Help with work equations 1)A spring of spring constant 220 N/m is sitting on a t

Question

Help with work equations

1)A spring of spring constant 220 N/m is sitting on a table. You pick it up and stretch it so that it is 8.0 cm
longer than it was on the table top. How much work did it take you to stretch the spring? (Hint: This work
is just negative the work done by the spring on you!)

2)A block of mass 5.0 kg sits on a rough horizontal surface of coefficient of friction 0.12. A force of
magnitude F = 10.0 N pulls on the mass at an angle of 30? above the horizontal. The block is observed to
move across the surface a distance of 2.3 m. (a) What is the work done by the force F? (b) What is the value
of the apparent weight of the block? (c) What is the work done by the normal force? (d) What is the work
done by friction? (e) What is the work done by the gravitational force acting on the block?

Explanation / Answer

1) work done = energy stored in the spring = 1/2 kx^2 = 0.5*220*0.08^2 = 0.704 J

2)

friction force = 0.12*(5*9.8-10sin30) = 5.28 N

force in horizontal direction = 10cos30 = 8.66 N

so the block will move in horizontal direction.

a) work done = net force*distance = 10 cos30 *2.3 = 19.92 J

b)apparent weight = mg-fsin30 = 5*9.8-10*sin30 = 44 N

c) work done by normal force = 0 as displacement in the direction of normal force is 0

d) work done by friction= friction force*distance = -5.28*2.3 = -12.144 J

e) work done by gravity is 0 as displacement in the direction of gravity is 0

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