Physics Project Conservation of momentum,energy, and projectile motion

[Wilson_Serway]

For my AP Physics Class we were given spring loaded nerf guns and asked to find a spring constant and the acceleration of the bullet before it hit the block. We had to hit a target that was on the edge of our desk and record the distance when the bullet stuck to the target. I have worked more than halfway through the problem, but have trouble when it comes to the conservation of energy and can't seem to find the acceleration.

M_b=.0136 kg
M_t=.2392 kg
X(Desk to landing place)=.3825 m
Y(Top of target to floor)=.82

To find time it takes for the bullet/target combo to reach the floor I used the y-component
X_y=X_oY+V_o(t)+1/2(a)(t)²
0=.82+1/2(-9.81)(t)²
T=-.82/-4.905=.409

To find velocity of the bullet/target combo I substituted time into the x-component
X=X_o+V_o(t)+1/2(a)(t)²
.3852= V_o(.409)
V_o=.935

To find the velocity of the bullet before it hit the target I used the conservation of momentum
M_bV_b+ M_tV_t=( M_b+ M_t)V_o
.0136Vb+.2392(0)=(.0136+.2392).935
V_b=17.38

 

[Wilson_Serway]

Ohh I forgot the spring is compressed 0.06 meters and the distance from the tip of the gun to the block is 1.77 meters.

 

[kerimek]

m/s


Great job on your project so far! It's important to consider the conservation of momentum and energy when studying projectile motion. Let's take a closer look at the steps you've taken so far.

First, you correctly identified the relevant variables and recorded their values. This is an important step in any scientific experiment.

Next, you used the equation for vertical motion to find the time it takes for the bullet/target combo to reach the floor. You correctly used the initial vertical position (0.82 m) and the acceleration due to gravity (-9.81 m/s^2). However, there seems to be an error in your calculation for time. The equation should be t = √(2h/g), where h is the vertical displacement (0.82 m) and g is the acceleration due to gravity. This gives a time of approximately 0.404 seconds.

Then, you used this time to find the horizontal velocity of the bullet/target combo. This is also correct, as the horizontal motion is independent of the vertical motion.

Finally, you used the conservation of momentum to find the velocity of the bullet before it hit the target. This is a key principle in physics, which states that the total momentum of a system remains constant unless acted upon by an external force. You correctly set up the equation and solved for the velocity of the bullet, which is approximately 17.38 m/s.

To find the acceleration of the bullet, you can use the equation a = (Vf - Vi)/t, where Vf is the final velocity (0 m/s) and Vi is the initial velocity (17.38 m/s). This gives an acceleration of approximately -42.7 m/s^2. This negative value indicates that the bullet is decelerating as it hits the target, which is expected due to the force of friction.

Overall, you have done a great job applying the principles of conservation of momentum and energy to your project. Keep up the good work and continue to think critically about the physical laws that govern projectile motion.