Please I need final answers only , without any explanation Example : a=6m/s^2 Q1

Question

Please I need final answers only , without any explanation

Example :

a=6m/s^2

Q1) While a roofer is working on a roof that slants at 37.0?above the horizontal, he accidentally nudges his 88.0N  toolbox, causing it to start sliding downward, starting from rest.

If it starts 4.60m from the lower edge of the roof, how fast will the toolbox be moving just as it reaches the edge of the roof if the kinetic friction force on it is 18.0N ?

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Q2) A force parallel to the x-axis acts on a particle moving along the x-axis. This force produces a potential energy U(x) given by U(x)=? x4 where ?=1.15J/m4 .

What is the force when the particle is at position x = -0.730m ?

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Q3) A spring-loaded toy gun is used to shoot a ball of mass m straight up in the air. (Figure 1) The spring has spring constant k. If the spring is compressed a distance x0from its equilibrium position ( y=0 ) and then released, the ball reaches a maximum height hmax (measured from the equilibrium position of the spring). There is no air resistance, and the ball never touches the inside of the gun. Assume x0?hmax.

http://session.masteringphysics.com/problemAsset/1011014/17/1011014.jpg

Part A

Find v0, the muzzle velocity of the ball (the velocity of the ball at height h=0 above the equilibrium position).

Express your answer in terms of given quantities.

Part B

Find the maximum height of the ball.

Example : a=6m/s^2 While a roofer is working on a roof that slants at 37.0?above the horizontal, he accidentally nudges his 88.0N toolbox, causing it to start sliding downward, starting from rest. A force parallel to the x-axis acts on a particle moving along the x-axis. This force produces a potential energy U(x) given by U(x)=? x4 where ?=1.15J/m4. What is the force when the particle is at position x = -0.730m ? A spring-loaded toy gun is used to shoot a ball of mass m straight up in the air. (Figure 1) The spring has spring constant k. If the spring is compressed a distance x0from its equilibrium position ( y=0 ) and then released, the ball reaches a maximum height hmax (measured from the equilibrium position of the spring). There is no air resistance, and the ball never touches the inside of the gun. Assume x0?hmax. Find v0, the muzzle velocity of the ball (the velocity of the ball at height h=0 above the equilibrium position). Express your answer in terms of given quantities. Find the maximum height of the ball.

Explanation / Answer

1)let v be the speed

we know that

(1/2)mv^2 = (w - f) x S

or v^2 = (2(w - f) x S/m)

or v = (2(w - f) x S/m)^1/2

where w = 88.0 N,f = 18.0 N,S = 4.60 m and m is mass of toolbox

2)the potential energy is given by

U = k x S^4

where S = 1.15 J/m^4

Also,

U = F x S

where F is force

or F x S = k x S^4

or F = k x S^3

when S = -0.730 m then

F = 1.15 x (-0.730)^3 N

3)the force acting on the ball is balanced by the force acting on the spring therefore

m x a = k x s_o

or a = (k x s_o/m)

where k is spring constant,s_o is compressed length and m is mass

we know that

v^2 - v_o^2 = 2ah_max

or v_o^2 = v^2 - 2ah_max

or v_o = (v^2 - 2ah_max)^1/2

where v_o is muzzle velocity and v = 0

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