A block of mass m=2 kg is initially at rest on a horizontal surface. At time t=0, we begin pushing on it with a horizontal force that varies with time as F(t)=Beta t^2, where Beta = 1.0 N/s^2. We stop pushing at time t1, 5s [F(t)=0 for t>1].
(a) First, assume the surface is frictionless. What is the magnitude of the final momentum at t1=5s?
P final(t=t1)=
(b) lets now consider a new situation where the object is initially at rest on a rough surface. The coefficient of static friction is 0.2. What is the speed of the block at time t2=5s?
v(t=t2)=
(c) What is the power P provided by the force F(t) at time t3=4s (in Watts) i the case where there is friction (part(b))?
P(t=t3)=
Question No. 2 any ideas.
for a: 41.67
for b:
F - f_k = ma
F - f_k = mdv/dt
(F - f_k)dt = mdv
∫(F - f_k)dt = ∫mdv
mv_f - mv_i = (β/3)(t_f)^3 - (f_k)t_f - [(β/3)(t_i)^3 - (f_k)t_i] [Note: v_i = 0 and t_i = 0]
mv_f = (β/3)(t_f)^3 - (f_k)t_f
v_f ≅ 10.83, but that's not the answer, so any suggeston any one???
Are you sure about a?
ellie, Thanks. I thought this is the most difficult question. I had trouble with these type of problems throughout the course. I do not have any suggestions. at this point.
I did pretty much the same of what you're showing and I got a) 25, b) 2.5 and c) 0.64 I haven't check it yet because it is my last submission and I want to be sure.
guys a is 25 for sure
have you check your data, because for a got a green mark, so A is ok, but b and c were not. There might be some where m = 3 and beta=1.2
For question 5 ballistic missile m1= 5*10^24kg; r1=6000km; m2<<m1; alpha=30 degrees; r2=(5/2)r1=15000; G=6.674*10^-11. What is the initial speed of the projectile? My solution:
Vo^2=g*range/sin(theta)
Vo^2=6.674*10^-11*(r1+r2/sin30degrees)
Vo^2=(6.674*10^-11)*(21000/0.5)
Vo^2=0.00000280308
Vo=sqrt(0.00000280308)
Vo=0.00167424
Is this done correctly. Thanks for all your help.