Answer:
F = 1475.75 N
Explanation:
Given:-
- The mass of the wagon m = 10 kg
- The slope angle θ = 37°
- The initial velocity of wagon at top of hill, vi = 0 m/s
- The amount of distance it plows into haystack, s2 = 2.0 m
-The wagon rolls down the slope for distance, s1 = 50 m
Find:-
Determine The force the haystack exerts on the wagon?
Solution:-
- First we must note that the wagon rolls down the slope with a constant acceleration due to gravity ( g ) component acting down the slope. The acceleration ( a ) of the wagon can be given as:
a = g*sin ( θ ).
- Since, the acceleration of the cart is constant we can apply third kinematic equation of motion with initial velocity at top of hill vi = 0 m/s and the velocity " v1 " right before it plows into the haystack at the bottom of hill after traveling a distance of s1 = 50 meters.
v1^2 = vi^2 + 2*a*s1
v1^2 = 0 + 2*g*sin ( θ )*s1
v1^2 = 2*9.81*sin ( 37 )*50
v1 = √590.381
v1 = 24.30 m/s
- The constant force exerted by the haystack ( F ) as the wagon plows the haystack with a velocity "v1" by a distance of s2 and comes to, final velocity vf = 0, a stop.
Apply principle of work-done energy:
- Where, work is done on the wagon by haystack for W = F*s2.
W = Δ K.E
W = 0.5*m* ( vf^2 - v1^2 )
F*s2 = 0.5*m*( v1 )^2
F = 0.5*m*( v1 )^2 / s2
F = 0.5*10*590.30 / 2
F = 1475.75 N
