A resultant force of 12N acts on a body mass of 10kg with momentum of 400kgm/s. How long does the force act on the body.
The force acts on the body for 0.03 seconds. This can be calculated using the equation F = m*a, where F is the force, m is the mass, and a is the acceleration. Rearranging the equation to solve for a, we get a = F/m. Then, using the equation p = m*v, where p is the momentum and v is the velocity, we can solve for v, which is equal to 400/10 = 40 m/s. Finally, we can use the equation v = a*t, where t is the time, to solve for t, which is equal to 40/12 = 0.03 seconds.
To find the time the force acts on the body, we can use the impulse-momentum theorem. The impulse-momentum theorem states that the change in momentum of an object is equal to the force applied multiplied by the time over which the force acts.
The formula for impulse is given by:
Impulse = Force * Time
And the formula for momentum is given by:
Momentum = Mass * Velocity
Given:
Resultant Force (F) = 12 N
Mass (m) = 10 kg
Momentum (p) = 400 kgm/s
To find the time (Δt) we need to rearrange the impulse formula:
Impulse = Momentum(final) - Momentum(initial)
Initial momentum (p_initial) = 0 kgm/s (assuming the object starts from rest)
Impulse = F * Δt
Impulse = (m * v_final) - (m * v_initial)
Impulse = m * (v_final - v_initial)
Since the object starts from rest, v_initial is 0, so the formula becomes:
Impulse = m * v_final
Now we can substitute the given values:
12 N * Δt = 10 kg * (v_final)
To find v_final, we can use the formula for momentum:
v_final = p / m
v_final = 400 kgm/s / 10 kg
v_final = 40 m/s
Substituting the value of v_final:
12 N * Δt = 10 kg * 40 m/s
Rearranging the equation to solve for Δt:
Δt = (10 kg * 40 m/s) / 12 N
Δt = 400 kgm/s / 12 N
Calculating the result:
Δt ≈ 33.33 seconds
Therefore, the force acts on the body for approximately 33.33 seconds.
To calculate the time the force acts on the body, we need to use the formula:
Impulse = Force * Time
The impulse is given by the change in momentum, which can be calculated as:
Impulse = Mass * Change in velocity
Given that the mass of the body is 10 kg and the initial momentum is 400 kg⋅m/s, we can calculate the initial velocity using the formula:
Initial momentum = Mass * Initial velocity
Rearranging the formula to find the initial velocity:
Initial velocity = Initial momentum / Mass
= 400 kg⋅m/s / 10 kg
= 40 m/s
Now, we can find the change in velocity using the formula:
Change in velocity = Final velocity - Initial velocity
Let's assume the final velocity is zero since the body comes to rest after the force stops acting on it:
Final velocity = 0 m/s
Therefore, the change in velocity is:
Change in velocity = 0 m/s - 40 m/s
= -40 m/s
Now, we can calculate the impulse using the formula:
Impulse = Mass * Change in velocity
= 10 kg * (-40 m/s)
= -400 kg⋅m/s
Finally, we can find the time the force acts on the body by rearranging the impulse formula:
Time = Impulse / Force
= -400 kg⋅m/s / 12 N
≈ -33.33 s
Keep in mind that time can only be positive, so we consider the magnitude of time:
Time = | -33.33 s |
≈ 33.33 s
Therefore, the force acts on the body for approximately 33.33 seconds.