#6 Please answer the question neatly with steps and show all units, for good rat

Question

#6 Please answer the question neatly with steps and show all units, for good rating!

S. A 4.0kg block slides at 3.0m/s on a horizontal frictionless surface and bumps into one end of a spring whose Hooke's law constant is 100N (Assume the other end ofthe spring is tigidly held ace. And ignore any loss of energy in the joining of the mass with the end ofthe spring. Also, ignore the mass of the spring.) How far is the spring compressed when the block comes a How fast would the block and spring be movingat the point spring has been compressed 0.44m? 6, A 5.0kg object is subjected to the force of F -[(10Nm)xhit mg it GONyk. fa furetion 3m) to a How much work is done by this foroe from a starting position of (xa, yo, z)-(1m, 2m, by the final position of (x, yr, zo (3m, 5m,00? fbl Determine the work on a 0.14kg baseball pitcher in delivering a pitch at a speed of95mihr 42.5m's Note that the ball starts from rest as the pitcher begins his motion and leaves his at (chifthe baseball in PertA is on a displacement distance 2.0m during the delivery, what is the average or constant force acting it? What is the of pitcher Watts? in hp? average power ofthe in (Note that Parts b, c, & dbave no connection to Part a)

Explanation / Answer

5)

initial kinetic energy Ki = (1/2)*m*v^2

final elastic poptential stored in spring Uf = (1/2)*k*x^2

from energy c0nservation

Uf = KI

(1/2)*100*x^2 = (1/2)*4*3^2

x = 0.6 m <<<<------------answer

(b)

from energy conservation

Ki = Kf + Uf

(1/2)*m*v^2 = (1/2)*m*v1^2 + (1/2)*k*x1^2

5*3^2 = 5*v1^2 + 100*0.44^2

speed v1 = 2.26 m/s <<<<-----answer

=================

(6)

work = F.r

r = r2 - r1 = (3-1)i + (5-2)j + (0-3)k

r = 2i + 3 j - 3 k

F = -10i +(-mg) j + (30 ) k = -10i - (5*9.8)j + 30 k

W = ( - 10i - 49 j + 30 k) . (2i + 3j - 3k)

W = -(10*2) - (49*3) - (30*3)

W = -257 J <<<-------answer

(b)

work = change in KE = Kf - Ki

Ki = 0

W = Kf = (1/2)*m*v^2

W = (1/2)*0.14*42.5^2 =126.44 J

(c)

W = F*x

F = W/x = 126.44/2 = 63.22 N

(d)

power = (1/2)*F*V = (1/2)*63.22*42.5 = 1343.425 W = 1343.425/746 = 1.8 hp <<<<-------answer

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