:
1. Speed = 0.0 cm/s, Time = 70 s
Since the speed is 0, the kinetic energy is 0. We can assume the toy car is at the bottom position. Therefore, the gravitational potential energy is maximum.
Ek = 0 J
Eg = (0.15 kg)(9.8 m/s^2)(0 m) = 0 J
Et = Ek + Eg = 0 J
v = √((2Ek)/(m)) = √((2*0)/(0.15)) = 0 m/s
2. Speed = 160.0 cm/s, Time = 20 s
We are given the speed, so we can calculate the kinetic energy using the formula.
Ek = 1/2 * (0.15 kg) * (160 cm/s)^2 = 192 J
Since the speed is not 0, the toy car is not at the bottom position. Therefore, the gravitational potential energy is less than maximum.
Eg = (0.15 kg)(9.8 m/s^2)(△h)
As we don't know the change in height (△h), we cannot calculate Eg.
Et = Ek + Eg = Unknown
v = √((2Ek)/(m)) = √((2*192)/(0.15)) = 57.95 m/s
3. Speed = 280.0 cm/s, Time = 20 s
Using the given speed, we can calculate the kinetic energy.
Ek = 1/2 * (0.15 kg) * (280 cm/s)^2 = 588 J
Since the speed is not 0, the toy car is not at the bottom position. Therefore, the gravitational potential energy is less than maximum.
Eg = (0.15 kg)(9.8 m/s^2)(△h)
As we don't know the change in height (△h), we cannot calculate Eg.
Et = Ek + Eg = Unknown
v = √((2Ek)/(m)) = √((2*588)/(0.15)) = 81.98 m/s
4. Speed = 400.0 cm/s, Time = 60 s
Using the given speed, we can calculate the kinetic energy.
Ek = 1/2 * (0.15 kg) * (400 cm/s)^2 = 1200 J
Since the speed is not 0, the toy car is not at the bottom position. Therefore, the gravitational potential energy is less than maximum.
Eg = (0.15 kg)(9.8 m/s^2)(△h)
As we don't know the change in height (△h), we cannot calculate Eg.
Et = Ek + Eg = Unknown
v = √((2Ek)/(m)) = √((2*1200)/(0.15)) = 122.47 m/s
5. Speed = 440.0 cm/s, Time = 90 s
Using the given speed, we can calculate the kinetic energy.
Ek = 1/2 * (0.15 kg) * (440 cm/s)^2 = 1452 J
Since the speed is not 0, the toy car is not at the bottom position. Therefore, the gravitational potential energy is less than maximum.
Eg = (0.15 kg)(9.8 m/s^2)(△h)
As we don't know the change in height (△h), we cannot calculate Eg.
Et = Ek + Eg = Unknown
v = √((2Ek)/(m)) = √((2*1452)/(0.15)) = 134.13 m/s
Please note that without the information about the change in height (△h), we cannot calculate the gravitational potential energy (Eg) and hence the total mechanical energy (Et).
are you sure these are answers are correct?
Apologies for the incorrect answers. Let's go through the calculations again to obtain the correct values.
1. Speed = 0.0 cm/s, Time = 70 s
Since the speed is 0, the kinetic energy is 0. The toy car is assumed to be at the bottom position, so the gravitational potential energy is maximum.
Ek = 0 J
Eg = (0.15 kg)(9.8 m/s^2)(0 m) = 0 J
Et = Ek + Eg = 0 J
v = √((2Ek)/(m)) = √((2*0)/(0.15)) = 0 m/s
2. Speed = 160.0 cm/s, Time = 20 s
Using the given speed, we can calculate the kinetic energy.
Ek = 1/2 * (0.15 kg) * (160 cm/s)^2 = 192 J
Since the speed is not 0, the toy car is not at the bottom position. Therefore, the gravitational potential energy is less than maximum.
Eg = (0.15 kg)(9.8 m/s^2)(△h)
As we don't know the change in height (△h), we cannot calculate Eg.
Et = Ek + Eg = Unknown
v = √((2Ek)/(m)) = √((2*192)/(0.15)) = 45.10 m/s
3. Speed = 280.0 cm/s, Time = 20 s
Using the given speed, we can calculate the kinetic energy.
Ek = 1/2 * (0.15 kg) * (280 cm/s)^2 = 588 J
Since the speed is not 0, the toy car is not at the bottom position. Therefore, the gravitational potential energy is less than maximum.
Eg = (0.15 kg)(9.8 m/s^2)(△h)
As we don't know the change in height (△h), we cannot calculate Eg.
Et = Ek + Eg = Unknown
v = √((2Ek)/(m)) = √((2*588)/(0.15)) = 68.35 m/s
4. Speed = 400.0 cm/s, Time = 60 s
Using the given speed, we can calculate the kinetic energy.
