What is the force exerted by a catcher's glove on a 0.15-kg baseball moving at 35 m/s that is stopped in 0.02 s?
the acceleration is -35m/s / .02s = -1750 m/s^2
F = ma = 0.15(-1750) = -262.5 N
To calculate the force exerted by a catcher's glove on a baseball, we can use Newton's second law of motion, which states that force (F) is equal to the change in momentum (Δp) divided by the change in time (Δt).
Step 1: Calculate the initial momentum (p_initial) of the baseball.
Momentum (p) is calculated by multiplying the mass (m) of an object by its velocity (v).
p_initial = m * v
Given:
mass (m) = 0.15 kg
velocity (v) = 35 m/s
p_initial = 0.15 kg * 35 m/s
p_initial = 5.25 kg·m/s
Step 2: Calculate the final momentum (p_final) of the baseball.
Since the baseball is stopped, the final momentum is zero.
p_final = 0 kg·m/s
Step 3: Calculate the change in momentum (Δp).
Δp = p_final - p_initial
Δp = 0 - 5.25 kg·m/s
Δp = -5.25 kg·m/s
Step 4: Calculate the force (F) exerted by the glove.
F = Δp / Δt
Given:
change in time (Δt) = 0.02 s
F = -5.25 kg·m/s / 0.02 s
F ≈ -262.5 N
The negative sign indicates that the force is acting in the opposite direction of the motion of the baseball. So, the force exerted by the catcher's glove on the baseball is approximately 262.5 N in the opposite direction of motion.
To find the force exerted by the catcher's glove on the baseball, we can use Newton's second law of motion, which states that force (F) is equal to the mass (m) of an object multiplied by its acceleration (a). In this case, the acceleration of the baseball can be found by using the equation for acceleration, which is the change in velocity (Δv) divided by the time taken (Δt).
Given:
Mass of the baseball (m) = 0.15 kg
Initial velocity of the baseball (u) = 35 m/s
Final velocity of the baseball (v) = 0 m/s
Time taken (Δt) = 0.02 s
First, we find the change in velocity (Δv):
Δv = v - u
Δv = 0 - 35
Δv = -35 m/s
Next, we find the acceleration of the baseball:
a = Δv / Δt
a = -35 / 0.02
a = -1750 m/s^2
Now, we can calculate the force exerted by the glove using Newton's second law:
F = m * a
F = 0.15 kg * -1750 m/s^2
Calculating this will give us the force exerted by the glove on the baseball.
Note: The negative sign in the acceleration indicates that the acceleration is in the opposite direction to the initial velocity. This makes sense as the baseball is being brought to a stop.
Please perform the calculation to find the exact value of the force exerted by the glove.