A 20 ton truck is pulling a 5 ton trailer.their common uniform velocity is 54 kmph.if the frictional force is 20N per both the truck and the trailer then power developed is?
F= (20+5) 20=500N
velocity= 54km/h =15m/s
Power = F. V=500 x 15=7500 W
=7.5kW
P=F.v
v=54km/hr=15m/s
F=20N/ton
F=25×20=500N
P=500×15=7500W
=7.5kW
Yes, your solution is correct.
To calculate the power developed by the truck while pulling the trailer, we need to use the formula for power:
Power = Force x Velocity
First, let's find the total force exerted by the truck and the trailer. In this case, we have the force of friction acting on both the truck and the trailer, and we need to add it to the force required to move both vehicles.
Total force = Frictional force + Force required to move the truck and trailer
Given:
- Frictional force = 20 N (for both the truck and the trailer)
- Mass of the truck = 20 tons = 20,000 kg
- Mass of the trailer = 5 tons = 5,000 kg
- Common velocity = 54 km/h = 15 m/s (since 1 km/h = 1000/3600 m/s)
Now, let's calculate the total force required:
Force = Mass x Acceleration (using F = ma)
For the truck:
Force truck = Mass truck x Acceleration truck
But since the truck and the trailer have a common velocity, their acceleration is the same. So:
Force truck = Mass truck x Acceleration
Likewise, for the trailer:
Force trailer = Mass trailer x Acceleration
Since the truck and the trailer are connected, the total force required to move both is the sum of their individual forces:
Force required to move the truck and trailer = Force truck + Force trailer
Now, let's calculate the forces:
Force truck = 20,000 kg x Acceleration
Force trailer = 5,000 kg x Acceleration
Since the total force is given by:
Total force = Frictional force + Force required to move the truck and trailer
We can substitute the forces:
Total force = 20 N + (20,000 kg x Acceleration) + (5,000 kg x Acceleration)
Given that the total force is the product of power and velocity, we can rewrite the equation as:
Power x Velocity = 20 N + (20,000 kg x Acceleration) + (5,000 kg x Acceleration)
Let's solve for Acceleration:
Acceleration = (Power x Velocity - 20 N) / (20,000 kg + 5,000 kg)
Acceleration = (Power x 15 m/s - 20 N) / 25,000 kg
Now, let's find the power developed. Since the velocity is constant (uniform velocity), there is no net acceleration. Hence, the net force should be zero. So:
Total force = Frictional force + Force required to move the truck and trailer
0 = 20 N + (20,000 kg x Acceleration) + (5,000 kg x Acceleration)
Solving for Acceleration:
Acceleration = -20 N / (20,000 kg + 5,000 kg)
Acceleration = -20 N / 25,000 kg
Since the two acceleration values derived above (Power x 15 m/s - 20 N) / 25,000 kg and -20 N / 25,000 kg) are the same, we can equate them:
(Power x 15 m/s - 20 N) / 25,000 kg = -20 N / 25,000 kg
Let's solve for Power:
Power x 15 m/s - 20 N = -20 N
Power x 15 m/s = 0
Therefore, to satisfy the equation, the power developed must be 0.
Hence, the power developed by the truck while pulling the trailer is 0.
power=work/time=20N*velocity
change 54km/hr to m/s
I am not certain what you mean 20 N per both...
Perhaps friction is 40N, I don't know what you mean by "per"