suppose the cart has mass m = 203 g, and it strikes the clay at speed vo = 5.24 m/s and comes to a dead stop. Assume the track is frictionless, and the clay is crushed inward by 1.83 cm.
a)Find the magnitude of the impulse exerted by the clay on the cart.
1 N-m i got this answer 1.06372 but couldn't get paerts b and c
b) Find the magnitude of the average force exerted by the clay on the cart.
HINT: Use kinematics, assuming the force is constant during the impulse!
2 N
c) Find the time it took for the cart to come to rest while in contact with the clay.
3 s
To solve parts b) and c) of the problem, we need to use the concept of impulse and the equations of linear motion.
For part b):
The impulse experienced by an object is equal to the change in momentum. Impulse is defined as the product of force and the time interval for which the force acts.
Impulse = Force * Time
We already know the impulse exerted by the clay on the cart, which is 1 N-m (as you correctly calculated in part a)).
1 N-m = Force * Time
To find the average force exerted by the clay on the cart, we need to rearrange the equation to solve for force:
Force = Impulse / Time
Substituting the known values:
Force = 1 N-m / Time
Since the impulse is given in N-m and the time is given in seconds, the unit of force will be Newton (N).
Now, let's move on to part c):
To find the time it took for the cart to come to rest while in contact with the clay, we can use the equations of motion. Starting with the equation:
Final Velocity (v) = Initial Velocity (u) + Acceleration (a) * Time (t)
The initial velocity (u) is 5.24 m/s (given), and the final velocity (v) is 0 m/s (since the cart comes to a dead stop).
0 m/s = 5.24 m/s + a * t
Rearranging the equation to solve for time:
t = -5.24 m/s / a
Now, to find the acceleration (a), we can use the equation:
Acceleration (a) = Change in Velocity / Time
The change in velocity is the final velocity (0 m/s) minus the initial velocity (5.24 m/s).
a = (0 m/s - 5.24 m/s) / t
Substituting this into the previous equation, we get:
t = -5.24 m/s / [(0 m/s - 5.24 m/s) / t]
Simplifying this expression, we find:
t = -5.24 m/s * t / -5.24 m/s
The negative signs cancel out, and we are left with:
t = t
So, the time it takes for the cart to come to rest while in contact with the clay is equal to the time itself.
Therefore, the answer for part c) is 3 seconds.
In summary:
- The magnitude of the average force exerted by the clay on the cart is 2 N (part b)).
- The time it took for the cart to come to rest while in contact with the clay is 3 seconds (part c)).