An object of mass m = 2.7 kg moves with initial speed vinitial = 2.2 m/s, then interacts with its environment, releasing 4.4 J of work. What is the speed of the object after the interaction is completed?
My ans:
I found KE initially and then subtracted 4.4J and with the new value i recalculated v...but the answer was wrong. So I am not sure what i am doing wrong
If the initial KE you got was 6.53 J, and you subtract 4.4 because of doing work, then the remaining KE is 2.13 J. Convert that back to velocity. It is about 57% of the initial velocity. If you got similar answers and the book says it is wrong, the difference may be in how the answer was rounded off. I would keep three significant figures until the last calculation, and then round the answer off to two figures. I cannot see what you did, or what the "book" answer is, so can't find the source of the discrepancy
To find the final speed of the object, we need to use the principle of conservation of mechanical energy. The initial mechanical energy (KE_initial) of the object is equal to its final mechanical energy (KE_final).
The initial kinetic energy (KE_initial) can be calculated using the formula:
KE_initial = (1/2) * m * (v_initial)^2
Given:
m = 2.7 kg (mass of the object)
v_initial = 2.2 m/s (initial speed)
Substituting the values:
KE_initial = (1/2) * 2.7 kg * (2.2 m/s)^2
= 6.726 J
Now, as the object interacts with its environment, it releases 4.4 J of work. This work is in the form of energy transferred out of the object, causing a decrease in its final kinetic energy.
So, the final kinetic energy (KE_final) can be calculated by subtracting the work done from the initial kinetic energy:
KE_final = KE_initial - Work
Substituting the values:
KE_final = 6.726 J - 4.4 J
= 2.326 J
Now, we can calculate the final speed (v_final) using the formula for kinetic energy:
KE_final = (1/2) * m * (v_final)^2
Rearranging the equation and solving for v_final, we get:
(v_final)^2 = (2 * KE_final) / m
v_final = √ ( (2 * KE_final) / m )
Substituting the values:
v_final = √ ( (2 * 2.326 J) / 2.7 kg )
= √ (4.652/2.7) m/s
= √1.72 m/s
= 1.31 m/s (rounded to two decimal places)
Therefore, the speed of the object after the interaction is completed is 1.31 m/s.