Question 1) How much work is needed to push a 137- kg packing crate a distance o

Question

Question 1) How much work is needed to push a 137- kg packing crate a distance of 2.65 m up an inclined plane that makes an angle of 34 o with the horizontal, when inclined plane is frictionless? The coefficient of friction between the crate and the inclined plane is 0.28?

Question 2)

A block of mass m = 750 g is released from rest and slides down a frictionless track of height h = 64.5 cm. At the bottom of the track the block slides freely along a horizontal table until it hits a spring attached to a heavy, immovable wall. The spring compressed by 2.51 cm at the maximum compression. What is the value of the spring constant k?

Explanation / Answer

here,

1)

mass , m = 137 kg

distance , d = 2.65 m

theta = 34 degree

the work done needed , W = ( m * g * sin(theta) + uk * m * g * cos(theta)) * d

W = ( sin(34) + 0.28 * cos(34)) * 137 * 9.8 * 2.65

W = 2815.44 J

the work done needed is 2815.44 J

2)

m = 0.75 kg

h = 0.645 m

compression in the spring , x = 0.0251 m

let the spring constant be k

potential energy is converted into spring energy

m * g * h = 0.5 * k * x^2

0.75 * 9.8 * 0.645 = 0.5 * k * 0.0251^2

k = 15049.76 N/m

the spring constant is 15049.76 N/m

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