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.
1. The truck has a velocity of 8.30 m/s and comes to a stop in 15.0 s.
2. The truck, initially at rest, reaches a velocity of 8.30 m/s in 20.0 s.
3. The truck is at rest. In 5.00 s, the truck backs up to a speed of 1.38 m/s.
4. The truck is moving backward with a velocity of 1.38 m/s and comes to a stop in 5.00 s.
I'll do one of these. I don't see wht you can't do the others yourself. Give is a try.
1. The truck has a velocity of 8.30 m/s and comes to a stop in 15.0 s.
vi (inital) = 8.30 m/s
vf (final) = 0
pi (inital momentum) = 2840*8.3 = 23,572 kg*m/s
pf = 0
Impulse = pf - pi = -23672 kg*m/s
Force required = (impluse/time) =
-23672/15 = -1571 newtons
It is negative becasue the force must oppose the motion.
-1571 n
Sure! Let's solve each situation step by step:
1. The truck has a velocity of 8.30 m/s and comes to a stop in 15.0 s.
- Initial velocity (vi) = 8.30 m/s
- Final velocity (vf) = 0 m/s (comes to a stop)
- Initial momentum (pi) = mass * vi = 2840 kg * 8.30 m/s
- Final momentum (pf) = mass * vf = 2840 kg * 0 m/s
- Impulse vector (Ft) = pf - pi = mass * (vf - vi) = 2840 kg * (0 m/s - 8.30 m/s)
- Amount of force needed for the change to occur = Ft / t = (2840 kg * (0 m/s - 8.30 m/s)) / 15.0 s
2. The truck, initially at rest, reaches a velocity of 8.30 m/s in 20.0 s.
- Initial velocity (vi) = 0 m/s (initially at rest)
- Final velocity (vf) = 8.30 m/s
- Initial momentum (pi) = mass * vi = 2840 kg * 0 m/s
- Final momentum (pf) = mass * vf = 2840 kg * 8.30 m/s
- Impulse vector (Ft) = pf - pi = mass * (vf - vi) = 2840 kg * (8.30 m/s - 0 m/s)
- Amount of force needed for the change to occur = Ft / t = (2840 kg * (8.30 m/s - 0 m/s)) / 20.0 s
3. The truck is at rest. In 5.00 s, the truck backs up to a speed of 1.38 m/s.
- Initial velocity (vi) = 0 m/s (initially at rest)
- Final velocity (vf) = -1.38 m/s (negative value indicates backing up)
- Initial momentum (pi) = mass * vi = 2840 kg * 0 m/s
- Final momentum (pf) = mass * vf = 2840 kg * (-1.38 m/s)
- Impulse vector (Ft) = pf - pi = mass * (vf - vi) = 2840 kg * (-1.38 m/s - 0 m/s)
- Amount of force needed for the change to occur = Ft / t = (2840 kg * (-1.38 m/s - 0 m/s)) / 5.00 s
4. The truck is moving backward with a velocity of 1.38 m/s and comes to a stop in 5.00 s.
- Initial velocity (vi) = -1.38 m/s (negative value indicates backward motion)
- Final velocity (vf) = 0 m/s (comes to a stop)
- Initial momentum (pi) = mass * vi = 2840 kg * (-1.38 m/s)
- Final momentum (pf) = mass * vf = 2840 kg * 0 m/s
- Impulse vector (Ft) = pf - pi = mass * (vf - vi) = 2840 kg * (0 m/s - (-1.38 m/s))
- Amount of force needed for the change to occur = Ft / t = (2840 kg * (0 m/s - (-1.38 m/s))) / 5.00 s
Please note that the final answers for force needed (amount of force) will depend on the actual calculation of the values in the given equations.
To find the values of vi, vf, pi, pf, impulse vector Ft, and the amount of force needed for each situation, we can use the equations of motion and impulse-momentum principle. Here's how to calculate them for each scenario:
1. The truck has a velocity of 8.30 m/s and comes to a stop in 15.0 s.
- Initial velocity (vi) = 8.30 m/s
- Final velocity (vf) = 0 m/s (since the truck comes to a stop)
- Initial momentum (pi) = m * vi = 2840 kg * 8.30 m/s
- Final momentum (pf) = m * vf = 2840 kg * 0 m/s
- Impulse vector (Ft) = pf - pi = m * vf - m * vi
- Amount of force needed = Ft / t (where t is the time taken for the change)
2. The truck, initially at rest, reaches a velocity of 8.30 m/s in 20.0 s.
- Initial velocity (vi) = 0 m/s (since the truck is initially at rest)
- Final velocity (vf) = 8.30 m/s
- Initial momentum (pi) = m * vi = 2840 kg * 0 m/s
- Final momentum (pf) = m * vf = 2840 kg * 8.30 m/s
- Impulse vector (Ft) = pf - pi = m * vf - m * vi
- Amount of force needed = Ft / t (where t is the time taken for the change)
3. The truck is at rest. In 5.00 s, the truck backs up to a speed of 1.38 m/s.
- Initial velocity (vi) = 0 m/s (since the truck is initially at rest)
- Final velocity (vf) = -1.38 m/s (negative sign indicates the truck is moving backward)
- Initial momentum (pi) = m * vi = 2840 kg * 0 m/s
- Final momentum (pf) = m * vf = 2840 kg * (-1.38 m/s)
- Impulse vector (Ft) = pf - pi = m * vf - m * vi
- Amount of force needed = Ft / t (where t is the time taken for the change)
4. The truck is moving backward with a velocity of 1.38 m/s and comes to a stop in 5.00 s.
- Initial velocity (vi) = -1.38 m/s (negative sign indicates the backward direction)
- Final velocity (vf) = 0 m/s (since the truck comes to a stop)
- Initial momentum (pi) = m * vi = 2840 kg * (-1.38 m/s)
- Final momentum (pf) = m * vf = 2840 kg * 0 m/s
- Impulse vector (Ft) = pf - pi = m * vf - m * vi
- Amount of force needed = Ft / t (where t is the time taken for the change)
To calculate the values for each situation, use the given mass of the truck (2840 kg) and substitute it into the appropriate formulas.