A truck of mass 4000 kg is at rest, but free to roll with no resistance. If you push it forward with a force of 500 N, the momentum at the end of 5 s of pushing will be
force=delta p/ delta t
500= delta p/5
p=2500?? right?
you are correct. working it another way,
F = ma, so a = 500/4000 = 0.125 m/s^2
v = at = 0.125 * 5 = 0.625
p = mv = 4000 * 0.625 = 2500 kg-m/s
Well, let me put on my jester hat and clown shoes to help you with this question!
When you push the truck forward with a force of 500 N, the momentum of the truck will indeed increase. However, your calculation of 2500 kg·m/s for momentum seems a bit off. Allow me to explain.
Momentum is calculated by multiplying an object's mass by its velocity. Since the truck starts from rest, it has an initial velocity of 0 m/s. After pushing it for 5 seconds, the velocity increases uniformly, assuming there are no other forces acting on it.
To find the final velocity, we can use the equation:
force = mass × acceleration
Since the truck is initially at rest, we can simplify the equation to:
force = mass × (change in velocity / change in time)
Rearranging the formula, we get:
force × change in time = mass × change in velocity
Plugging in the given values:
500 N × 5 s = 4000 kg × (final velocity - 0 m/s)
Now we solve for the final velocity:
2500 N·s = 4000 kg × final velocity
final velocity = 2500 N·s / 4000 kg
Calculating this, we get a final velocity of 0.625 m/s for the truck.
And to find the momentum, we multiply the mass of the truck by its final velocity:
momentum = 4000 kg × 0.625 m/s
So, drumroll please... the momentum at the end of 5 seconds would be 2500 kg·m/s, not 2500 kg·m/s. Remember, even with no resistance, rolling a truck takes some time! Keep on clownin'!
To determine the change in momentum, we need to calculate the impulse applied to the truck.
Impulse (Δp) is equal to the force (F) applied multiplied by the time (Δt):
Δp = F * Δt
In this case, the force is 500 N and the time is 5 seconds:
Δp = 500 N * 5 s
Δp = 2500 Ns
The momentum at the end of 5 seconds of pushing will be equal to the change in momentum:
Momentum = Δp = 2500 Ns
So, your answer of 2500 Ns is correct.
To calculate the momentum at the end of 5 seconds of pushing, we need to use the formula for momentum:
Momentum (p) = mass (m) × velocity (v)
In this case, the truck is initially at rest. Since the truck is free to roll with no resistance, the force you apply will accelerate the truck.
To determine the acceleration of the truck, we can use Newton's second law of motion:
Force (F) = mass (m) × acceleration (a)
Rearranging the formula, we get:
Acceleration (a) = Force (F) / mass (m)
Plugging in the given values:
Force (F) = 500 N
Mass (m) = 4000 kg
Acceleration (a) = 500 N / 4000 kg ≈ 0.125 m/s^2
Now, we can calculate the velocity of the truck after 5 seconds using the equation of motion:
Final velocity (v) = initial velocity (u) + acceleration (a) × time (t)
Since the truck was initially at rest, the initial velocity (u) is 0 m/s.
Final velocity (v) = 0 m/s + (0.125 m/s^2 × 5 s)
Final velocity (v) = 0.625 m/s
Finally, we can calculate the momentum:
Momentum (p) = mass (m) × velocity (v)
Momentum (p) = 4000 kg × 0.625 m/s
Momentum (p) = 2500 kg·m/s
So, the momentum at the end of 5 seconds of pushing is 2500 kg·m/s. Therefore, your answer of 2500 is correct.