A net force of 12 N changes the momentum of a 250-g ball by 3.7 kgm/s. The force acts for
Force * time = impulse = change of momentum = m (V2-V1)
12 * t = 3.7
t = 3.7 /12 = 0.308 seconds
...as long as it takes to make a really bad joke. Why did the scarecrow win an award? Because he was outstanding in his field! Now, back to your question. To find the time, we can use Newton's second law of motion, F = Δp/t, where F is the net force, Δp is the change in momentum, and t is the time. Rearranging the equation gives us t = Δp / F. Plugging in the values, we get t = 3.7 kgm/s / 12 N. Simplifying that gives us t = 0.3083333333 seconds. So, the force acts for approximately 0.3083333333 seconds... or about as long as it takes for me to tell a terrible joke!
To find the time the force acts for, we can use the formula for impulse,
Impulse = Force * Time
Given that the impulse is equal to the change in momentum, which is 3.7 kgm/s, and the force is 12 N, we can rearrange the formula as follows:
3.7 kgm/s = 12 N * Time
Now, we can solve for Time:
Time = 3.7 kgm/s / 12 N
Time ≈ 0.3083 s
Therefore, the force acts for approximately 0.3083 seconds.
To determine the time for which the force acts, we can use the formula for impulse:
Impulse = Force * Time
Given:
Net force (F) = 12 N
Change in momentum (Δp) = 3.7 kgm/s
We need to solve for time (t).
Rearranging the equation, we get:
Time (t) = Impulse / Net force
Substituting the given values, we have:
t = Δp / F
t = 3.7 kgm/s / 12 N
Now, we need to convert the mass to kilograms:
Mass (m) = 250 g
m = 250 g * (1 kg / 1000 g) = 0.25 kg
Substituting the values, we have:
t = 3.7 kgm/s / 12 N
t = 0.25 kg * 3.7 kgm/s / 12 N
t = 0.925 kgm/s / 12 N
t ≈ 0.0771 s
Therefore, the force acts for approximately 0.0771 seconds to change the momentum of the 250-g ball by 3.7 kgm/s.