I need a 1.00 W motor to push a garbage compactor so that it squishes some garbage. The garbage has a spring constant of 49.7 N/m. If I am going to squish it 30 cm, determine how much time the compactor takes.
Average force = Fav
= (1/2)*49.7 N/m*(0.30 m)
= 7.46 N
Work = Fav*X = 2.24 J
Power*T = 2.24 J
T = 2.24 seconds
thats not right. you forgot to square the x value. 0.30 should have been 0.09
To determine the time it takes for the compactor to squish the garbage, we can use the concept of work and power.
First, let's find the force required to compress the spring. We know that the spring constant is 49.7 N/m and the displacement is 30 cm (which is 0.3 m).
Using Hooke's Law, the force required to compress the spring can be calculated as:
Force = Spring constant * Displacement
= 49.7 N/m * 0.3 m
= 14.91 N
Now, let's calculate the work done to compress the spring. Given that work is equal to the product of force and displacement, the work done is:
Work = Force * Displacement
= 14.91 N * 0.3 m
= 4.473 J (Joules)
Since power is defined as the rate at which work is done, we can use the formula:
Power = Work / Time
Given that the power of the motor is 1.00 W (watt) and the work done is 4.473 J, we can rearrange the formula to solve for time:
Time = Work / Power
= 4.473 J / 1.00 W
= 4.473 seconds
Therefore, it would take approximately 4.473 seconds for the compactor to squish the garbage.