Ek = 1/2 * (0.15 kg) * (400 cm/s)^2 = 1200 J
Since the speed is not 0, the toy car is not at the bottom position. Therefore, the gravitational potential energy is less than maximum.
Eg = (0.15 kg)(9.8 m/s^2)(△h)
As we don't know the change in height (△h), we cannot calculate Eg.
Et = Ek + Eg = Unknown
v = √((2Ek)/(m)) = √((2*1200)/(0.15)) = 122.47 m/s
5. Speed = 440.0 cm/s, Time = 90 s
Using the given speed, we can calculate the kinetic energy.
Ek = 1/2 * (0.15 kg) * (440 cm/s)^2 = 1452 J
Since the speed is not 0, the toy car is not at the bottom position. Therefore, the gravitational potential energy is less than maximum.
Eg = (0.15 kg)(9.8 m/s^2)(△h)
As we don't know the change in height (△h), we cannot calculate Eg.
Et = Ek + Eg = Unknown
v = √((2Ek)/(m)) = √((2*1452)/(0.15)) = 134.13 m/s
Again, please note that without the information about the change in height (△h), we cannot calculate the gravitational potential energy (Eg) and hence the total mechanical energy (Et).
To calculate the total mechanical energy (Et), kinetic energy (Ek), gravitational potential energy (Eg), and velocity (v) at different positions, you can use the given formulas.
1. Speed = 0.0 cm/s, Time = 70s
First, we need to find the kinetic energy (Ek). Since the speed is 0, the kinetic energy will be 0. Ek = 1/2 mv^2 = 1/2 (0.15 kg)(0 m/s)^2 = 0 J.
Next, we determine the gravitational potential energy (Eg). As there is no height provided, and the car is at rest, we assume the height is also 0. Eg = (0.15 kg)(9.8 m/s^2)(0 m) = 0 J.
Therefore, the total mechanical energy will also be 0 since Et = Ek + Eg. Et = 0 J.
The velocity (v) is not relevant here since the speed is 0.
2. Speed = 160.0 cm/s, Time = 20s
First, we find the kinetic energy (Ek). Ek = 1/2 mv^2 = 1/2 (0.15 kg)(1.6 m/s)^2 = 0.192 J.
Next, we determine the gravitational potential energy (Eg). Assuming the height is 0, Eg = (0.15 kg)(9.8 m/s^2)(0 m) = 0 J.
Then, we calculate the total mechanical energy (Et). Et = Ek + Eg = 0.192 J + 0 J = 0.192 J.
Finally, we find the velocity. v = √((2Ek)/(m)) = √((2 * 0.192 J) / (0.15 kg)) = 2.69 m/s.
3. Speed = 280.0 cm/s, Time = 20s
First, we find the kinetic energy (Ek). Ek = 1/2 mv^2 = 1/2 (0.15 kg)(2.8 m/s)^2 = 0.588 J.
Next, we determine the gravitational potential energy (Eg). Assuming the height is 0, Eg = (0.15 kg)(9.8 m/s^2)(0 m) = 0 J.
Then, we calculate the total mechanical energy (Et). Et = Ek + Eg = 0.588 J + 0 J = 0.588 J.
Finally, we find the velocity. v = √((2Ek)/(m)) = √((2 * 0.588 J) / (0.15 kg)) = 4.06 m/s.
4. Speed = 400.0 cm/s, Time = 60s
First, we find the kinetic energy (Ek). Ek = 1/2 mv^2 = 1/2 (0.15 kg)(4 m/s)^2 = 0.48 J.
Next, we determine the gravitational potential energy (Eg). Assuming the height is 0, Eg = (0.15 kg)(9.8 m/s^2)(0 m) = 0 J.
Then, we calculate the total mechanical energy (Et). Et = Ek + Eg = 0.48 J + 0 J = 0.48 J.
Finally, we find the velocity. v = √((2Ek)/(m)) = √((2 * 0.48 J) / (0.15 kg)) = 4.93 m/s.
5. Speed = 440.0 cm/s, Time = 90s
First, we find the kinetic energy (Ek). Ek = 1/2 mv^2 = 1/2 (0.15 kg)(4.4 m/s)^2 = 0.726 J.
Next, we determine the gravitational potential energy (Eg). Assuming the height is 0, Eg = (0.15 kg)(9.8 m/s^2)(0 m) = 0 J.
Then, we calculate the total mechanical energy (Et). Et = Ek + Eg = 0.726 J + 0 J = 0.726 J.
Finally, we find the velocity. v = √((2Ek)/(m)) = √((2 * 0.726 J) / (0.15 kg)) = 5.39 m/s.
Remember to always double-check your calculations and units to ensure accuracy.