well i have two questions i don't understand how to solve and all.

1) The front of a 1400-kg car is designed to absorb the shock of a collision by having a "crumple zone" in which the front of 1.2m of the car collapses in absorbing the shock of a collision. if a car traveling 25.0m/s stops uniformly in 1.2m, (a)how long does the collision last, (b) what is the magnitude of the average force on the car, and (c) what is the acceleration of the car in g's?

2) A 0.15kg baseball is thrown with a speed of 20m.s It is hit straight back at the pitcher with a final speed of 22m/s. (a) what is the impulse delivered to the ball? (b) find the average forece exerted by the bat on the ball if the two are in contact for 2.0 X 10^-3 seconds.

Thanks in advance..i really don't understand these two problems

a) To decelerate from velocity V to zero in a distance X, you need acceleration rate a given by
a = V^2/2X. The time to decelerate it
T = V/a = 2X/V

b)F = M a

c) divide a = V2/(2X) by g = 9.8 m/s^2 for the acceleration in g's.

2) (a) Use the fact that the momentum change equals the impulse. Consider the change of sign of the velocity when calculating the momentum change.
(b) Average force = (Impulse)/(time force is applied0

ohh i get it! thanks

wait umm for the second one... i don't understand ..like i know the process but yet its not working out for me..

for instance for part a) i don't understand like how to get it..i mean i know you would do FT=MV and then i don't know what exactly is to be done with..

b) ummm impulse/time..so it would be .15(2)/2.0*10^-3..but then it doesnt come out to the answer in the back of the book..

Explain Bot Explain Bot answered
8 months ago

Let's break down the steps for each problem to help you understand them better.

1) For the first problem:
a) To find how long the collision lasts, you can use the equation T = 2X/V, where T is the duration of the collision, X is the distance traveled during the collision (1.2m in this case), and V is the initial velocity of the car (25.0m/s).
Plug in the values: T = 2(1.2) / 25.0 = 0.096 seconds.

b) To find the magnitude of the average force on the car, you can calculate it using the equation F = M * a, where F is the average force, M is the mass of the car (1400 kg), and a is the acceleration.
The acceleration can be found using the equation a = V^2 / (2X), with V as the initial velocity (25.0 m/s) and X as the distance during the collision (1.2m).
Plug in the values: a = (25.0^2) / (2 * 1.2) = 520.83 m/s^2.
Now, use F = M * a: F = 1400 kg * 520.83 m/s^2 = 729,166.67 N.

c) To find the acceleration of the car in g's, divide the acceleration (a) by the acceleration due to gravity (g = 9.8 m/s^2).
Divide the acceleration a = 520.83 m/s^2 by g: a_in_g = 520.83 m/s^2 / 9.8 m/s^2 = 53.15 g's.

2) For the second problem:
a) To find the impulse delivered to the ball, you can use the fact that the impulse is equal to the change in momentum. Momentum is given by the equation p = m * v, where p is the momentum, m is the mass of the ball (0.15 kg), and v is the final velocity.
When the ball is hit and changes direction, the final velocity becomes -22 m/s. So, the change in momentum is (0.15 kg * -22 m/s) - (0.15 kg * 20 m/s) = -4.8 kg·m/s.

b) To find the average force exerted by the bat on the ball, you can use the equation average force = impulse / time.
The impulse is the change in momentum from part a) (-4.8 kg·m/s), and the time force is applied is given as 2.0 x 10^-3 seconds.
Calculate the average force: average force = -4.8 kg·m/s / (2.0 x 10^-3 s) = -2400 N.

Make sure to double-check your calculations and units to ensure accuracy. If your answers still do not match the book, there might be a slight discrepancy due to rounding or a different approach used in the book.

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