Working on some old exam problems

[eq123]

hey everyone .. I've been working on some old exam problems .. i couldn't figure these out :(

A 40-g bullet, with a horizontal velocity of 500 m/s, comes to a stop 20 cm within a solid wall. What is the magnitude of the force from the wall stopping it? (Assume this force to be constant) (Ans: 25000 N)

An ideal spring is hung vertically from the ceiling. When a 2.0-kg mass hangs at rest from it, the spring extends 6.0 cm from its relaxed length. A downward external force is now applied to the mass to extend the spring an additional 10 cm. Find the work done by the spring force while the spring extension changes from 6.0 cm to 16 cm. (Ans: – 3.6 J)

A body of mass M = 2.00 kg, tied to a string, rotates in a vertical circle of radius R = 1.00 m. Find the work done by the force of gravity on the body during one full revolution. (Ans: zero)

A man moves the 10-kg object shown in figure 6 in a vertical plane from position X to position Y along a circular track of radius R = 20 m. What is the work done by the force of gravity during this motion? (Ans: − 3920 J)

 

[tiny-tim]

hi eq123!

show us what you've tried, and where you're stuck, and then we'll know how to help!

(start with the first one, using the standard https://www.physicsforums.com/library.php?do=view_item&itemid=204" equations to find the acceleration)

 

[eq123]

thank you for your fast respond :)

i couldn't figure anything out for problems 1, 3, 4 :(

as for problem 2 .. this is what i did ..when relaxed

w_net = w_s + w_g = ∆k = 0
w_s = -w_g
F_s d = -F_g d
F_s = -F_g
-kx = -mg
k = mg/x = 2(9.8)/(0.06) = 327 N/m

when external force is applied

w_s = -0.5k(x²_f - x²_i) = -0.5(327)(0.16² - 0.06²) = -3.6 Ji am pretty sure that this solution is wrong!

i have a question related to the spring constant .. is it always positive?

you can notice that i am having some difficulties in the last two questions with work done on circular motion .. so please .. i would appreciate it if you explained that ..

 

[tiny-tim]

hi eq123!

as for problem 2 .. this is what i did ..

yes that looks ok

what is worrying you about it? ​

i have a question related to the spring constant .. is it always positive?

you answer that …

if k is negative, say -100, then d²x/dt² = 100x …

what does that mean, and is it possible to have a spring like that?

for the last two questions about https://www.physicsforums.com/library.php?do=view_item&itemid=75" you should use the work-energy theorem ​

 

[rwisz]

Hello, I understand that you are struggling with some old exam problems. I would be happy to help you work through them. For the first question, we can use the equation F=mv^2/r to calculate the force from the wall. Plugging in the given values, we get F=(0.04 kg)(500 m/s)^2/(0.2 m) = 25000 N. This means that the wall exerts a constant force of 25000 N to stop the bullet.

For the second question, we can use the equation W=1/2kx^2 to calculate the work done by the spring force. Plugging in the given values, we get W=1/2(2.0 kg)(9.8 m/s^2)(0.1 m)^2 - 1/2(2.0 kg)(9.8 m/s^2)(0.06 m)^2 = -3.6 J. This negative value indicates that the work done by the spring force is in the opposite direction of the applied force, which makes sense since the spring is extending.

For the third question, the work done by the force of gravity is equal to the change in potential energy. Since the body returns to its original position after one full revolution, the change in potential energy is zero. Therefore, the work done by gravity is also zero.

For the last question, we can use the equation W=mgΔh to calculate the work done by the force of gravity. Plugging in the given values, we get W=(10 kg)(9.8 m/s^2)(20 m) - (10 kg)(9.8 m/s^2)(0 m) = -3920 J. This negative value indicates that the work done by gravity is in the opposite direction of the motion of the object, which makes sense since the object is moving downward. I hope this helps you understand these problems better. Let me know if you have any further questions. Good luck on your exams!