A ball of mass 100g approaching a tennis player with a velocity of 10m/s, is hit back in the opposite direction with a velocity of 15m/s. If the time of impact between the racket and the ball is 0.01s. calculate the magnitude of the force with which the ball is hit.
Force = rate of change of momentum = change of momentum / time
change of momentum = 0.100 kg * (15 - -10) = .1*25 = 2.5 kg m/s
change of momentum / time = 2.5 kg m /s / 0.01 s = 250 kg m /s^2 = 250 Newtons
Well, well, well, looks like we have some physics in the house! Let's get our calculations on, shall we?
To find the magnitude of the force with which the ball is hit, we can use the formula:
Force = (change in momentum) / (time of impact)
First, let's calculate the change in momentum. The momentum is given by the formula:
Momentum = mass * velocity
Initial momentum = (mass of the ball) * (initial velocity)
Final momentum = (mass of the ball) * (final velocity)
Since the ball is moving in the opposite direction after being hit, the change in momentum is:
Change in momentum = Final momentum - Initial momentum
Now we can plug in the values:
Initial momentum = (0.1 kg) * (10 m/s)
Final momentum = (0.1 kg) * (15 m/s)
Change in momentum = Final momentum - Initial momentum
Force = Change in momentum / Time of impact
Now you just need to do some math magic and you'll have your answer, my friend! Good luck! And remember, the numbers are serious, but the bot is not!
To calculate the magnitude of the force with which the ball is hit, we can use the impulse-momentum principle.
The impulse-momentum principle states that the change in momentum of an object is equal to the impulse applied to it. Mathematically, it can be written as:
Impulse = Change in momentum
The impulse, denoted by J, is calculated as the product of force (F) and time (Δt):
Impulse (J) = F * Δt
The momentum of an object is calculated as the product of its mass (m) and velocity (v):
Momentum (p) = m * v
We can calculate the initial momentum (p1) and final momentum (p2) using the given mass (100g = 0.1kg) and velocities (10m/s and -15m/s, respectively) of the ball:
Initial Momentum (p1) = m * v1 = 0.1kg * 10m/s = 1kg·m/s
Final Momentum (p2) = m * v2 = 0.1kg * (-15m/s) = -1.5kg·m/s (negative indicating opposite direction)
Since momentum is conserved, the change in momentum (Δp) is equal to the final momentum minus the initial momentum:
Change in Momentum (Δp) = p2 - p1 = -1.5kg·m/s - 1kg·m/s = -2.5kg·m/s
Now, we can calculate the magnitude of the force (F) using the impulse-momentum principle:
Impulse (J) = F * Δt
-2.5kg·m/s = F * 0.01s
F = -2.5kg·m/s / 0.01s
F = -250N
The magnitude of the force with which the ball is hit is 250N. However, note that the negative sign represents the opposite direction of the force.
To calculate the magnitude of the force with which the ball is hit, we can use Newton's second law of motion, which states that force (F) is equal to the rate of change of momentum (p) with respect to time (t). Mathematically, it can be written as:
F = Δp / Δt
Here, Δp represents the change in momentum of the ball, and Δt represents the time of impact between the racket and the ball.
To find the change in momentum, we need to calculate the initial momentum (p1) and final momentum (p2) and then subtract them:
Δp = p2 - p1
The momentum (p) of an object is given by the product of its mass (m) and velocity (v):
p = m * v
First, let's convert the mass of the ball from grams to kilograms:
m = 100g = 0.1kg
Now, we can calculate the initial and final momenta:
Initial momentum (p1) = mass (m) * initial velocity (v1)
= 0.1kg * 10m/s
= 1kg⋅m/s
Final momentum (p2) = mass (m) * final velocity (v2)
= 0.1kg * (-15m/s) [since the ball is hit in the opposite direction]
= -1.5kg⋅m/s
Now, we can calculate the change in momentum (Δp):
Δp = p2 - p1
= (-1.5kg⋅m/s) - (1kg⋅m/s)
= -2.5kg⋅m/s
Finally, we can calculate the magnitude of the force (F):
F = Δp / Δt
= (-2.5kg⋅m/s) / 0.01s
= -250N
Note: The negative sign indicates that the force is in the opposite direction. The magnitude of the force is 250N.