A catcher's mitt recoils a distance of 0.177 m in bringing a 0.176 kg baseball to a stop. If the applied force is 504 N, then what was the speed of the baseball at the moment of contact with the catcher's mitt?
Work = F*d = 504 * 0.177 = 89.2 J.
Work = Change in kinetic energy:
Work = 0.5M*V^2 = 89.2,
0.5*0.176V^2 = 89.2,
V =
Hmm, a catcher's mitt that recoils? Sounds like it's doing a little dance! Who knew mitts had moves?
Now, let's tackle this math problem and help our mitt groove. We need to find the speed of the baseball at the moment of contact with the mitt.
To do that, we can use the work-energy principle. The work done by the force is equal to the change in kinetic energy. So, we can write:
Work = Change in Kinetic Energy
The work done by the force is equal to the force times the distance the mitt recoiled:
Work = Force x Distance
So, we can write:
Force x Distance = Change in Kinetic Energy
Now let's plug in the given values. The force applied is 504 N, and the distance the mitt recoiled is 0.177 m. We don't know the change in kinetic energy, but we do know the mass of the baseball is 0.176 kg.
504 N x 0.177 m = Change in Kinetic Energy x 0.176 kg
Solving for the change in kinetic energy, we get:
Change in Kinetic Energy = (504 N x 0.177 m) / 0.176 kg
Alright, now that we've found the change in kinetic energy, we can use that to find the speed of the baseball. The change in kinetic energy is equal to the final kinetic energy minus the initial kinetic energy:
Change in Kinetic Energy = (1/2)mv^2 - (1/2)m(0)^2
Since the baseball starts from rest (initial velocity is 0), we can simplify this equation:
Change in Kinetic Energy = (1/2)mv^2
Now we can solve for the speed, v:
v = √((2 x Change in Kinetic Energy) / m)
Remember that you found the change in kinetic energy earlier, so you can plug in that value along with the mass of the baseball to calculate the speed.
Math is quite the juggler, but with a little balancing act, you'll find the answer!
To find the speed of the baseball at the moment of contact with the catcher's mitt, we can use the work-energy principle. According to the principle, the work done on an object is equal to the change in its kinetic energy.
In this case, the applied force does work on the ball to bring it to a stop. The work done can be calculated using the formula:
Work = Force × Displacement × cosθ
Where:
Force = 504 N (applied force)
Displacement = 0.177 m (distance the mitt recoils)
cosθ = 1 (assuming force is applied along the direction of displacement)
So, the work done on the ball is:
Work = 504 N × 0.177 m × 1
Work = 89.208 J
Since the work done on the ball is equal to the change in its kinetic energy, we can equate this to the initial kinetic energy of the ball:
Initial Kinetic Energy = 89.208 J
The formula for kinetic energy is:
Kinetic Energy = (1/2) × mass × velocity^2
Rearranging the formula to solve for velocity, we have:
velocity = sqrt((2 × Initial Kinetic Energy) / mass)
Plugging in the given values:
velocity = sqrt((2 × 89.208 J) / 0.176 kg)
velocity = sqrt(1013.80 m^2/s^2 / 0.176 kg)
velocity = sqrt(5760.227 kg·m^2/s^2 / 0.176 kg)
velocity = sqrt(32727.239)
Therefore, the speed of the baseball at the moment of contact with the catcher's mitt is approximately 180.88 m/s.
To find the speed of the baseball at the moment of contact with the catcher's mitt, we can use the work-energy principle. According to this principle, the work done on an object is equal to the change in its kinetic energy.
The work done on the baseball is given by the force applied multiplied by the distance over which it is applied:
Work = Force x Distance
In this case, the force is 504 N and the distance is the recoil distance of 0.177 m. Therefore, the work done on the baseball is:
Work = 504 N x 0.177 m = 89.208 N·m
According to the work-energy principle, this work done is equal to the change in kinetic energy. Initially, the baseball is at rest, so its initial kinetic energy is zero. At the moment of contact with the mitt, the baseball comes to a stop. Therefore, the change in kinetic energy is:
Change in Kinetic Energy = Final Kinetic Energy - Initial Kinetic Energy
= 0 - 0 = 0
We know that the work done is equal to the change in kinetic energy, so:
89.208 N·m = 0
Since the work done is zero, it means that the applied force did not do any work on the baseball. This suggests that there must be another force at play that brought the baseball to a stop. In this case, that force is likely the force of friction between the mitt and the baseball.
Therefore, we cannot determine the speed of the baseball at the moment of contact with the catcher's mitt solely based on the given information. We need additional information about the friction force or any other forces involved to calculate the initial speed of the baseball.