Question #1 A 0.140kg- baseball traveling 30.0m/s strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 14.0cm .

What was the magnitude of the average force applied by the ball on the glove?

question #2

How much tension must a rope withstand if it is used to accelerate a 1180kg car horizontally along a frictionless surface at 1.20m/s^2 ?

#1

a ={v(f)^2 – v(i)^2}/2•s = - v(i)^2}/2•s = 30^2/2•0.14=3.21•10^3 m/s^2
F = m•a =0.14•3.21•10^3 =450 N
#2
T=F= m•a = 1180•1.2 =1416 N

Question #1: To find the magnitude of the average force applied by the ball on the glove, we can use the principle of Newton's second law of motion, which states that the force applied on an object is equal to the object's mass multiplied by its acceleration.

Given:
- Mass of the baseball (m) = 0.140 kg
- Initial velocity of the baseball (u) = 30.0 m/s
- Final velocity of the baseball (v) = 0 m/s (brought to rest)
- Displacement of the glove (Δx) = -14.0 cm = -0.14 m (negative because it is in the opposite direction)

We can use the equation: v^2 = u^2 + 2aΔx

Rearranging the equation to solve for the acceleration (a):
a = (v^2 - u^2) / (2Δx)

Substituting the known values:
a = (0 - (30.0)^2) / (2 * (-0.14))

Calculating the acceleration:
a = -900 / (-0.28)
a = 3214.29 m/s^2 (approximately)

Now, we can calculate the force applied by the ball on the glove using the formula: F = ma
F = (0.140 kg)(3214.29 m/s^2)

Calculating the force:
F = 450 kg*m/s^2
F = 450 N

Therefore, the magnitude of the average force applied by the ball on the glove is 450 N.

Question #2: To find the tension required for the rope, we can use the equation for force (F = ma), where the force applied is the tension in the rope and the mass is the mass of the car.

Given:
- Mass of the car (m) = 1180 kg
- Acceleration of the car (a) = 1.20 m/s^2

Using the formula: F = ma

Substituting the known values:
F = (1180 kg)(1.20 m/s^2)

Calculating the force:
F = 1416 N

Therefore, the tension the rope must withstand is 1416 N.

To find the answers to these questions, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration:

Force = mass * acceleration

Question #1: What was the magnitude of the average force applied by the ball on the glove?
In this case, the ball comes to rest, so its final velocity is 0 m/s. The initial velocity of the ball is 30.0 m/s. The change in velocity is the difference between the initial and final velocities: Δv = 0 - 30.0 = -30.0 m/s.

To calculate the acceleration, we can use the equation:
acceleration = Δv / Δt
where Δt is the time taken for the ball to come to rest.
Since the question does not provide the time, we have to assume it is not given. Without the time, we cannot find the acceleration, and thus the force. Therefore, we cannot answer this question without the time.

Question #2: How much tension must a rope withstand if it is used to accelerate a 1180 kg car horizontally at 1.20 m/s² along a frictionless surface?
Here, the mass of the car is given as 1180 kg, and the acceleration is given as 1.20 m/s². We can use Newton's second law of motion to find the force needed to accelerate the car:

Force = mass * acceleration
Force = 1180 kg * 1.20 m/s²
Force = 1416 N

Therefore, the tension the rope must withstand is 1416 N in order to accelerate the car horizontally along a frictionless surface at 1.20 m/s².

here 10 years later SHEEEEEESH