Question

a spring is compressed 15 centimeters when a 8.5 kilogram weight is set upon it. how much power would be needed to stretch out the same spring 1.5 meters horizontally in 4 seconds?

Answer 1

159.38 Watts

Step-by-step explanation:

Initially;

• Mass on the spring is 8.5 kg
• Therefore, compression force is 85 N
• Compression distance is 15 cm or 0.15 m

But;

F = kx

where F is the force of compression, k is the spring constant and x is the compression distance.

Thus;

k = F/x

= 85 N ÷0.15

= 566.67 N/m

We are required to determine the power needed to stretch the same spring for 1.5 m in 4 secs.

Power = Work done ÷ time

Work done is given by 0.5kx²

Therefore;

Power = 0.5kx²÷ t

= (0.5×566.67 N/m × 1.5² ) ÷ 4 seconds

= 159.38 Watts

Thus, the power needed is 159.38 watts