I need help with 3 questions, please. Thanks! A 165 g textbook slides up an 18.1

Question

I need help with 3 questions, please. Thanks!

A 165 g textbook slides up an 18.1° incline that is 2.75 m long. Using conservation of energy and assuming the incline is frictionless, what minimum initial speed is needed to accomplish this?

A pinball traveling with speed v on a horizontal frictionless surface hits and compresses a spring by 8.60 cm. If the speed of the pinball was instead 2v, what will the compression of the spring become?

You are lawn bowling and bowl a 430 g ball with a speed of 5.89 m/s. Unfortunately, your ball hits a large rock, resulting in a perfectly elastic collision. If the final velocity of the rock after the collision is 2.32 m/s, what must the mass of the rock be?

Explanation / Answer

height of the incline h = L*sintheta

initial mechnaical enenrgy Ei = (1/2)*m*v^2

final mechanical energy Ef = m*g*h

from conservation of energy Ef = Ei

(1/2)*m*v^2 = m*g*h

v = sqrt(2*g*h)

v = sqrt(2*g*L*sintheta)

v = sqrt(2*9.8*sin18.1)

v = 2.47 m/s

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

intial mechanical energy Ei = (1/2)*m*v^2

final mechanical energy Ef = (1/2)*k*x^2

Ef = Ei

(1/2)*k*x^2 = (1/2)*m*v^2

x = v*sqrt(k/m)

x2/x1 = v2/v1

x2/8.6 = 2v/v

x2 = 17.2 cm <<<<----------ANSWER

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

momentu before collision = momentum after collison

m1*v1i + m2*v2i = m1*v1f + m2*v2f

430*5.89 + 0 = 430*v1f + m2*2.32 ............(1)

from conservation of kinetic energy

kinetic energy before collision = kinetic energy after collision

(1/2)*m1*V1i^2 + (1/2)*m2*v2i^2 + (1/2)*m1*v1f^2 + (1/2)*m2*v2f^2

430*5.89^2 + 0 = 430*v1f^2 + (m2*2.32^2) ............(2)

solving 1 &2

m2 = 1753.4 g   <<<<---------ANSWER

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