Starting at = 0 , a horizontal net force 0.265 (-0.445 is applied to a box that has an initial momentum -2.95 3.85 .
What is the momentum of the box at = 2.15 ?
To find the momentum of the box at t = 2.15, we can use the formula for momentum:
momentum = mass × velocity
However, since the problem does not provide the mass or velocity of the box directly, we need to find them using the information given.
Given:
Initial momentum (at t = 0) = -2.95 Ns
Force = 0.265 N
Time = 2.15 s
To find the mass of the box, we can rearrange the formula for force:
force = mass × acceleration
Since force and acceleration are both given, we can solve for mass:
mass = force / acceleration
In this case, the acceleration is given as the net force applied to the box. Therefore, we have:
mass = 0.265 N / (-0.445 m/s^2)
Simplifying the expression, we find:
mass = -0.596 kg
Next, we need to find the final velocity of the box at t = 2.15 s. To do this, we can use the equation:
final velocity = initial velocity + (acceleration × time)
Given:
Initial momentum (at t = 0) = -2.95 Ns
Initial velocity = (initial momentum) / (mass) = (-2.95 Ns) / (-0.596 kg) = 4.95 m/s
Acceleration = net force / mass = (-0.445 m/s^2) / (-0.596 kg) = 0.747 m/s^2
Time = 2.15 s
Substituting the values into the equation, we find:
final velocity = 4.95 m/s + (0.747 m/s^2 × 2.15 s)
Simplifying the expression, we have:
final velocity = 4.95 m/s + 1.61 m/s = 6.56 m/s
Finally, we can calculate the momentum of the box using the formula:
momentum = mass × velocity
Substituting the values, we find:
momentum = -0.596 kg × 6.56 m/s = -3.91 Ns
Therefore, the momentum of the box at t = 2.15 s is -3.91 Ns.
To find the momentum of the box at time t = 2.15 seconds, we need to use the principle of impulse-momentum, which states that the change in momentum of an object is equal to the net force applied to it multiplied by the time over which the force is applied.
The formula for impulse-momentum is given by:
Impulse = Force * Time
Given:
Initial momentum (p) = (-2.95, 3.85) (components of momentum in the x and y directions respectively)
Net force (F) = (0.265, -0.445) (components of force in the x and y directions respectively)
Time (t) = 2.15 seconds
Now, let's calculate the change in momentum (Δp) using the given formula:
Δp = F * t
Δp = (0.265, -0.445) * 2.15
= (0.57075, -0.95675)
To find the final momentum (p_final), we need to add the change in momentum to the initial momentum:
p_final = p + Δp
p_final = (-2.95, 3.85) + (0.57075, -0.95675)
= (-2.37925, 2.89325)
Therefore, the momentum of the box at t = 2.15 seconds is approximately (-2.37925, 2.89325).