A 4 kg puck can slide with negligible friction over a horizontal surface, taken as the xy plane.
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The puck has a velocity of 3i m / s at one instant ti = 0 . Eight seconds later, its velocity is to be
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8i+10 j m / s . Find the magnitude and direction of the net force acting on the puck.
To find the net force acting on the puck, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration. The acceleration of the puck can be determined by using its initial and final velocities.
1. Calculate the acceleration:
Since the acceleration is the change in velocity over time, we can determine it using the formula:
acceleration = (final velocity - initial velocity) / time
Given:
Initial velocity (vi) = 3i m/s
Final velocity (vf) = 8i + 10j m/s
Time (t) = 8 seconds
Substituting the values into the formula, we get:
acceleration = (8i + 10j - 3i) / 8
= (5i + 10j) / 8
2. Calculate the net force:
Now that we have the acceleration, we can find the net force using Newton's second law:
net force = mass × acceleration
Given:
Mass (m) = 4 kg
Acceleration (a) = (5i + 10j) / 8
Substituting the values into the formula, we get:
net force = 4 kg × (5i + 10j) / 8
= (20/8) kg × (5/8)i + (20/8) kg × (10/8)j
= 2.5i + 5j
Therefore, the magnitude of the net force acting on the puck is √(2.5^2 + 5^2) ≈ √(6.25 + 25) ≈ √31.25 ≈ 5.59 Newtons.
The direction of the net force can be determined by finding the angle it makes with the positive x-axis. Using trigonometry, we can calculate the angle θ:
θ = arctan(Fy / Fx) = arctan(5 / 2.5) = arctan(2) ≈ 63.43°
Thus, the magnitude of the net force acting on the puck is approximately 5.59 Newtons, and it is directed at an angle of approximately 63.43° with the positive x-axis.