A 0.025 kg golf ball moving at 27 m/s crashes through the window of a house in 5.0 10-4 s. After the crash, the ball continues in the same direction with a speed of 10 m/s. Assuming the force exerted on the ball by the window was constant, what was the magnitude of this force?
1850 N
To find the magnitude of the force exerted on the ball by the window, we can use the concept of impulse.
Step 1: Find the change in momentum of the golf ball.
The change in momentum, Δp, can be calculated using the formula:
Δp = m * Δv
Where:
Δp is the change in momentum
m is the mass of the golf ball
Δv is the change in velocity
Given:
m = 0.025 kg (mass of the golf ball)
Δv = 10 m/s - 27 m/s = -17 m/s (negative sign indicates a change in direction)
Substituting the values into the formula:
Δp = 0.025 kg * (-17 m/s) = -0.425 kg·m/s
Step 2: Use the concept of impulse to calculate the magnitude of the force.
Impulse, J, is defined as the change in momentum and can be expressed as:
J = F * Δt
Where:
J is the impulse
F is the force exerted on the ball by the window
Δt is the time interval of the collision
Given:
Δt = 5.0 * 10^-4 s (time interval of the collision)
Δp = -0.425 kg·m/s (change in momentum)
Substituting the values into the formula:
-0.425 kg·m/s = F * 5.0 * 10^-4 s
Solving for F:
F = (-0.425 kg·m/s) / (5.0 * 10^-4 s)
F ≈ -850 N
The magnitude of the force exerted on the ball by the window is approximately 850 Newtons.
To find the magnitude of the force exerted on the golf ball by the window, we can use Newton's second law of motion, which states that F = m * a, where F is the force, m is the mass of the object, and a is the acceleration.
First, let's find the acceleration of the golf ball during the crash. We can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
Given:
Initial velocity (u) = 27 m/s
Final velocity (v) = 10 m/s
Time (t) = 5.0 * 10^-4 s
Rearranging the equation, we have:
a = (v - u) / t
Plugging in the values, we get:
a = (10 m/s - 27 m/s) / (5.0 * 10^-4 s) = -34,000 m/s^2
Since the ball continues in the same direction after the crash, the negative sign indicates that the acceleration is in the opposite direction of the initial velocity. This means that the force exerted on the ball by the window is in the opposite direction of the ball's initial motion.
Now, we can calculate the magnitude of the force by multiplying the mass of the golf ball (0.025 kg) by the magnitude of the acceleration (34,000 m/s^2):
F = m * a = 0.025 kg * 34,000 m/s^2 = 850 N
Therefore, the magnitude of the force exerted on the golf ball by the window is 850 Newtons.
m= .025 kg
initial velocity= 27 m/s
time= 5.0*10^-4
final velocity= 10 m/s
Force*time=mass( final vecolicy - negative initial velocity)
F(5.0*10^-4)=(.025)(10-(-27))
F=(.025)(10-(-27))/(5.0*10^-4)