Solving Impulse & Power: mΔv vs. FΔt

[Bengalfan985]

Homework Statement

A boy pulls his brother in a wagon (total mass of 35kg). He exerts a force of 72 N at an angle of 45° above the horizontal.
a) How much power is he using if he walks 10 meters in 6.4 seconds?
b) How fast will his brother be going after 6.4 seconds
c) What is the impulse imparted to the brother and wagon (assume they start at rest)?

Homework Equations

P = W/t
W = ΔK
Δp = mΔv = FΔt

The Attempt at a Solution

a) P = W/t = F_x d/t = Fcosθd/t = 72cos(45°)(10)/6.4 = 79.5 Watts

b) W = ΔK = K_f - K_i = K_f - 0 = 1/2 m (v_f)^2
v_f = √(2Fcosθd/m) = √(2(72)cos(45°)10/35) = 5.4 m/s

c) Δp = mΔv = 35(v_f - v_i) = 35(5.4 - 0) = 189 kg⋅m/s

Hi, I have a question about part c. The answer was correct with 189 kg⋅m/s, but I first tried solving it with Δp = FΔt. Why doesn't Δp = FΔt work?

Δp = FΔt = F_x t = Fcosθt = 72cos(45°)6.4 = 326N⋅s

The units are the same, right? N⋅s = kg⋅m/s

 

[Nathanael]

I believe the question is inconsistent. If he constantly applies 72N (at a constant 45°) and he starts at rest, then he won't travel 10 meters in 6.4 seconds. In other words, the "assume they start at rest" in part C is an incorrect assumption; the initial speed is already uniquely determined by part A (and it is not zero).

The v calculated in part B is wrong (it assumed it started at rest) so FΔt would actually be the correct answer (and mΔv would indeed give the same answer if the speeds were properly calculated).

 

[Bengalfan985]

You're right, thanks! 326 would be the correct answer. With a constant force, if he travels 10 meters, he can't start from rest (he'd start with a velocity of -3.1m/s). If he starts from rest, he can't travel only 10 meters (he traveled 29.8 meters).