Read each statement below. For each situation, calculate vi, vf, pi, pf, the impulse vector Ft, and the amount of force needed for the change to occur. All situations refer to a truck with a mass of 2840 kg
3.) The truck is at rest. In 5.00s, the truck backs up to a speed of 1.38m/s.
To solve this problem, we can use the basic principles of Newton's second law and the definition of impulse.
First, let's identify the given values:
- Mass of the truck (m): 2840 kg
- Initial velocity (vi) of the truck: 0 m/s (since it is at rest initially)
- Final velocity (vf) of the truck: 1.38 m/s
- Time (t): 5.00 s
Next, let's calculate the initial momentum (pi) of the truck. The formula for momentum (p) is given by:
p = m * v
where m is the mass and v is the velocity.
pi = m * vi
= 2840 kg * 0 m/s
= 0 kg·m/s
Since the truck is initially at rest, its initial momentum is 0 kg·m/s.
Now, let's calculate the final momentum (pf) of the truck. The formula for momentum is the same as above:
pf = m * vf
= 2840 kg * 1.38 m/s
= 3919.2 kg·m/s
The change in momentum (Δp) is given by:
Δp = pf - pi
Δp = 3919.2 kg·m/s - 0 kg·m/s
= 3919.2 kg·m/s
The impulse (Ft) experienced by the truck is equal to the change in momentum. The impulse can also be calculated using the formula:
Ft = Δp
= m * (vf - vi)
Ft = 2840 kg * (1.38 m/s - 0 m/s)
= 3919.2 kg·m/s
Finally, we can calculate the average force (F) exerted on the truck to produce this change in momentum. The formula for average force is:
F = Ft / t
F = 3919.2 kg·m/s / 5.00 s
= 783.84 N
Therefore, in order for the truck to back up to a speed of 1.38 m/s in 5.00 s, an average force of 783.84 N is required.