A 75 particle is moving to the left at 29 . How much work must be done on the particle to cause it to move to the right at 46 ?
To calculate the amount of work done on a particle, we can use the formula:
Work = force x distance
In this scenario, we are given the initial velocity of the particle (29 m/s to the left) and we want to find the work done to make it move to the right with a velocity of 46 m/s.
First, we need to find the force acting on the particle. The force required to change the direction of motion is given by the change in momentum.
Since momentum is defined as mass multiplied by velocity (p = mv), the initial momentum (p1) of the particle moving to the left is given by:
p1 = mass x initial velocity = 75 kg x (-29 m/s) = -2175 kg•m/s
Next, the final momentum (p2) of the particle moving to the right is given by:
p2 = mass x final velocity = 75 kg x 46 m/s = 3450 kg•m/s
The change in momentum (Δp) is calculated by subtracting the initial momentum from the final momentum:
Δp = p2 - p1 = 3450 kg•m/s - (-2175 kg•m/s) = 5625 kg•m/s
Now, the force required to change the direction of motion is equal to the rate of change of momentum. Therefore, we can calculate the force (F) using the equation:
F = Δp / Δt
In this case, since we are only interested in the magnitude of the force, we can omit the time interval (Δt). Therefore, the force (F) is equal to the change in momentum (Δp):
F = 5625 kg•m/s
Finally, we can calculate the work (W) done on the particle using the formula:
W = F x d
Where "d" represents the distance over which the force, and hence the work, is performed. However, in this case, the distance is not given, and we cannot calculate the work without this information.
Therefore, to find the work done, we need to know the distance over which the force is applied.