Calculating velocity at position C: At position A, the car has gravitational potential energy and kinetic energy. The gravitational potential energy at position A is given by: PEA = mx g x hA where m is the mass of the car and passenger (1000 kg), g is the acceleration due to gravity (9.8), and he is the height of position A from the ground (18 m). Substituting the values, we get: PEA = 1,000kg x 9.8 × 18m = 176, 400J At position A, the car also has kinetic energy given by: KEA = 0.5 x m X v² where v_A is the velocity at position A (2 m/s). Substituting the values, we get: KEA = 0.5 × 1,000kg × (2)² = 2,000J The total mechanical energy at position A is the sum of the gravitational potential energy and kinetic energy: EA = PEA + KEA = 176, 400J + 2,000J = 178, 400J At position C, the car has gravitational potential energy and kinetic energy. The gravitational potential energy at position C is given by: PEc = mx g x hc where h_C is the height of position C from the ground (15 m). Substituting the values, we get: PEc = 1,000kg x 9.8 × 15m= 147,000J
Calculating velocity at position C: At position A, the car has gravitational potential energy and kinetic energy. The gravitational potential energy at position A is given by: PEA = mx g x hA where m is the mass of the car and passenger (1000 kg), g is the acceleration due to gravity (9.8), and he is the height of position A from the ground (18 m). Substituting the values, we get: PEA = 1,000kg x 9.8 × 18m = 176, 400J At position A, the car also has kinetic energy given by: KEA = 0.5 x m X v² where v_A is the velocity at position A (2 m/s). Substituting the values, we get: KEA = 0.5 × 1,000kg × (2)² = 2,000J The total mechanical energy at position A is the sum of the gravitational potential energy and kinetic energy: EA = PEA + KEA = 176, 400J + 2,000J = 178, 400J At position C, the car has gravitational potential energy and kinetic energy. The gravitational potential energy at position C is given by: PEc = mx g x hc where h_C is the height of position C from the ground (15 m). Substituting the values, we get: PEc = 1,000kg x 9.8 × 15m= 147,000J
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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what answer do you get if you replace 15metres for 13 metres for position c
Transcribed Image Text:Calculating velocity at position C:
At position A, the car has gravitational potential energy
and kinetic energy. The gravitational potential energy at
position A is given by:
PEA = mxgx hA
where m is the mass of the car and passenger (1000 kg), g
is the acceleration due to gravity (9.8), and he is the
height of position A from the ground (18 m). Substituting
the values, we get:
PEA = 1,000kg x 9.8 × 18m = 176, 400J
At position A, the car also has kinetic energy given by:
KEA = 0.5 x m X v²
where v_A is the velocity at position A (2 m/s).
Substituting the values, we get:
KEA = 0.5 × 1,000kg × (2)² = 2,000J
The total mechanical energy at position A is the sum of
the gravitational potential energy and kinetic energy:
EA = PEA + KEA = 176, 400J + 2,000J = 178, 400J
At position C, the car has gravitational potential energy
and kinetic energy. The gravitational potential energy at
position C is given by:
PEc = mxgx hc
where h_C is the height of position C from the ground (15
m). Substituting the values, we get:
PEc = 1,000kg x 9.8 × 15m= 147,000J
Transcribed Image Text:Since the total mechanical energy is conserved, the total
mechanical energy at position C is equal to the total
mechanical energy at position A:
Ec=EA 178, 400J
At position C, the car also has kinetic energy given by:
KEC = 0.5 x mx v²
where vc is the velocity at position C (to be determined).
Since the total mechanical energy is conserved, we can
write:
Ec = PEc + KEc
Substituting the known values:
178, 400J = 147,000J +0.5 × 1,000kg x v²
Simplifying:
178, 400J - 147,000J = 0.5 × 1,000kg x vc
31, 400J = 500kg x vc
Dividing both sides by 500 kg:
v² = 31, 400-500 kg
v² = 62.8²2
Taking the square root of both sides:
VC =
√(62.8²)
Vc~ 7.93
Therefore, the velocity at position C, at the top of the
second incline, is approximately 7.93 m/s
2). Calculating average resistance force:
To calculate the average resistance force between points
A and C, we need to use the work-energy principle. The
work done by the resistance force is equal to the change
in mechanical energy.
The initial mechanical energy at position A is
EA = 178,400J.
The final mechanical energy at position C is
Ec = 178, 400J (as calculated earlier).
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