what impulse occurs when an average force of 10n is exerted on a cart of 2.5 s? What change in momentumdoes the cart undergo/ If the mass of the cart is 2K and the cart is initally at rest, calculate it's final speed.
To find the impulse, we can use the formula:
Impulse = Force x Time
Given that the average force exerted on the cart is 10 N, and the time is 2.5 s:
Impulse = 10 N x 2.5 s = 25 N·s
The change in momentum of the cart is equal to the impulse. So, the change in momentum is 25 N·s.
To calculate the final speed of the cart, we can use the equation:
Impulse = Change in momentum = mass x (final velocity - initial velocity)
Since the mass of the cart is given as 2 kg, and the cart is initially at rest (so the initial velocity is 0 m/s):
25 N·s = 2 kg x (final velocity - 0 m/s)
Simplifying the equation:
25 N·s = 2 x final velocity
Dividing both sides by 2 kg:
final velocity = 25 N·s / 2 kg = 12.5 m/s
Therefore, the final speed of the cart is 12.5 m/s.
To find the impulse, we can use the formula:
Impulse = Force * Time
Given that the force exerted on the cart is 10N and the time is 2.5s:
Impulse = 10N * 2.5s = 25 Ns
The impulse experienced by the cart is 25 Newton-seconds (Ns).
To calculate the change in momentum, we can use the formula:
Change in momentum = Mass * Final velocity - Mass * Initial velocity
Given that the mass of the cart is 2 kg and the cart is initially at rest (hence, Initial velocity = 0), we can simplify the formula to:
Change in momentum = Mass * Final velocity
Plugging in the values:
Change in momentum = 2kg * Final velocity
Therefore, the change in momentum is 2 times the final velocity in kg·m/s.
To find the final velocity, we need to use the concept of impulse-momentum, which states:
Impulse = Change in momentum
Since we know that impulse is 25Ns:
25 Ns = 2kg * Final velocity
Solving for the final velocity:
Final velocity = 25 Ns / 2kg
Final velocity = 12.5 m/s
Hence, the final speed of the cart is 12.5 meters per second (m/s).