physics need help?

Question

1. A lawn mower (25kg) is pushed downward w/ a force of 50N at an angle of 60 degree w/ the horizontal distance of 5m. The frictional force opposing the motion is 20N. If it starts at rest, what will the speed of the lawnmower be after traveling 5m?

2. When a 7.0kg metal shell is fired from a cannon barrel that has a length of 2.5m, the explosive force exerted on the shell while it is in the barrel varies in the manner shown in the graph below (weblink). Assume the barrel is horizontal and neglect the effects of the friction inside the barrel. Determine the approximate muzzle velocity of the shell at the instant it leaves the barrel.

http://i23.photobucket.com/albums/b354/Sunshinegirl93534/graph.jpg

Answer 1

1. was answered by jsardi56
2. the energy is integral of Fdx along the barrel, it is also 0.5mv^2.
a. integral of Fdx is also the area below the graph we can divide the graph to 3 sections 0..1, 1..1.5 and 1.5..2.5.
0..1 the area is (15,000 + 10,000) / 2 = 12,500j
1..1/5 the area is 10,000 * 0.5 = 5,000j
1.5..2.5 the area is 10,000 / 2 = 5,000j
in total 22,500j = 7 / 2 * v^2
v = sqrt(45,000 / 7) = sqrt(6,428.6) = 80.2 m/s

Answer 2

1.) f(net horizontal) = 50(cos60) -20 = 5 N
a = 5/25 = .2 m/s^2
s = (1/2)at^2
t = √(2s/a) = √10/.2 = 5√2
v = at = .2(5√2)
= 1.414 m/s